Results filed under: “gambling”

jesse
@ November 8, 2012


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Let's just get this ugliness over, shall we?

Last week: 1-4 (20%), Overall: 23-20-2 (53.4%), Fake rank: 225 (out of 745)

Ugh.

week 9.JPG

To make matters worse, the Giants took a huge hit to their Super Bowl chances by surrendering a 10-point, 4th-quarter lead to the Steelers. They are basically off the board - in 100 simulated runs, they won zero of them. Part of this is because the Bears are basically sucking up all the oxygen in the room - they are winning the NFC in half of my simulated runs, leaving table scraps for Atlanta, San Fransisco, Green Bay, and the Giants to fight over.

On the flip side, a team that has managed to claw back into their division race with a win is San Diego, who spent he last 3 weeks in a freefall after collapsing late against Denver. Their odds of winning the division nearly doubled after their win last week, increasing from 17% to 31%. Still, Denver remains the favorite for the AFC West. That, along with the AFC North, which is basically a coin flip between Baltimore and Pittsburgh right now, are the only divisions that remain meaningfully competitive at this point.



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jesse
@ October 31, 2012


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I recovered from my 1-3-1 performance last week with another 3-2 week.

Last week: 3-2 (60%), Overall: 22-16-2 (57.9%), Fake rank: 99 (out of 745)

This week's picks:

AZ +11
MIN +4.5
BUF +10.5
KC +7.5
CAR +3

Yes, I picked Arizona again, even after that abominable performance on Monday night. I also have a terrible track record picking against Houston, but here I am again with Buffalo +10.5. So...3-2 again? I'm happy with 3-2 again.

week 8.JPG

 

Am I alone here in not really believing in the Falcons? Nobody from last week's top 5 lost (Houston was on a bye week), but San Fransisco's path to the NFC West became much clearer with losses by both Seattle and Arizona. New England continues to benefit from a weak division. At this point, the odds are being driven by standings, since the following divisions show a winner with 90%+ confidence at this point:

NFC East (Giants win 98% of 100 simulations run)

NFC South (Atlanta, 96%)

NFC North (Chicago, 93%)

NFC West (San Fransisco, 100%)

AFC South (Houston, 100%)

I left New England (89%) and Denver (82%) off this list. The only truly competitive division at this point appears to be the AFC North, with PIttsburgh (37%) and Baltimore (61%) slugging it out.



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jesse
@ October 25, 2012


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With tipoff about a week away, its time to warmup the NBA gambling engine with some win total predictions.

This is my second year with this model, but it is still a work in progress. Personally, it looks to me like it doesn't respect the... curviness that an NBA season seems to have. Just to make sure I wasn't imagining things, I checked the win totals from the last full season, 2010-2011.

 

nba win totals.JPGIt's a subtle difference, but you can see that my model expects there to be one really good team (the Chicago Bulls, by the way), a couple of awful teams (Charlotte and Brooklyn), and then everybody bunched a little closer than usual. Part of this may be the effect of using some data from a strike-shortened season to do my evaluation. Part of it could be a bad model. Or, it could actually be saying that there is more talent than usual spread out around the league and it will be a closely contended season. That, as they say, is why they play the games.

As for the over/unders, here are my projections, listed in order of how strongly I feel about the bets, strongest first. Note that the site I got my lines from had Dallas and Minnesota currently off the board due to injuries.

Brooklyn UNDER 44.5 +110
Houston OVER 30.5 +110
Philly OVER 46.5 +100
Denver UNDER 50.5 +105
Atlanta OVER 42.5 -120
L.A. Lakers UNDER 57.5 -120
Miami UNDER 60.5 -105
Orlando OVER 23.5 +100
OKC UNDER 60.5 -130
Portland OVER 33.5 -110
Chicago OVER 47.5 -135
Boston UNDER 50.5 -110
Toronto OVER 33.5 -140
Washington OVER 27.5 -115
Phoenix OVER 33.5 -110
Memphis UNDER 48.5 -115
Charlotte UNDER 19.5 -120 (I really can't believe I'm taking under on this number)
Indiana OVER 51.5 -115
Milwaukee OVER 36.5 -135
Detroit OVER 31.5 -125
L.A. Clippers UNDER 49.5 -115
Sacramento UNDER 30.5 -105
San Antonio UNDER 55.5 +110
Utah UNDER 42.5 +105

Based on the juice, I've taken an unpopular opinion on Brooklyn, Houston, Philly, Denver, San Antonio, and Utah. I've taken a VERY popular opinion on Milwaukee, Toronto, Chicago, and OKC.

Again, the point here is not to actually bet these lines - it is for me to make a public prediction which I can evaluate at the end of the year to see if I am doing a good job of handicapping these teams.



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jesse
@ October 24, 2012


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 I was due for a losing week, I guess. The lines this week were very sharp: 5 games ended within +/- 1 point of the number. I picked 3 of those games for the SuperContest, and went 0-2-1 in those games. And yes, I'm aware these are bitter whiney sour grapes and I don't care.

Last week: 1-3-1 (25%), Overall: 19-14-2 (57.6%), Fake rank: 154 (out of 745)

This week's picks:

JAX +14

TB +6.5

AZ +6.5

IND +3.5

SEA +2

 

week 7.JPGA new challenger has emerged!

Making their first appearance on the big board are the Chicago Bears, who ROCKET to the #1 spot. This despite 3 of the teams they jumped ahead of winning, and another having a bye week (and still being 6-0). So what's going on here? Is my model whacked?

Well, that's always one possible answer. To consider other possible answers to the question, I ran two versions of my model this week. In addition to the final one, I ran one before the Monday night game, so I could separate out how the Bears performance in that game impacted their standings, vs. what was happening around them in the league. To facilitate this, here is a detailed chart of Chicago's progress.

  chicago week 7.JPG

Let's start by looking at their week-to-week win projections. Chicago's stock has been rising steadily ever since their week 2 loss to Green Bay. This building process is important. Much of sports analysis seems to take place in a vacuum. To use their week 2 opponent as a particularly illustrative example, one week, the Green Bay Packers are losing at Seattle on a bogus official's call, and the punditry is asking what has "happened" to Aaron Rodgers and the Packers. Then the reigning MVP throws 9 TDs and 0 INTs in his next two games, and the story is, do the Packers have their groove back? Both statements were dumb.

Instead, each piece of new information should build upon itself. Based on the Packers recent track record, a couple of early season wins should not be looked upon as the new normal, but as a bump in the road. Even the Saints 0-4 start may have less to do with Bountygate as it did with fluky luck.

That being said, we are now nearly halfway through the season, and your record at this point matters. The Saints are 4 games behind the Falcons with 9 left to play. Thus, their odds to win the division are only 3%. The Packers are trailing the division leading Bears AND the Vikings, leaving only a 7% slice of the division pie for them.

Getting back to my main point: each new data point should move the needle, but by how much? How much data does it take to convince us that what we are seeing is real?

In the case of the Bears, the answer was "alot". But once the model is convinced, each new datapoint will go a long ways towards convincing it that what it is seeing is real. Last week, the Bears were projected to win 10.6 games on average. After everybody else had played, but before the Monday night game, this number was 12.2. After the Monday night game, this increased to 13.2.

Why did they go from 10.6 to 12.2 before they even played? Let's look at their schedule moving forward: Carolina, Tennessee, Houston, San Fransisco, Minnesota, Seattle, Minnesota again, Green Bay, Arizona, Detroit. Collectively, these teams went 6-3 (excluding Detroit). But that doesn't tell the whole story. Only one team (Houston) looked truly impressive in victory. Everybody else either lost, or won by a touchdown or less. After putting a win in the books and Detroit looking pathetic, they gained another game in their expected outcome. Out of the 2.6 win increase modeled for Chicago, only 1.0 had anything to do with their performance Monday night. The other 1.6 had to do with what the rest of their future opponents did, which, other than the Texans, was be mostly mediocre.

This jump from 10.6 to 13.2 basically explains everything else. They went from being projected as the 4th best team in the league to the best. This gives them, on average, better playoff position, more bye weeks, and more home games, in addition to the model just thinking they are better to begin with.

On the one hand, the model's change in opinion regarding Chicago was very drastic this week. On the other, it took several wins in a row before the needle moved on Chicago at all, meaning it wasn't REALLY that drastic. The initial skepticism it had regarding Chicago meant that it took a few weeks to catch up to what somebody with a stronger starting opinion about Chicago might have already thought.



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jesse
@ October 17, 2012


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Okay, I'm being coy, this is really just a hedge of a hedge. But here is where we stand.

We started with a freeroll $10 bet on the Yankees to win the World Series at 7/1. When the decisive game between Baltimore and New York came in round 1, I hedged my bet with a $8.83 play on Baltimore that lost. Then, before the ALCS started, I further hedged with a $19.29 play on Detroit at +105 to win the series.

With three consecutive losses, the value of my Yankees World Series proposition has significantly deteriorated, while my Detroit play looks smart. I currently calculate that the Yankees, from their current position, have a 4.5% chance of winning the World Series. Detroit, for their part, as a 91.5% chance of winning the ALCS.

(If you think that my odds are too high... well, they might be. The team leading a 4-game series 3-0 has won 30 out of 31 times, and yes I know what the one goddamn exception is jesus christ. That means the team down 3-0 has only won 3.2% of the time, yet I have them at a 4.5% chance to not only win this series, but the one after that as well. In all likelihood, the Yankees will lose this series, but I think that in general they are of a better caliber than the typical team that goes down 3-0 in a playoff series. Moving on.)

If the Yankees win tonight, those numbers change. The Yankees World Series odds improve to 8.3%, and Detroit's ALCS odds degrade to 84.3%. Now, keep in mind that I already hedged this Yankees bet with a $8.83 play on Baltimore, so some of the value has already been soaked up. With all that in mind... how much should I bet on the Yankees tonight?

Current value of my Yankees World Series ticket: ($70 x 4.5%) - $19.29 - $8.83 = -$24.96

Value if the Yankees win tonight: ($70 x 8.3%) - $19.29 - $8.83 = -$22.31

Current value of Tigers wager: ($19.29 x (105/100) x 91.5%) - $8.83 = $9.70
Value if the Yankees win tonight: ($19.29 x (105/100) x 84.3%) - $8.83 = $7.43

If I bet $Z on the Yankees at current price of -118, and they win, the total value of that win is:

(post-win WS value - current WS value) + wager winnings - (post-win ALCS value - current ALCS value) = -$22.31 - (-$24.96) + $Z x (100/118) + $7.43 - $9.70 = 0.85Z + $0.38

If they lose, then I am done and cash out with:

Detroit ALCS winnings - Baltimore hedge losses - Yankees hedge losses = $19.29 x (105/100) - $8.83 - $Z = $11.42 - Z

Finally, I have to take into account what I think the odds of the Yankees winning tonight is. I have them at 55% odds to win tonight. Let's bring it on home:

.55 x (0.85Z + 0.38) = 0.45 (11.42 - Z)
Z = $5.36

I should bet $5.36 on the Yankees tonight to maximize my potential profit.

If the Yankees win, I'll have the chance to do the same thing tomorrow night. I'm going to save the math until then, because I'm an optimist (yes, this means I'm optimistic about getting to do more math).



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jesse
@ October 13, 2012


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So the Yankees won last night. And it was awesome. CC finally had a big game for the Yankees in the playoffs, and it was wonderful to watch. More importantly, my Yankees World Series bet is still alive.

Yesterday, I talked about how I had $10 on the Yankees at 7/1 to win the World Series (I should have mentioned that this was actually a freeroll bet, so I didn't actually RISK the $10 - this would have changed the math). I hedged this bet with a $8.83 play on the Orioles at +180. Now we come to the ALCS.

To win my world series bet, two things need to happen:

- The Yankees have to win the ALCS against the Tigers

- The Yankees have to win the World Series against the national league opponent

The odds of the Yankees beating the Tigers are, in my opinion, 56%. The odds of them beating their national league opponent have gone up slightly since yesterday because the Nationals were a more formidable opponent than the Cards, so those odds are up to 53% (from 52% yesterday). That puts their World Series odds right now at 29%.

The Tigers, on the other hand, have a 44% chance of beating the Yankees. The odds were posted this morning for the ALCS as Tigers +105.

As I did yesterday, I have to figure out how much the value of my Yankee bet increases if they beat the Tigers. Since I figure they have a 53% chance of beating the national league representative, the Yankees World Series bet is worth (0.53) x $70 - $8.83 = $28.27, conditional upon them beating the Tigers.

Now let's put it all together. If the Yankees beat the Tigers, AND I have hedged my Yankees bet with a wager of Y, the value of my Yankees world series bet is $28.27-Y. There is a 56% chance of this happening, or 0.56 x (28.27 - Y). Conversely, if the Tigers win, I will pick up 1.04 x Y. In this case I also need to cover for my lost Baltimore hedge. There is a 44% chance of this happening. This side of the wager is worth 0.44 x (1.04 Y - 8.83). Solving for Y yields a proper hedge of $19.29 on the Tigers.

Let's take a moment to look ahead to the World Series. If the Yankees are in it, I will have spent $28.12 hedging my bet. There is still plenty of value in my $70 bet to come out with a positive advantage.

There may also be some additional opportunities to hedge later in the series once one team or the other reaches a 3 game lead in the series. Basically, at that point I will be making a sports credit default swap. 



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jesse
@ October 12, 2012


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Before the baseball season started, I made a purely emotional bet: $10 at the Yankees at 7:1 to win the World Series. Staring down an elimination game for the Yankees against Baltimore tonight, I have an important decision to make: how do I hedge my bet?

The idea about hedging is to have two bets that, together, have a positive outcome - a no-lose situation. Imagine that one sports book had the Yankees at +150, and another had Baltimore at +150. If you made both bets, you would guarantee 0.50 BU of profit no matter who won. The idea is roughly the same.

However, we can refine this by taking into account the odds of each outcome. Currently, I have a bet that pays me $70 if the Yankees win the World Series. However, to get there, three things have to happen:

- they have to beat the Orioles tonight

- they have to beat the Tigers in the ALCS

- they have to beat the national league team in the World Series

If we roughly figured that the odds of each event happening was 50/50, then the odds of them currently winning the world series would be 1/8 (1/2 x 1/2 x 1/2 = 1/8). My computer model that I use to guide my sports betting tells a slightly different story for each of those events:

- Yankees beat the Orioles tonight 58% of the time

- Yankees beat the Tigers 56% of the time

- Yankees beat the national league team 52% of the time (to do this one, I have to run through the odds of each national league team making the World Series, and then compare each one against the Yankees - spreadsheets are fun)

Taken together, this represents a 17% chance that the Yankees win the World Series from where things stand right now. A 17% chance of winning $70 is worth $11.90. In other words, if somebody offered me $11.90 or more in exchange for my Yankees 7/1 ticket, I should take it - if they offered me less, I should tell them to shove it (quick tangent: this is basically how that game show Deal or No Deal works - they have rednecks on because they can't possibly do this much math).

So how much do I bet on Baltimore tonight to hedge my bet? It's a little bit complicated by the fact that it's not a perfect hedge: the Yankees could win tonight but then lose in the ALCS or World Series, leaving both bets as losers. However, those future contests will also represent future chances to hedge and cover this loss as well.

Since I said that the Yankees have a 58% of winning tonight, that implies Baltimore has a 42% chance of winning tonight. The current moneyline is Baltimore +180. If I bet on Baltimore and the win, I get 1.8X (X being my bet size). If the Yankees win, then I need to deduct X from the expected value of my World Series bet. However, that also implies that they have already won tonight, so the odds of the ticket winning and that point increase to 29%, and the value of my World Series ticket becomes $20.40 - X. Still with me? 

So, I have a 42% chance of winning 1.8X, and a 58% chance of holding a ticket worth $20.40 - X. The expected value of the first position is 1.8X x 0.42 = 0.756X. The expected value of the second position is (20.40 - X) x 0.58 = 11.8 - 0.58X. My position is maximized when these two positions are equal, i.e. 11.8 - 0.58X = 0.756X. Solving for X tells me I should bet $8.83 on the Orioles tonight.

Now, lets say the Yankees win. Can I continue to hedge? I sure can. There is no line yet because the team to face them hasn't won, but let's say the Tigers are +100 to win a series against the Yankees. I already said I thought the Yankees would win that series 56% of the time. I can essentially do the same exercise, except now I have to take into account that my Yankees position is worth slightly less because of the hedge against the Orioles. Here's hoping I get a chance to do that math after tonight.  



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jesse
@ October 11, 2012


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I think I'm doing pretty darn good at this fake Supercontest thing. In fact, after another solid week, I tried to explain to Suzi how good I was doing. In doing so, I made the mistake of noting that you have to finish in the top 20 before indicating my current standing.

Then I said: "And out of 745, I would currently be tied for 50th! That's in the top 7% of all entries!"

Blank stare, followed by: "so you AREN'T in the top 20."

Goddammit.

Last week: 3-2 (60%), Overall: 15-9-1 (64.6%), Fake rank: 50 (out of 745)

This week's picks:

IND +3
KC +3.5
NYG +4.5
OAK +8.5
BUF +4.5

week 5.JPG

New England retains the top spot after taking care of business in Denver. Philly loses to Pittsburgh, but still leapfrogs San Diego after their loss to New Orleans. And Atlanta finally appears on the list after a 5-0 start.

After running this model for a month now, I'm noticing that it takes some pretty wild changes week to week on Super Bowl odds. This is because it is a highly dynamic model that is sensitive to changes in the initial conditions.

The way each model run starts is by simulating each game of the season, and predicting winners and losers. It then seeds everybody based on NFL playoff tiebreaker rules and plays out the playoff brackets to determine a Super Bowl winner. So not only does this model tell me Super Bowl winner odds, but season win totals, division winners, and conference winners as well. Let's look at how our front runner, New England, has changed over the course of the season in each of these categories.

new england week 5.JPG

 

Starting with our win predictions, we see that in the preseason the model thought New England would win an average of 13.7 games this year. After 5 games and a 3-2 start, this has dropped to 11.8. However, their division odds have actually INCREASED from the preseason. They started at 91%, and have gone up to 95%. Why have they gone up if their expected win total has dropped?

This is where the importance of a dynamic model comes in. Division odds are not just a function of New England's performance, but the performance of the three other teams in the division as well. Pre-season, I was very bullish on Miami: the model predicted 10.7 wins for them. Now, they still figure to finish in 2nd place in the division, but their expected win total is down to 7.6. This drop by their nearest competitor has allowed New England to stay strong in the division.

This dynamic plays out on a larger scale at the conference and Super Bowl level. Relatively small changes in the initial conditions week to week play out as significant swings at the Super Bowl level.

The second part of judging a forecast is to look back at how it has done. At the end of the season, I will have made 18 predictions for each team (1 per week plus 1 preseason) that can be tested. However, because there are many more results than predictions, it may take a few years before I can have any confidence that this method is accurate predicting outcomes - and more importantly, how that level of confidence changes as we get closer and closer to the end of the season.



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jesse
@ September 27, 2012


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This week's fake SuperContest picks:

NO +7.5

TEN +12

CLE +12

WAS +3

MIN +6.5

Last week: 3-2, Overall: 8-6-1, Fake rank: 120 (out of 745), top 17%

Thoughts:

First, an updated Super Bowl odds graph.

week 3.JPG

For starters, Philly and New Orleans have fallen out of the top 5, to be replaced by Baltimore and San Diego. Second, this is a good opportunity to revisit some pre-season bets..

Before the season, I proposed some futures bets for super bowl, conference, and division winners. As the season progresses, books will update some of these lines. This gives us the opportunity to revisit these lines and perhaps take advantage of some additional value.

In our original strategy, it was not enough for a line by itself to have positive outcome value, because these bets are all mutually exclusive - since only one team can win the super bowl, a winning bet on Pittsburgh also implies losing bets on San Francisco, New Orleans, et al. (Also implying a losing bet on New Orleans? Betting on New Orleans, apparently.) That is still true. This means that any new bets we make must meet that same standard - a winning bet must have a positive expected value even after all other bets are losers. With that said, here's some additional super bowl plays after Week 3.

Original bets: PIT 14/1 (4.06 BU), MIA 75/1 (0.54 BU), SF 9/1 (1.64 BU), NO 18/1 (1.12 BU), 7.36 BU total.

San Diego Chargers (25/1): 2.7 BU
Pittsburgh Steelers (20/1): 2.8 BU
Seattle Seahawks (30/1): 1.8 BU

Before we made these bets, a total of 7.36 BU had been wagered on the Super Bowl. This brings the total to 14.66 BU. The consequences of these additions is that some of our pre-season bets have become less valuable. Specifically, if SF and NO were to win, they are still positive, but just barely. The threshold for adding additional teams from this point forward will be that much higher as a result, i.e. it will need to make up for the fact that some pre-season bets become losers even if they win. You will also notice that we are putting additional money on Pittsburgh at 20/1. This is because additional Pittsburgh money does not cancel out our original Pittsburgh bet, so its easier to have a positive outcome. The second reason is that the odds have gotten longer, so even with the Steelers at 1-2 right now this looks like a chance to grab some more value.

We can run the same exercise on our conference wagers (new division lines have not been posted).

Original conference bets: SF 9/2 (3.74 BU), NO 9/1 (2.04 BU), MIA 30/1 (1.32 BU), PIT 6/1 (6.56 BU)

Additional conference bets:
SEA (14/1): 4.1 BU
SD (10/1): 3.6 BU
PIT (9/1): 3.8 BU
CAR (40/1): 0.7 BU

This will be the last time I add any NFC Conference teams, because I have essentially soaked all the value from my original SF bet - any more money on the NFC and it becomes negative even if it wins. There is still some headroom in the AFC for additional plays if they become attractive.  



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jesse
@ September 20, 2012


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Here is who I am on for this week's fake SuperContest entry:

 

STL +7.5

MIN +7

AZ +4

JAX +3

CLE +3

Thoughts:

In my last post, I mentioned Nate Silver, the statistical whiz behind FiveThirtyEight. In an election season, one of the features of FiveThirtyEight is its ongoing predictions. Nate not only calculates his predicted odds at any given moment, but keeps a historical record of where the race stood earlier in the year so that you can visually see how the race has progressed.

I plan to do something similar. I had hoped to unveil this after Week 1, but my ongoing predictive model had a bug that I've only now sorted out. In this space I will be keeping track of changes in projected Super Bowl odds, division odds, and win totals.

TOP 5 SUPER BOWL CONTENDERS:

#1: NEW ENGLAND (last week: 1, preaseason: 2)
#2: SAN DIEGO (last week: <5, preseason: <5)
#3: PIT (last week: 3, preseason: 1)
#4: NO (last week: 2, preseason: 3)
#5: PHI (last week: 5, preseason: <5)

falling off the list: SEA (was 4, <5 preseason), GB (was preseason 4), SF (was preseason 5)

  week 2.JPGLast week: 3-1-1 (7 pts)

Overall: 5-3-1 (11 pts)



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jesse
@ September 12, 2012


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Lacking the guts and necessary bankroll to actually participate in the $1000 buy-in LVH SuperContest, aka the World Series of Sports Betting, all I can do is play along at home. Here are this weeks picks.

AZ +13.5 over NE

CLE +7 over CIN

SEA +3 over DAL

MIA +2.5 over OAK

JAX +7 over HOU

Thoughts:

Nate Silver, the statistical genius behind FiveThirtyEight, has a new book coming out called The Signal and the Noise. In an excerpt posted in the New York Times over the last weekend, he talks about how computer modeling has not necessarily made us better forecasters of the future, with one notable exception: weather forecasters. That is because weather forecasters have mastered the art of knowing when to listen to their computer models and understanding their shortcomings.

This is an art that I have yet to master with my sports prediction algorithms (or, as I call it, Gamblor). Gamblor is capable of producing some great insights, and I am confident that I will continue to find success with Gamblor moving forward. However, if I am to truly become great at this sports prediction business, I must begin intrinsically recognizing the shortcomings of my program.

All this is to say that I should have thrown myself in front of my MIA and PIT selections last week. Sometimes teams undergo too much change over an off-season for the computer to properly understand, and in those cases, sometimes discretion is the better part of valor.

And yet here is MIA back in my Top 5 picks. I am tempted to throw it out and replace it with my next selection, CHI +6 over GB. But unlike last week MIA isn't playing a good team. And they are at home. Let it ride, Gamblor.

Last week: 2-3

Overall: 2-3 (4 pts) 

 

 



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jesse
@ September 5, 2012


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I have a dream. Specifically, a gambling dream. In this dream, like in many dreams, it starts with flying. I am flying through the sky, borne westward towards a gleaming city of lights. And hookers. Lights and hookers. I descend, the glittering lights (and hookers) stretching towards me and past me, and now I am among them, gliding across the landscape until I reach the palace at its heart. Once there, I am suddenly thrust into an arena, thrown into combat against the best of the best, until I am the last man standing, crowned champion of the Las Vegas Hotel Supercontest.

Put on every year by the Las Vegas Hotel, the Supercontest is becoming the World Series of sports betting. With an annual purse of nearly $1M, a $1500 entry fee gets you a chance to pit your NFL picking skills against the very best. The only problem? The $1500 entry fee. Until such time as my successful gambling renders me capable of tossing down $1500 on what is essentially a game, the best I can do is play along at home.

Each week, the hotel posts the card with the lines to be used for that game. Contest entrants must select 5 plays among those games to submit. A win gets you 2 points, a push 1 point, and a loss nothing. I will be picking along this year and keeping track of my virtual standing against the pros. Here are my Week 1 picks.

MIA +13 over HOU

By now, my foolish infatuation with this Miami team is well documented. I've picked them OVER wins, I picked them as part of my Super Bowl plays, my Conference plays, and my Division winner plays; and now I'm betting on them week 1.

IND +9.5 over CHI

Apparently I have a thing for picking rookie quarterbacks.

PIT +1.5 over DEN

This one at least makes sense. Jump on the betting against Peyton bandwagon now while there is still room. This is going to be a full ride by Week 4. That is, if Peyton is still playing in Week 4 and hasn't been sidelined with further neck trauma.

JAX +3.5 over MIN

Yeah, they are both bad, but Minnesota is worse than people realize, especially without a healthy AP.

CLE +8.5 over PHI

Did we learn nothing from overrating PHI last year? I sure hope not...

Also receiving consideration: SF +5 over GB, DAL +4 over NYG, CAR -2.5 over TB.



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jesse
@ September 4, 2012


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Future bet is a stupid name, isn't it? If you know anybody who is allowing bets on games that happened in the past, let me know. In the betting world, a future bet refers to season-long bets, like betting on who will win the NBA Finals or the Super Bowl before the season starts.

NFL futures, for the purpose of this article, will be restricted to Super Bowl Champs, conference champs, and division champs, and the odds thereof. All the possible combinations of bets (will/won't make the playoffs, will/won't win a playoff game, etc. etc.) are outside of the scope of this analysis.

This analysis was conducted by extrapolating my weekly NFL model out for an entire season, including the playoffs. The season was run 500 times, and the odds of a given future bet from Vegas is compared against the odds that they won during that 500-run sample.

Potential Divisional Plays

Miami to win the AFC East +1500

Okay, I have to face it: between this and my over/under analysis, my model likes Miami WAY more than Vegas, or anybody else, does. I'm not sure why. I personally hate Miami. My model's love for Miami has done more to undermine my confidence in it than any losing streak does. I feel betrayed right now. Out of 500 runs, Miami won the AFC East 166 times, or 1 out of 3. That means that my model would put the odds at +300 instead of +1500.

San Diego to win the AFC West +240

This feels much more defensible. They won my virtual season 278 times out of 500, or more than half - I have them as the favorite to win the AFC West.

Pittsburgh to win the AFC North +110

My model ALSO likes Pittsburgh much more than Vegas, at all stages of the playoffs. It has them winning the division over 80% of the time!

Other bets I like: New Orleans to win the NFC South +130 (won nearly 70% of simulated season); Dallas to win the NFC East +260 (won 42% of simulations); and Jacksonville to win the AFC South +2000 (won 6.6% of simulations, which, while not alot, is better than the 5% that +2000 implies)

Overpriced: out of 500 simulations, St. Louis, Tampa Bay, and Cleveland all won zero; New England at -400 is definitely the favorite, but not by that much (probably because my model thinks Miami wins it too many times. Dammit.)

Divisional histogram:

nfl futures figure 1.JPG 

Potential Conference Plays

In addition to still loving Miami, Pittsburgh, and New Orleans, the San Francisco 49ers at 11/2 become attractive here (this is another way of saying that they are +550). I have them winning the league 156 times out of 500, which is nearly 1/3.

Potential Super Bowl Plays

Pittsburgh at 14/1 is my top play. They won 25% of simulated super bowls, far more than any other team. Still "love" Miami at 75/1 as well. Also think there is value in New Orleans at 18/1 and San Francisco at 9/1. That's it: every other team is overpriced.

Super Bowl histogram:

 

nfl futures figure 2.JPG

Betting Procedure

When playing the futures market, we start running into the problem of mutually exclusive outcomes. That means that, even though Pittsburgh and New Orleans might both be positive expected value outcomes, they can't both be winners. We need to select our bet sizes and our teams to give us the best overall expected outcome - we need our winnings to not only cover our losses for that bet, but for all the other bets we made that are now losers. Let's look at the Super Bowl to sort this out. There are a total of 6 teams that I calculate are positive expected value teams.

Team EV of $100 bet
PIT $284
MIA $204
NO $101
SF $74
GB $3.6
HOU $1.4

 

To select a bet size I use the Kelly criterion (*see note at the bottom). My bet sizes are as follows:

Team EV of $100 bet Kelly Bet (assuming $100 available)
PIT $284 $20.30
MIA $204 $2.70
NO $101 $5.60
SF $74 $8.20
GB $3.6 $0.60
HOU $1.4 $0.10

 

Now we look at the TOTAL outcome if I make all of these plays, and one of them wins.

Team EV of $100 bet Kelly Bet Outcome if winner
PIT $284 $20.30 $266
MIA $204 $2.70 $169
NO $101 $5.60 $69
SF $74 $8.20 $44
GB $3.6 $0.60 -$33
HOU $1.4 $0.10 -$36

 

The outcome will always be less than the total value because I have to cover the losses of my other bets. For this reason, Green Bay and Houston become bad plays, and I drop them. This also makes the other 4 bets slightly more attractive (only slightly because the amount being risked on those outcomes were small).

Team EV of $100 bet Kelly Bet Outcome if winner
PIT $284 $20.30 $267
MIA $204 $2.70 $170
NO $101 $5.60 $70
SF $74 $8.20 $45

 

We can go through the same procedure at the league level as well. When I do so I come out with the following plays:

Team EV of $100 bet Kelly Bet Outcome if winner
MIA $198 $6.60 $163
PIT $197 $32.80 $188.8
SF $103 $18.70 $93
NO $92 $10.20 $73

 

For the divisions, this only applies if more than 1 team in any division looks like a good play. As it happens, I am only picking one team per division to bet on.

 
Team EV of $100 bet Kelly Bet
MIA $431 $28.70
SD $89 $37.10
PIT $69 $62.60
NO $60 $46.20
DAL $52 $20.00
HOU $18 $40.20
GB $14 $31.80
SF $14 $34.90

 

Because this is an untested system, I am not actually making any of these bets yet. This season will be the first test. At the end of the year I will revisit this and see if I would have made money. I will revisit during the year if for no other reason than to see how dumb my Miami plays were.



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jesse
@ August 29, 2012


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0

Back when the first NFL over/under lines came out, I took a look at where I perceived the value to be. Now that we are closing in on the start of the NFL season, let's take a look at how Vegas has responded with the lines that I thought were the most playable after they first came out in June.

Miami
The play in June: OVER 7.5 WINS (-110)
The play today:  OVER 6.5 WINS (+140)
Value up or down? Up - the over is an even more attractive bet now
What happened: They have selected Ryan Tannehill, a rookie and mediocre Big Ten quarterback, as their starter, which has everybody running scared. If anybody else wants to join me on this bandwagon, there is plenty of room...

New England
The play in June: UNDER 12 WINS (-110)
The play today:  UNDER 12 WINS (-105)
Value up or down? Up... by a nickel
What happened:  Nothing. That's why it has only moved a nickel.

Philadelphia
The play in June: UNDER 10 WINS (-105)
The play today:  ...um...
Value up or down? Down? I think?
What happened: So the new line is 10.5 wins, +120 on the over, and -150 on the under. Do you see the weirdness here? They raised the line by half a game - that's what you do when the over is getting pounded. But THEN they jacked up the juice on the under, which is what you do when the under is getting pounded. Weird. In any case, I don't see any value at that number and these prices. Obviously if I liked under 10 wins I like under 10.5, just not paying -150 for it.

Tampa Bay
The play in June: UNDER 6 WINS (-120)
The play today:  UNDER 6 WINS (+105)
Value up or down? Up and away
What happened: It seems that bettors believe last year was the fluke, not their 2010 campaign (when they unexpectedly went 10-6). They can go right on believing that as far as I'm concerned.

New Orleans
The play in June:  OVER 10 WINS (-125)
The play today:  OVER 10 WINS (+125)
Value up or down? Waaaay, way up
What happened: Bettors are more worried about Bountygate than Vegas thought they would be. Bookmakers don't like to move the win total, because it gives sharp bettors the opportunity to catch a middle. Instead, they'll move the juice. How big a move is this? Moving from -125 to +125 changes the implied odds from 55.6% to 44.4%. That means Vegas anticipated about 55 out of every 100 bettors would take the over, and instead only 44 did. Vegas is begging and pleading with you to take the over, so that they have somebody on the other side of all that under cash.

San Francisco
The play in June: OVER 10 WINS (+105)
The play today:  OVER 10 WINS (+110)
value up or down? Up, also by a nickel
What happened: Bettors think Seattle got better, which maybe takes an easy win off the board. (Bettors are wrong, by the way.)

New York Giants
The play in June: UNDER 9.5 WINS (-120)
The play today:  UNDER 9 WINS (-140)
Value up or down? The market has all but collapsed
What happened: Nobody, but I mean nobody, is believing in this Giants football team. Half a win and two dimes is a huge move. They might win 10 games out of spite now. Ok not really.

Kansas City
The play in June: UNDER 8 WINS (-110)
The play today:  UNDER 8 WINS (-130)
Value up or down? Down a smidgen
What happened: The market seems to think that Todd Haley was the problem, and not this crappy football team.

Denver
The play in June: UNDER 9.5 (-120)
The play today:  UNDER 9 (-110)
Value up or down? Basically unchanged
The half of a game turns a 9-7 season from a win to a push, but since they aren't going to get to 9 games, I wouldn't worry about it.

Baltimore
The play in June:  OVER 10 WINS (-110)
The play today:  OVER 10 WINS (+130)
What happened: They are the San Antonio Spurs of the NFL. Here's another team that Vegas is suddenly paying you to take the over on. Every year they get older, lose some players to free agency and retirement, have a couple of injuries, and the public is ready to count them out. And every year they still win 10 games.

Seattle
The play in June: OVER 7 WINS (-110)
The play today:  UNDER 7 WINS (+135)
What happened: The public really likes Matt Flynn, I guess. Except he's not even the starter now, some other guy is, after they paid Flynn all that money? *confused*

Atlanta
The play in June: OVER 9 WINS (+105)
The play today:  OVER 9 WINS (-135)
What happened: I wasn't the only one who liked the over. And I STILL like the over, although obviously not quite as much.



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jesse
@ August 2, 2012


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0

ABSTRACT

A previous essay presented a methodology for optimizing bet size based on implied odds and betting advantage, balancing risk and profit. Risk, in that case, was narrowly defined as the risk related to "gambler's ruin", i.e. the risk of encountering a prolonged losing streak that will wipe out one's original stake. There is a second, equally important definition of risk which must also be addressed: the risk that betting advantage has been incorrectly calculated. To avoid confusion, I will refer to this as "uncertainty". Uncertainty has impacts for how betting advantage is calculated, which in turn impacts betting unit selection and the overall performance of a betting system. 

ANALYSIS

In my last post I explored the way in which implied odds from a moneyline and the calculated odds of a particular outcome can be used to calculate an optimum bet size to balance risk and return. Risk, in this case, was narrowly defined as the risk related to "gambler's ruin", a mathematical concept which states that a gambler of finite means that plays against a house of infinite means for long enough will encounter a losing streak sufficient to wipe out his entire bankroll. The smaller the bet, the longer the losing streak must be to wipe out the bankroll; therefore, the lower the risk. However, smaller bet also implies smaller return. The reduced return is essentially an insurance policy that you are purchasing to guard against gambler's ruin. As bets get smaller, this policy becomes more and more expensive in exchange for a smaller and smaller amount of insurance. Hence the need for balance.

There is another kind of risk, which, to avoid confusion, I will refer to as uncertainty: this is the uncertainty inherent in evaluating the odds of an outcome. "I'm 100% sure that the Giants are beating the Mets tonight" is an egregious example of ignoring uncertainty that gambler's employ on a day to day basis. However, the mistake does not need to be nearly that bad in order for the effects to be catastrophic. Let's look at an example.

In our example, the Giants are +100 against the Mets. Being smart bettors, we won't make foolish statements like the outcome is 100% guaranteed. But we do think that the Giants should have been a slight favorite in this game: rather than +100, they should have been -110. Put into terms of betting advantage*, we see an advantage of roughly 0.047.

*I defined betting advantage in my last post, but will do it again since the concept may remain unfamiliar. I define it as (calculated odds) / (implied odds) - 1. In this example, the implied odds from a +100 bet are 50%. The implied odds from a -110 bet would be 52.38%. 52.38% / 50% - 1 = 0.047.

Going through the approach I outlined yesterday, a +100 bet with a betting advantage of 0.047 would lead you to make a bet of 4.76% of your bankroll. I have plotted this point on the bet optimization chart* for a +100 moneyline (the big red X marks the spot):

figure 11.JPG

*For an explanation of this chart, see my previous post on betting unit optimization. The general idea is that for a given bet line and betting advantage, there is an optimum betting unit to balance risk and reward, which is what the black circles indicate.

Okay, so this, ideally, is the process. In reality, however, the data coming out of this analysis is only as good as the data going in. At the very top, I made a judgment call: that the Giants in this hypothetical matchup should have been priced at -110 instead of +100. Whether this analysis came out of a computer program or my gut instinct, the question is the same: what are the consequences of being wrong? Instead of -110, the proper price should have been -105. What are the consequences of this error?

figure 12.JPG

Whoops! My "optimal" bet of 4.76% was actually a slightly negative median outcome proposition (the median outcome is for my starting $1000 to end up at $960 by the end of the run). The real optimal bet here was not 4.76% of my bankroll, but actually 2.5% of my bankroll. Basically, I bet twice as much as I should have on this game by mistaking a -105 team for a -110 team against a +100 price.

On the one hand, this is not that big of a mistake. Missing a moneyline by 5 cents seems trivial. On the other hand, the model recommended betting almost 5% of your bankroll based on a perceived 10 cent miss by the house (or, if you prefer, the market). The issue of value cuts both ways. It isn't just the market that is capable of misevaluating teams, it is you. Having a healthy respect for the margins of error involved on both sides, and what that means for your betting approach.*

*much of this line of thought was inspired by reading a chapter excerpted on-line from the 2nd edition of Tim Harford's excellent "The Undercover Economist". The chapter covers the 2008 market collapse and how its roots can be traced back to relatively small miscalculations in the risks related to mortgage foreclosures. These small errors had huge consequences for the market because investors put too much faith in the models and bet too much of their bankroll on the mortgage market as a result. Here is a link to the Harford piece.

Selecting the optimal betting unit requires you to take uncertainty into account. Constantly evaluating your approach, and how it reflects the real world, is vital to understanding the risks you are truly taking. This is a two step process. The first is evaluating, on average, how close your evaluations match up with results. The second is understanding the uncertainty.

Part of my process is to continually track how my calculated odds match up with what really happened. In other words: of all the times I thought teams had a 65% chance of winning a game, what percentage of them actually DID win the game? If it is not close to 65%, then I need to make an adjustment.

figure 13.JPG

This is a chart of my predicted win % vs. actual win % for MLB. If my program were perfect, then the slope of the best fit line would be 1. Instead, I see a slope of 0.861. That means that my system tends to exaggerate the odds of a team winning a match by about 15%. Once this is known, it can be corrected for.

I can also estimate the uncertainty by looking at how much the variation over the range deviates from the best fit line. This is done by calculating the weighted standard deviation for the data set (I weight it based on how many games fell within each range; for example, I have 620 games in my database where my prediction was between 51% and 52%, but only 158 where it was between 72% and 73%).

Once I have my standard deviation (based on the data in the above chart, it is 1.69%), I can calculate a confidence interval. Selecting this confidence interval is yet another point of analysis that I will revisit at a later date. For now, I will simply share what confidence interval I use. Based on my analysis, the proper confidence interval for my system is 81%.

Because I am only worried about overconfidence (underconfidence may cost me money, but it doesn't put me at risk for negative outcomes, i.e. it is much cheaper than overconfidence), my confidence interval is weighted to one side. Here is the same chart as above, zoomed in and with a line to represent the bottom of my 81% confidence interval.

 

figure 14.JPG

Back to the example problem, of the Giants facing the Mets with a moneyline of +100. I think that the line should be -110, which translates to a predicted win percentage of 52.38%. Before, I pulled the trigger on a 4.76% bet. Now, before going to the betting window, I look at where this wager falls on my confidence interval.

 

figure 15.JPG

This analysis shows that, while I think the line should be -110, my error analysis indicates there is a 19% chance that the line may be as low as +107. In other words, instead of betting on San Francisco, the value may be on the Mets.

This does NOT mean I won't place a wager. What it does mean is that I will dial back its size. This level of uncertainty in the model restricts the size of my bets from 1% to 3% of my bankroll.

But what about when my model and the betting markets have a very large disagreement? You'll notice that this chart cuts off at a predicted win % of just over 70%. There's a reason I cut it here. This chart illustrates why.

figure 16.JPGWhen my computer program predicts win percentages above 73% it starts getting kind of... stupid. Or, in technical terms, when I include predictions above the 73% threshold, the coefficient of correlation drops from 0.88 (indicating high correlation between prediction and reality, even if the predicted win percentages are slightly too high) to 0.028 (indicating no correlation at all). Recognizing the limits of where your model breaks down will allow you to assess your limitations, and make improvements.

CONCLUSIONS

The impact of uncertainty and confidence on betting strategy has been discussed. First, the potential negative impacts of ignoring uncertainty in your models is illustrated. Then, an analytical method for analyzing, understanding and incorporating the uncertainty of a modeling approach, using my MLB model as an example, is presented.

Even if you don't use a computer program (and many excellent bettors don't), every time you make a bet you are explicitly assigning a probability of a particular outcome. If you don't go back and evaluate how your probabilities reflect reality, it will be very difficult to experience long-term success.



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jesse
@ August 1, 2012


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0

ABSTRACT

Through empirical analysis and Monte Carlo simulation, a proposed method for finding an optimal balance between risk and reward in sports betting is presented. The model assumes that the implied odds, as represented by the betting line, and the actual outcome odds of any given proposition are known. Risk, in this case, is not the risk associated with improperly assessing these odds. Rather, risk here is the risk of experiencing "gambler's ruin", a mathematical concept which states that, given a finite bankroll, a gambler playing against an opponent with an infinite bankroll, i.e. the house, will eventually lose his entire stake. The balance is finding a small enough betting size to minimize the risk of gambler's ruin without making the bet size so small that the money that is won becomes insignificant. 

ANALYSIS

In making any investment, there are two choices that have to be made. The first is what the investment should be (pick a side). The second is how much to invest. The same is true in sports gambling.

Selecting a bet size is all about managing your bankroll, which is another way of saying that its all about managing risk. Gambling is a constant struggle against a pervasive (but awesomely named) mathematical enemy: gambler's ruin.

The casino has two tools working against you. The first is one that everybody understands: the odds are tilted in their favor. The second is gambler's ruin. It's a very simple concept to understand. Let's play a coin flip game. Heads you win $1, tails I win $1. The only difference is I have infinite money, and you only have $10 bucks. Even though the coin flip is a 50/50 chance, this game will end with me having all of your $10. The reason is, once you lose your last $1 on the mathematically inevitable streak of bad luck, you don't have any more dollars to bet against me. That, in a nutshell, is gambler's ruin*.

(*This is why the idea of playing the roulette wheel and doubling your bet each time you lose doesn't work. Eventually you will go on a losing streak long enough to squash you - and because your bet doubles after each loss, the losing streak doesn't even need to be that long. Gambler's ruin!!)

Our example might seem trivial, but the implications are pretty staggering. To illustrate why, I'm going to use a technique called Monte-Carlo simulation. I'll select a starting bankroll, a standard betting unit, the odds of winning, and the payoff for that bet. Then I'll make that bet 6000 times in a computer (roughly equivalent to one season of baseball bets.) And I'll do THAT 1000 times, also in the computer (i.e. 1000 different baseball seasons). Then, out of those 1000 seasons, we'll see how many times I go broke before the season is over.

figure 1.JPG

In the initial example, I started with betting $1 with a $10 bankroll, which is a 10% betting unit. But what the chart above shows that, even if I dropped down to a 1% bet, ten cents, I'd still have a 20% chance of being flat broke before I got to the end of a season.

So, how do we bet on sports while avoiding gambler's ruin? Well, first of all, we don't make bets that don't have any value. We only want to make bets with positive expected outcomes. So let's change the scenario. I'm not going to change it much. We'll keep the payout at even money, but change the odds of winning from 50% to 51.5%. This has what I call a betting advantage (calculated or known odds of winning / implied odds* - 1) of 0.03.

*implied odds is what the odds of winning would have to be for the betting advantage to be zero. They are calculated as: 1 - (money won) / (money risked + money won). If the odds are +100, the implied odds are 1 - ($100) / ($100 + $100) = 50%. In the case of -200, the implied odds are 1 - ($100) / ($200 + $100) = 66%. In the case of -110, the implied odds are 1 - ($100) / ($110 + $100) = 52.3%. And so on.

figure 2.JPG

This relatively small change in winning % has a huge impact on going broke. A 1% bet standard goes from an 18% of busting after 6000 bets to less than 1 in 100. However, it is also true that reducing my betting unit will reduce my opportunity to make money. What we want to do is balance risk and investment.

Reducing our betting unit reduces our risk, but it also reduces our return, since we get paid less money on smaller bets. It follows that there should be an optimal betting unit based on risk, return, and betting advantage. Let's take another swing at our monte carlo simulation, with one modification: instead of keeping the absolute value of the betting unit constant, we will keep the percentage we bet constant instead. If we lose money, we reduce our betting unit, and if we win money, we increase our betting unit, such that we are always betting the same % of our bankroll with each bet. While this change technically eliminates the risk of "gambler's ruin" because our bankroll will never go to zero, it doesn't eliminate the risk of being left with no more than a few nickels to rub together with the wrong luck and too large of a betting unit.

figure 3.JPG In this case, we want to use the median value, NOT the average value, to evaluate the outcome. When evaluating bets that we will be making many times over, the average value is the right number to use. However, when evaluating a bet that can be made only once, the median value is a better reflection of the expected outcome - it is not skewed upwards or downwards by one or two highly lucky outcomes in the simulation.

The above figure shows the expected outcomes for our starting proposition: a 50/50 coinflip that pays even money. This graph shows that the maximum median outcome is with a standard bet of 0%, i.e. we should not make this bet. This result makes intuitive sense - there is no value to us here, so why would we ever make this play? Let's change the odds to be more and more in our favor and see what happens.

figure 4.JPG

Boy, some of those numbers got very big! In reality, we would never get there, because no casino would take a 5% bet of a $100M bankroll. However, theoretically we see where the maximum median value occurs. We also see one of the variables that impacts betting size emerge: how much advantage we have over the implied odds. There is a black line here which charts maximum median value, betting advantage, and % stake. We can combine these three variables into a two variable chart: optimum % stake and betting advantage*. Here's that chart.

figure 5.JPG *betting advantage is % odds / % implied odds - 1, i.e. (51.5%/50%) -1 = 0.02. In each of the median value graphs the lines charted will represent 0, 0.02, 0.03, 0.04, 0.05, and 0.06 betting advantage.

Another variable that impacts this calculation is what the implied odds are. Let's look at another version of the previous two charts, except instead of 50% implied odds, let's consider a +150 bet, i.e. 40% implied odds, and see how the figures change.

figure 6.JPG figure 7.JPG Compared to a +100 bet, a +150 bet with the same betting advantage requires a smaller bet for optimum risk/value balance - nearly half the size. This is because an underdog bet is inherently riskier; there is a higher chance of going on an extended losing streak that can wipe you out. We can do the same thing for a whole range of bets. In fact, let's just skip ahead to that right now.

  figure 8.JPG Each of these is a roughly linear equation, with a different slope depending on the implied odds. We can plot the value of these slops as a function of the implied odds. This will allow us to find a correlation that can be used to calculate the optimum bet size once the implied odds and betting advantage are known over the entire range of values.

figure 9.JPG The result is a roughly polynomial curve over the range of interest (it is very rare in baseball to see odds outside of the range of +200 to -200). We now have all the tools in place to create a mathematical formula that tells us how much to bet to optimize risk and value capture.

  figure 10a.JPG Recall, the implied odds are calculated as: figure 10c.JPG CONCLUSIONS

A methodology for calculating the optimal betting unit based on balancing risk and reward for betting moneylines is presented. Inputs to this formula are the implied odds as calculated from the moneyline, and the calculated odds, i.e. the betting advantage anticipated by the bettor. The analysis is backed up by some intuitive results that occur from examination of the fomrula:

- The bigger the favorite, the more money should be risked. The bigger the underdog, the less money should be risked.

- The larger the betting advantage, the more money should be risked.

- If no betting advantage exists, the only way to win is not to play.

The risk discussed herein is the risk of experience "gambler's ruin", i.e. going on a long losing streak such that your stake is wiped out. There is a separate risk; that is, the risk of mis-evaluating your betting advantage. This is a very real risk: just ask anybody who used to work for Lehman Brothers. This will be discussed in a future post.



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jesse
@ July 12, 2012


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0

In which new betting strategy possibly emerges?

Previously I took a look at who the surprising teams - good and bad - had been in baseball this year from a gambler's perspective. Let's see how things have changed now that we are at the all star break, and I have nothing to gamble on until I perfect my WNBA engine (or, you know, kill myself - whichever comes first.) (Please let it be death.)

Okay! First, let's see how the quarter-pole teams are doing

1. Baltimore (+1082) -> 7 (+534)
2. NY Mets (+961) -> 2 (+1107)
3. LA Dodgers (+858) -> 12 (-64)
4. Oakland (+699) -> 3 (+1034)
5. Tampa Bay (+505) -> 13 (-67)

3 out of the 5 teams listed, to use a technical term, have sucked balls since then. In fact, since I posted my original list on May 23, LA, Tampa Bay, and Baltimore are the 2, 6, and 7 WORST teams to have bet on. In total, if you had started betting on all 5 of these teams on May 23, you are now DOWN a total of $1670 based on a standard bet size of $100 (or, if you prefer, down 16.7 betting units). Betting AGAINST these 5 teams was +919 over the same period.

In that spirit, here are the new top 5.

1. Pittsburgh (+1537)
2. NY Mets (+1107)
3. Oakland (+1034)
4. Kansas City (+682)
5. Chi. White sox (+621)

Now let's look at the flip side. How have our 5 worst teams fared since the quarter-pole? (Remember that these are the values if you had bet AGAINST these teams every game)

1. Colorado (+1392) -> 2 (+1495)
2. LA Angels (+883) -> 22 (-719)
3. NY Yankees (+765) -> 25 (-840)
4. Philadelphia (+622) -> 1 (+1673)
5. Milwaukee (+546) -> 8 (+375)

The Angels and Yankees are the #1 and #3 teams to have bet on since the previous update, while Philly has been... oh god, they have been terrible. Let's do the same exercise we did for the top 5: if you had bet against each of these 5 teams since May 23, you would have lost $2,426 with a standard $100 bet. Betting on them, on the other hand, nets $1213 over the same period.

Here's the new bottom 5.

1. Philadelphia (+1673)
2. Colorado (+1495)
3. Miami (+538)
4. St. Louis (+512)
5. San Diego (+482)

Now, am I advocating that betting ON the bottom 5 and betting AGAINST the top 5 will be a winning strategy? Err... maybe I am? At the very least I am curious, and will back with an update in 6 weeks. Stay tuned.



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jesse
@ June 26, 2012


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0

Baseball gambling (and hockey gambling, but who cares) has a wrinkle that sets it apart from basketball and football. This is called the run line.

You'll surely recall that the money line dictates how much a winning bet on a particular side will earn, and will be seen as such:

Pirates +130
Phillies -140

(A quick reminder on money lines. The above lines indicates that a $100 winning bet on the Pirates nets $130 in winnings, and a winning bet on the Phillies nets $71.4. Ideally, this line means that 35% of the action is on the Pirates, and 65% of the action is on the Phillies. In the event of a Pirates win, Vegas pays out $45.50 of very $100 bet. In the event of a Phillies win, Vegas pays out...$45.50 of very $100 bet. The space between $50 (an even split) and $45.50 is the money that goes to Vegas. Although, as we have discussed, Vegas bookmakers are themselves gamblers, and therefore aren't afraid to take a side every now and then.)

A run line for this same game would look like this:

Pirates +1.5 -165
Phillies -1.5 +145

This means that, if the Pirates win OR lose by only 1 run, then that bet wins, and pays out $60 per $100 bet. On the other hand, if the Phillies win by 2 or more runs, then that bet wins and pays out $145 per $100 bet.

Now, I said that this idea is unique to baseball (and hockey, but seriously, who gives a fuck) but that's not entirely true. Football line makers do this all the time. One book will have the Patriots -7, and another will have them at -6.5 (-115). You get a line that's a half-line lower, but it pays out slightly less. You'll also sometimes have the opportunity to "buy" points on a line by paying extra juice. This is all part of the same idea I discuss below.

It is probably helpful to nobody but myself to imagine each contest as a bell curve of possible outcomes. Construction of a bell curve requires the definition of two variables, a mean and a standard deviation. The mean tells you where to center your bell curve, and the standard deviation tells you how wide or skinny the bell should be.

Let's consider the possible outcomes of this Pirates/Phillies contest as such from Vegas' perspective. The lines tell us that Vegas expects Philly to win 65% of the time. The lines also tell us that Vegas expects Philly to win by 2 or more runs only 29.5% of the time. These two variables can be used to solve for the mean and standard deviation. This is illustrated in the chart below.


 

rl analysis chart 1.GIFThe easiest way to understand this chart is to look at the point where the Pittsburgh run differential is equal to zero. This happens when the cumulative odds are at 65%. In words, this says "the odds that Pittsburgh's run differential will be less than or equal to zero, i.e. negative, i.e. a loss, is 65%". Similarly, we can look at the run line value of -2 and see that this crosses at 29.5%. "The odds that Pittsburgh's run differential will be less than or equal to -2, i.e. a loss by 2 or more runs, is 29.5%".

When we think about money lines, all we care about is how my odds of this line crossing zero might be different from what Vegas thinks. Let's say I think the odds of a Philly win are much higher - say, 82%. Since I don't care what the standard deviation is, I'll just use the same one. Our graphs look like this.


rl analysis chart 2.GIFBut can I bet on the run line based on this as well? I could certainly try it, assuming that Vegas has the right standard deviation. But why do that when I could just increase my bet on the side, since that is where I feel I have an informational advantage? Betting on the run line without knowing the standard deviation is betting in the dark.

Let's look at a different case. What if I think that the mean outcome Vegas has identified is correct, but I think their standard deviation is off? That might look like this.

rl analysis chart 3.GIFIf I was just betting the money line, I wouldn't see much opportunity for value here. However, at -2, Vegas assumes the odds are 29%, but I think they are more like 38%. Now we have identified an opportunity for a value play where one did not exist when we only considered the mean outcome.

Most people don't think in terms of means and standard deviations, I realize. You'll more typically hear a gambler say something like "8 of their last 10 losses have been by 2 or more runs." This is what they are getting at. I prefer a more structured statistical analysis. For either approach, having the right information is the key.



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jesse
@ June 5, 2012


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0

Baseball is the only sport where a key player changes every day. While injuries and trades happen, by and large a football team has the same quarterback every week. Hockey doesn't rotate goalies. Basketball teams have the same starting five night after night. Only in baseball do we have a key player rotating night after night.

The starting pitcher can make a huge difference in the moneyline. In their 45 games this season, the Detroit Tigers average moneyline has been -108. When Justin Verlander starts, however, that line jumps to -177.

What to make of this? The offense is the same. The defense is the same. The bullpen is the same. But the starting pitcher drastically swings the line. What is a bettor to do?

To take a crack at this question, I've assembled a list of what I would call baseball's elite pitchers. Elite in this case, is not based on a sabermetric analysis of VORP or xFIP, but instead is grounded in public perception, because it is public perception, and not any intrinsic, actual value, that will move a betting line. I culled this list from the top 10 finishers for the AL and NL Cy Young award for the last two years (after removing the relievers). I also removed a couple of pitchers like Cliff Lee that changed teams over my analysis period, because it made my analysis harder and I didn't feel like dealing with it right now, okay? Here's the list, presented in a completely random order:

Clay Buchholz
Ian Kennedy
Justin Verlander
Clayton Kershaw
Trevor Cahill
David Price
Felix Hernandez
CC Sabathia
Ubaldo Jimenez
Jered Weaver
Ricky Romero
Bronson Arroyo
Josh Beckett
Matt Cain
Tim Hudson
James Shields
Josh Johnson
Cole Hamels
Francisco Liriano
Yovani Gallardo
Roy Halladay
Jon Lester
Adam Wainwright
Mat Latos
Dan Haren
Tim Lincecum

The table below presents four values. First, to take the long view of their performance, I've assessed their performance from a gambling perspective from the start of the 2010 season through today, as well as the performance of their team. I've assessed the average value per start for each pitcher based on a standard $10 bet. Then, I compared their average value against the average value of betting on their team over that same time period, to see if the variation can be credited to the pitcher or if the team's overall performance was surprising to bettors. I look at their game value for this season only. The last one is the average runs allowed in games started by that pitcher. Here's the ranking:

Name Overall vs. Team This Year Ave Runs
Justin Verlander $1.40 $1.22 -$0.55 2.5
David Price $1.34 $0.96 $2.15 3.3
Clay Buchholz $1.31 $1.71 -$0.87 5.5
Trevor Cahill $1.23 $1.01 -$1.87 4.9
Ian Kennedy $1.21 $1.43 -$2.95 2.9
Ricky Romero $0.82 $0.62 $0.50 3.5
James Shields $0.76 $0.37 $1.85 3.4
Clayton Kershaw $0.72 $1.10 -$0.57 2.7
Matt Cain $0.52 $0.42 $2.08 3.0
CC Sabathia $0.35 $0.73 $1.30 3.5
Cole Hamels $0.34 $0.22 $5.08 2.7
Bronson Arroyo $0.28 $0.45 $1.63 3.9
Josh Beckett $0.03 $0.43 -$0.82 3.5
Roy Halladay -$0.03 -$0.15 -$3.90 3.6
Jered Weaver -$0.03 $0.67 $1.20 2.8
Tim Hudson -$0.06 $0.40 $3.65 3.0
Josh Johnson -$0.18 $0.24 $0.90 4.4
Ubaldo Jimenez -$0.50 $0.72 -$1.38 5.0
Yovani Gallardo -$0.53 -$0.15 -$1.67 3.8
Jon Lester -$0.59 -$0.19 -$1.25 3.9
Mat Latos -$0.74 -$0.57 -$1.12 3.8
Felix Hernandez -$0.75 $0.88 -$0.35 3.5
Adam Wainwright -$0.76 -$0.43 -$1.13 4.9
Francisco Liriano -$0.77 $.06 -$3.85 5.2
Tim Lincecum -$1.40 -$1.50 -$8.43 3.9
Dan Haren -$1.91 -$1.21 -$5.13 3.7

 

As a whole, this group of pitchers has averaged a whopping $0.09/start, or a rate of return of 0.9%. Over this season they are even worse, averaging -$0.52/start. As a comparison, this season I have averaged $1.01 per $10 bet, or a 10.1% rate of return. In general, these pitchers have outperformed the teams as a whole, although not by a sufficient margin to make betting on them a winning prospect.

When trying to find value, the starting pitcher seems like it would be an obvious place. However, finding value doesn't just mean "bet on Justin Verlander." That worked last year, but the market has caught up this year.

So who hasn't the market caught up to yet? I did a simple test: I checked the ERA and strikeout leaders for this year and applied the "who?" test to the names. If I had to double check the spelling OR it sounded like their name was created by a video game name generator, even better. Here's what I found.

James McDonald  $6.47 per start
R.A. Dickey  $5.09
Gio Gonzalez $4.99
Brandon McCarthy $4.42
Jeff Samardzija  $3.26
Chris Sale  $3.23 
Felix Doubront $3.21
Dillon Gee $2.03
Brandon Morrow $1.77

These 9 "who?" pitchers are all exceeding the betting numbers put up by almost every one of the big stars in the table above, precisely because of their "who?" factor. I'm going to track these 9 pitchers for the next month, assuming they aren't pitching against each other, and report my findings. Is 1/3rd of a season long enough to establish a track record? We're going to find out.



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jesse
@ May 30, 2012


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0

 

If you're looking for a place to start in sports betting, here's as good a place as any: bet on the road dog.

In our previous discussion on NFL win totals, we noted the natural bias of the public to bet on the over, resulting in the market tilting slightly in that direction. While it was not enough on its own to make a blind bet on the under a winning proposition, it resulted in more value existing in under bets.

Vegas bookmaker Todd Fuhrman (@ToddFuhrman) recently tweeted that "those that call themselves 'dog' or 'favorite' bettors are limiting their opportunity for profit; value comes on both sides." What he is saying is that by blindly ignoring one side or the other, you will miss opportunities to capture value, and this is true. That's why I don't call myself a 'dog' bettor. However, I do find myself betting the dog much more often than the favorite, since that is where the value exists.

To illustrate this point, let's look at results from the last 4 years of football**, 2008-2011. The following results include both regular season and playoffs (week 1 from 2008 is missing in my database):

Road teams ATS: 534-486 (52.3%)
Underdogs ATS*: 538-483 (52.7%)
Road underdogs ATS: 364-317 (53.5%)
 
ATS = against the spread
 
*A quick sidebar: If Vegas was getting equal action on each side of these bets, then we would expect this record to be 0.500. This actually illustrates one of the common misunderstandings about Vegas (one that I myself had until a bookmaker set me straight on Chad Millman's "Behind the Bets" podcast). I will often refer to Vegas as a market-maker similar to a stock broker like e-Trade that just takes a cut out of each transaction, and I will continue to do so because it is a helpful analogy, but this isn't exactly right. Bookmakers mostly got their start by being sharp bettors themselves. They not only want to extract their fee, but they want to bet against the public as well. That's why you see that road underdogs are better than 50% ATS. A true market-maker would aim for this number to be 50%, but Vegas can let it drift higher because the majority of bettors continue to take the favorites. Vegas is betting on the underdogs, as they are winning.
 
**Another quick sidebar: my baseball database is not as extensive as my football database, so my conclusions are not as robust, but I will say this: blindly betting the away team in baseball has been a losing proposition so far this year, but not as much as blindly betting the home team (-$76.20 vs. -$139.75 assuming a standard $10 bet). Blindly betting the underdog to this point in the season has actually been quite profitable: $269.50 in the black vs. $485.44 in the red for the favorites. While I expect that will balance out over the year, the basic point remains: road teams and underdogs provide more opportunity for value.
Assuming a standard vig of -110 on every bet, a winning percentage of 52.4% is required to break even. That means that a completely blind system of betting road underdogs was profitable over the last 4 years of NFL games. Not terribly profitable, but also not terribly time-consuming either. Is this team an underdog? Are they on the road? Done and done.
 

The system I use is 55.6% over that same time span, albeit only betting on 70% of games. (I don't bet on every game, because if the game is priced right, then the cost of the vig means there is no value to be extracted. Think of it like a stock that is priced right - it isn't going to go up, so after I pay a broker $20 to buy it and then sell it at some point down the road, all I've done is lose $20.) This means that by refining your system with additional information - finding additional value that exists beyond these basics - you can further extend your lead on the betting public and, by proxy, Vegas.



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jesse
@ May 25, 2012


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0

Here's the first thing you need to know about betting win totals in the NFL: when in doubt, take the under. Remember, everyone likes to talk about beating Vegas, but talking about Vegas is like talking about beating eTrade. They are just making a market and taking a cut. The public, and their expectations about how a team will perform, is what truly sets the market. The public is who you have to beat.

Why take the under? Because the public likes the overs. It's a simple matter of math: unless the New York Giants beat a team of gridiron-loving aliens Space-Jam style, the NFL will finish every year with a .500 record: 256 wins, 256 losses. But, if you add up the win totals for every team that were just published by Cantor sportsbook, you don't get 256. You get 262.5.

So is beating the house just a simple matter of taking every under? No, because you have to pay Vegas for the privilege of betting on their market, also called the vig. If you were to bet every single under this year, the expected bet value is -90%. (Betting the over, by contrast, would have an expected outcome of -250%.)

Let me quickly define expected bet value. Obviously, every bet is either a win or lose. Expected bet value is, if we could make the bet multiple times, how much we would win on average. A bet with a positive value is what we are after. As long as we make enough of them and do the work right, the individual outcomes don't matter; we will come out on top in the end. In investing, we would call this an expected ROI, or return on investment.

We have to be smart about which teams we take. To that end, I have calculated expected win totals AND 95% confidence intervals for each team. The confidence interval is just as important as the win total, because it will change my opinion about whether to bet a number depending on if the vig is -110 or -130. Put simply, the more confident I am that a team can beat the total, the higher the expected bet value, and the more likely I am to take it. Here are my top 10 bets.

(Full disclosure: Note that, while I will be revisiting these bets throughout the year, I don't plan on actually laying any money on these myself, as this is a new, as-yet-untested betting system I am trying out here. Plus, I don't like tying up any significant portion of my bankroll on bets that don't pay out for 8 months.)

10. Atlanta Falcons OVER 9 wins (+105)
Last year: 10-6
This year: 9-7
Expected bet value: 7.3%  

Yes, after talking about unders for 500 words, I'm starting off the an over bet. Don't worry, the unders are coming later. I've actually got 4 overs and 6 unders in my 10 bets here, but the unders are all higher expected value.  This bet is a function of the +105 moneyline. The most likely outcome for Atlanta, in my estimation, is 9-10 wins this year. However, because Vegas is paying you to take this side of the bet - everybody else wants the under - the slightly better than 50/50 shot of winning has a positive expected value outcome.

9. Miami Dolphins OVER 7.5 wins (-110)
Last year: 6-10
This year projection: 9-7
Expected bet value: 7.7% 

In general, there are three reasons I'll bet a team: they were better/worse than everyone thought last year; their strength of schedule changed significantly between this year and last year; or an offseason roster change has resulted in the team being over/under valued. Miami falls into category 1: they were an unlucky 9-7 team last year.

8. New Orleans OVER 10 wins (-125)
Last year: 13-3
This year projection: 12-4
Expected bet value: 13.3%

Here's the biggest category 3 change on the board. The Saint's offseason turmoil is well documented. Head coach suspended, multiple players suspended, and QB Drew Brees still isn't under contract. However, they still play in an incredibly easy division and Brees, one way or another, will be back. I see a less than 10% chance that they go 9-7 or worse.

7. Kansas City UNDER 8 wins (-110)
Last year: 7-9
This year projection: 5-11
Expected bet value: 15.0%

KC was lucky to even get to 7 wins last year, grabbing a couple of late season victories after changing head coaches. Maybe Todd Haley was the problem, but I don't think Romeo Crennel is the solution.

6. Tampa Bay UNDER 6 wins (-120)
Last year: 4-12
This year projection: 5-11
Expected bet value: 16.2%

Firing the worst head coach in football was probably worth a win, but that's all I'm crediting them with.

5. San Fransisco OVER 10 wins (+105)
Last year: 12-4
This year projection: 11-5
Expected bet value: 17.8%

This is my last over bet on the board, and I was honestly surprised to see it one float to the top. So surprised, in fact, I had to go back to their schedule to see where their wins will come from. If they go 6-0 in their weak division, they have to go 4-6 against GB, DET, MIN, NYJ, BUF, NYG, CHI, NO, MIA, and NE. MIN, NYJ, and BUF are Ws. GB (away) and NE (away) are probably losses. That leaves them to win one of NYG, DET, and CHI at home.

If you have anymore doubt, look at that moneyline: +105. That means the public, who LOVES to bet overs, is fading SF this year. If you are on the wrong side of the public, you are probably doing it right.

5. Indianapolis UNDER 5.5 wins (-135)
Last year: 2-14
This year projection: 4-12
Expected bet value: 21.7%

Swap in Andrew Luck for Curtis Painter last year, does this team get 4 more wins? I don't think so.

3. New York Giants UNDER 9.5 wins (-120)
Last year: 9-7
This year projection: 7-9
Expected bet value: 23.9%

This one hurts me, but setting aside their glorious postseason last year, NOBODY thought this was a good team last year. They were one Tony Romo lob pass from staying home this past offseason, and probably firing their coach. Plus, this year the schedule gets tougher - in fact, they have what I figure to be the toughest schedule in the NFL this year; their out of division schedule includes games against GB, PIT, BAL, SF, and NO. They still play in one of the toughest divisions in football. I'll be delighted to be wrong about this one, but expectations are low.

2. Denver UNDER 9.5 wins (-120)
Last year: 8-8
This year projection: 6-10
Expected bet value: 25.2%

I know, I know, Peyton Manning. 6-10 might be low, but 10-6 is WAY too high. We all know that Denver was lucky to even get to 8 wins last year. Here's an over/under for you: how many games until Manning's neck explodes?

1. St. Louis UNDER 6 wins (-120)
Last year: 2-14
This year projection: 3-13
Expected bet value: 35.4%

 

Sam Bradford, aka David Bromstad from HGTV's Color Splash, is going to be out of the league in 2 years. They were terrible last year, and have the second toughest schedule in football this year, with two divisional matchups against SF, plus GB, NE, and DET. In fact, the only truly bad team they have on the schedule is TB, and that game is on the road. St. Louis fan(s), you have a rough season ahead.



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jesse
@ May 23, 2012


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0
[Note: I am tweeting my baseball gambling picks every day from @obscuresports99 on Twitter. As of this writing, I am +14.4 betting units on the season, although I have been predictably lackluster since making my picks public.]

Gambling on baseball is a bit different from gambling on football. In football, betting is usually discussed based on point spreads: if I bet the Giants +3.5 in the Super Bowl against the Patriots, then that means that the winner for gambling purposes is determined by adding 3.5 points to the Giants final score and seeing who has more points.

Every year, there are some surprises - a team doing better than they were expected to. In gambling circles, you'll hear about a team's ATS, or against the spread, record. If I team goes 11-5 ATS, that means that betting on them all year was a winning proposition. Since Vegas doesn't like when you have winning propositions, they want every team to finish 8-8 ATS, meaning that they make money.

In baseball, we have to talk about surprising teams a little differently because we bet the moneyline. Today, for example, the Yankees moneyline to beat the Royals is -210. That means that, to win $1.00 on the Yankees, you have to risk $2.10. Conversely, the Royals are +185. Risking $1.00 on the Royals will win you $1.85.

To talk about the surprising teams to bet on in baseball, we'll talk about what I'm calling their bet on and bet off value (real gamblers may have a word for this, but I don't know what it is). Bet on value is defined as the amount of money you would win if you bet on a team every game. Bet off value is defined as the amount of money you would win if you bet against a team every game. First, here are the top 5 bet on teams so far this year.

1. Baltimore (+1082)
2. NY Mets (+961)
3. LA Dodgers (+858)
4. Oakland (+699)
5. Tampa Bay (+505)

What do these teams have in common? In the case of Baltimore and the Mets, they were supposed to stink but have surprised everybody this year by contending in their divisions. Baltimore especially has exceeded expectations, leading the competitive AL East. This is also true of Oakland, who are only .500 but were supposed to be much worse. The Dodgers and Tampa Bay were expected to be good, but not necessarily this good. The Dodgers, in particular, sport the best record in baseball. In other words, making this list isn't necessarily just formerly bad teams being good. It's more a matter of expectations vs. reality. I was personally surprised to not see Washington on this list. They were bad last year, and good this year. But because that was widely expected, Vegas has them more accurately priced.

Here are the top 5 bet off teams:

1. Colorado (+1392)
2. LA Angels (+883)
3. NY Yankees (+765)
4. Philadelphia (+622)
5. Milwaukee (+546)

Oof. I especially feel the pain of Philadelphia, since I have personally overvalued them this year (even though the Yankees are my team, I have actually had positive outcomes wagering on them if gambling were legal). The Angels are obviously a direct result of expectations vs. reality of Albert Pujols in particular. They were supposed to be a juggernaut, but instead sit in last place in their division, 6 games below .500.

If you are curious, here are the top 5 teams I have made money on this year if gambling were legal:

1. Kansas City (by a country mile, I might add)
2. NY Mets
3. NY Yankees
4. Arizona
5. Seattle

And here are the 5 that have given me the most heartburn

1. Philadelphia (and again, not even close to #2)
2. Milwaukee
3. Texas
4. Pittsburgh
5. San Diego


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jesse
@ September 8, 2010


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1
Maybe you like to watch sports or listen to rock music while you are on the treadmill, but I prefer to pace myself with Wheel of Fortune. Jogging in place while the wheel clicks away gives me time to think about the important things in life. Things like "why is this asshole buying a vowel when he must know the answer" and "you're spinning?! But you've got 12 grand in the bank and there's only one goddamn consonant left!!"

In fact, since Wheel of Fortune is a game, I've decided that it must have a definite optimal solution. Consider the puzzle below, one which I imagine even the reddest red state moron would be able to tease out:

Word_Puzzle.jpgOne vowel, 2 Bs, an L, a C, and a K are left. You've already got $8,000 in the bank, including an all expenses paid vacation to the Sandals resort in Jamaica and a shopping spree on Etsy.com to spend on human centipede merchandise. Do you spin or solve?

It really comes down to how much risk you can tolerate. Based on this wheel, and assuming that the probability of landing on each spot is equal and that the Lose a Turn spot is essentially the same thing as the Bankrupt slot (the guy with the lifetime NRA membership next to you is DEFINITELY solving this puzzle), we can calculate the expected value of your next spin. Then we can make a chart. That chart looks like this:

wofgraph.gifIn this context, a singleton is a letter of which there is only one, i.e. the C, L, and K. The twofer is the letter of which there are multiples, i.e. the B. The twofer has a higher expected value because you get money for each instance of the letter appearing in the puzzle.

In our example, even if you have $8,000 in the bank, a spin with a twofer in the board will net you an average value of nearly $700.

Now: is there opportunity cost associated with solving? That is, by solving now, not only do I lose the value of this spin, but of all future spins. Consider the example above again, except start with only $5,000 in the bank. The average value of that spin was $921, because I was risking much less money on a bankrupt or lose a turn spot. There are still letters left. What is the value of those future spins?

On Spin 1, I start with $5,000, and the average value of my spin, because there is a twofer left, is $921. However, if I want to know the value of future spins, that presumes that I did not land on the bankruptcy spots; i.e., the starting value of future spins is not $5,921, but rather the average value of all non-bankruptcy spots on the wheel, which is $730 (or $1,460 with a twofer).

On Spin 2, I would theoretically start with an average of $6,460, and only have singletons left. The average value of that spin is only $130. Additionally, my leveraging (that is the ratio of money I'm risking to money I'm potentially earning) goes from a reasonable 5.4:1 to an absurd 50:1!

Here's how the value of the second spin changes with money in the bank, assuming you will use the twofer on your first spin:

wofgraph2.gifThis graph shows that, with anything about $2,000 in the bank, you become what I would consider over-leveraged on your spin (greater than 10:1) and with more than $6,000 in the bank, your bet becomes a loser. It also shows that, in most cases, there is little to no opportunity cost lost unless there are multiple twofers or higher left in the puzzle once you've solved it.

This confirms the strategy that I've long assumed to be correct on the show: once you've determined the answer to the puzzle, you keep going until there are only singletons left or you exceed $10,000 in the bank, whichever comes first. Wheel of Fortune: SOLVED. Next, please.


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jesse
@ January 18, 2010


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0
After yesterday's football results, three players remain out of 16 in the $50 buy-in suicide pool Suzi and I are participating in this year. Two of them are me and Suzi. The third is Suzi's boss, Colin. The rules of the pool are simple: you must pick a winning team to stay in it each week, and you cannot pick a team twice. Last man standing wins, with 2nd and 3rd place prizes also given out. The pool of teams which could be selected from was reset for the playoffs.

I claimed to Suzi that there was an optimal, clearly correct course of action to be taken. She resisted, saying that the facts were not all in yet. What follows is a wordy, esoteric, and ultimately pointless exercise in calculating the odds and value of each possible selection and outcome. However, there will be tables. So that's something to look forward to.


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jesse
@ November 18, 2009


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0
Its not your fault, Daytrader. Its not your fault. Its not your fault. Its not your fault.

After a week in which he got only two picks right - technically, he got one right and a coin he flipped got one right - we've decided that he'll take a mental health holiday from making NFL picks. I didn't do much better, as we both got caught up in the Underdog Swing. The season started with every favorite covering due to the plethora of horrible teams this year. The inevitable over-reaction came last week, when the lines dropped and underdogs were covering all over the place. So where does that leave us this week? After 10 weeks of football, have we finally figured these teams out? (Home team in CAPS.)

CAROLINA (-3) over Miami

I had to read this line a couple of times. Last week, Miami was maybe the best 3-5 football team in the history of the NFL. Since Chad Henne took over at quarterback, the team is 3-3 with losses to New Orleans, at New England, and at San Diego, all quality opponents. I just didn't understand what was going on. That is, until I saw this. Oh.

Confidence points: 4

Washington (+11) over DALLAS


They say that one of the signs of global warming is the shifting of the seasons. Maybe that explains why Dallas' annual December collapse is happening three weeks earlier than usual.

Confidence points: 3

DETROIT (-3.5) over Cleveland

I'm calling this game the Turd In the Punch Bowl. The combined statistics of Matt Stafford, Brady Quinn, and Derek Anderson: 51% passes completed, 5 yards per attempt, 9 touchdowns, 26 interceptions, a QB rating of 50.9. In other words, just flip a coin and move on with your life. Thinking about this game too much might cause brain damage. Instead of broadcasting this game there should just be a test pattern on the TV for 3 hours.

Confidence points: 1

San Fransisco (+6.5) over GREEN BAY

Which Green Bay is going to show up? The one that throttled a suddenly flailing Dallas team last week, or the one that couldn't fight their way out of a paper bag named Tampa Bay two weeks ago? Now that the Curse of Crabtree was broken by the even more powerful Curse of Cutler last week, I say San Fran gets back on track with a win.

Confidence points: 2

Pittsburgh (-10) over KANSAS CITY

Cincinatti showed everybody the blueprint on how to beat Pittsburgh last week: play good defense. Too bad for Kansas City they can't do that.

Confidence points: 12

Seattle (+10.5) over MINNESOTA

The line has moved down from 11 since it opened. That tells you I'm not the only one who thinks this is too high. If the Lions weren't so pathetic they could have capitalized on a sloppy Vikings team last week. Seattle is slightly less pathetic, so take the points.

Confidence points: 5

NEW YORK GIANTS (-6.5) over Atlanta

Either the Giants straightened out their defense over the bye week and will get back on track, or they lose this game and finish the season 7-9. The Giants have been punished by Drew Brees, Phillip Rivers, and Donovan McNabb over the last few games. Matt Ryan is good, but he's not in that class yet.

Confidence points: 6

TAMPA BAY (+11.5) over New Orleans

A shaky looking Saints team + an improved Tampa Bay team + waaay too many points = underdog cover.

Confidence points: 10

JACKSONVILLE (-9) over Buffalo

Do you still get a home field advantage when the home field is empty? In any case, Buffalo is a mess right now. Remember, only two things grow in upstate New York: rutabagas and despair. And Buffalo, you don't look like no rutabaga to me.

Confidence points: 11

Indianapolis (-1) over BALTIMORE

I'm giving this game my "WTF" Award of the week, because I saw this line, and said "WTF?" I didn't even say what the fuck, I actually said WTF, because that's how we talk now as a society and I'm kind of sad. This line opened with Baltimore favored by a point and moved 2 full points in one day. I don't know if this is supposed to be a trap game for Indy, or if the big win over the Cleveland Steamers got everybody back on the Baltimore bandwagon, but bet the farm on Indy.

Confidence points: 14

Arizona (-9) over St. Louis

Kurt Warner returns to the scene of the Greatest Show on Turf. He is going to light the Rams up. This is my suicide pool pick of the week as well.

Confidence points: 15

San Diego (PK) over DENVER

This game has no line, so we call it a pick 'em. The game is off the board because nobody knows if the starting QB for Denver will be Kyle "Neckbeard" Orton or Chris Simms. Is Chris Simms actually Phil Simms son, or did they just make a bad copy of Phil like Stewie did on Family Guy last Sunday?

Confidence points: 16

OAKLAND (+9.5) over Cincinnati

Trap game trap game trap game trap game trap game for Cincinaaaaaatti! Coming off the big win at Pittsburgh, Cincy is probably feeling pretty confident heading into matchups with Oakland and Detroit over the next two weeks. I predict Oakland catches them napping with a feisty, ugly 13-10 win.

Confidence points: 7

NEW ENGLAND (-10.5) over New York Jets

New England is like a man coming home from a bad day at the office (loss to Indy), stopped off at the bar for a few drinks on the way home (all the talk about Belichick's 4th down decision), and now he's home, stinking of beer and ready to beat his long suffering wife (the Jets). We're all okay with domestic violence metaphors, right?

Confidence points: 13

Philadelphia (-3) over CHICAGO

What's the only difference between Jay Cutler's time in Chicago and the Challenger explosion? Jay Cutler hasn't killed a teacher yet.

Confidence points: 9

Tennessee (+4.5) over HOUSTON

Poor Houston. Poor, snakebit Houston. They lose three games on goal-line fumbles. Three! Three games! Three whole games! And now they get an inexplicably hot Tennessee team featuring Chris Johnson, the best running back in the game right now. Sorry Houston, but I believe in Tennessee.

Confidence points: 8


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Jim
@ August 25, 2009


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1
Remember Tim Donaghy, the cousin of NBC executive Bill Donaghy, who looks a lot like Lloyd Braun from Seinfeld, the NBA ref who fixed a bunch of games and then got caught?

Well, according to the AP, he just got violated. For missing work.

Apparently, he's been working in sales at ShotPak. His office phone and e-mail are even on the web site.

I can't describe how awesome it is that this company is hiring ex-cons.


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jesse
@ January 9, 2009


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1
Jim, I bet you think your taunting has gone unnoticed.  Maybe I'm the only one who read your Plaxico Burress-inspired version of "Janie's Got a Gun" in the comment thread for this article, but I read it.  But guess what? The Giants are going to beat the Eagles on Sunday.

Who have the Eagles won against? They beat the Giants immediately after Plaxico shot himself.  Then they beat a terrible Cleveland team that had quit on their coach.  They followed that up with a loss against a Washington team with nothing to play for in which they only scored three points.  They beat a terrible Cowboys team to make the playoffs.

And then they played the Vikings, the only possible playoff matchup that gave the Eagles an advantage at either coach or quarterback.  The Vikings were barely able to beat the Giants backups a week earlier.

Meanwhile, the G-Men have had a week off.  More importantly, Brandon Jacobs is healthy.  I've learned my lesson about betting on my teams in the playoffs, but if I didn't have a stake in this game, I'd be putting cash on the Giants.  Mark it down: the Giants are going to the Super Bowl.  For realz.

Giants 28, Eagles 10.


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jesse
@ October 27, 2008


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6
With Game 5 of the World Series mere hours away, I have good news for Jim, our resident Philadelphia sports fan: I'm rooting for the Tampa Bay Rays.  The reason for this good news is a story Jim knows only too well: in the 8th inning of Game 7 of the 2001 World Series, my hubris invoked the wrath of the sports gods.  The teams that I root for have been paying the price ever since. 

Everyone knows that gambling makes sports more exciting. While a true fan can always appreciate the skill of the athletes involved, adding a few dollars to the mix can add a degree of personal investment that otherwise only comes with years of devoted following.  But where a wager can make the most boring athletic matchup exciting, experienced gamblers also know the opposite is true: when your team is involved, you are already emotionally invested.  Don't add gambling to the mix.  Never, ever gamble when your team is involved.


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jesse
@ September 19, 2008


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9
[This entry is long, and I am irate.  You have been warned.]

When a horse named Barbaro started the 2006 Preakness Stakes, he was a heavy favorite.  Barbaro had already won the Kentucky Derby, and some horse racing experts were predicting that he be the first horse to win the Triple Crown since Secretariat.

There are bettors that like to bet large sums of money that huge favorites like Barbaro will "show" - that is, finish in the top three.  A typical payout is that, for every $1 that you wager, you'll get 5 cents back.  To make serious money, a bettor must lay out an incredible amount of cash.  A $100,000 bet would win you $5,000.  In horse racing circles, there is a name for these types of bettors.  They are called bridge jumpers.

Barbaro did not win the 2006 Preakness Stakes.  He did not place, and he did not show.  He shattered his leg before the first turn, and despite several surgeries, he had to eventually be put down. The bridge jumpers were left to deal with the consequences of their decision.

Chumps.  They should have been investment bankers.


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jesse
@ July 16, 2008


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0
There are a number of big, important topics that I was thinking of writing about today. 

The New Yorker has taken to making anti-Obama propaganda and calling it satire.
The mortgage crisis continues to spiral out of control, dragging down the rest of the economy with it.
This guy blended an iPhone.

Well, fuck all that shit, cause Comfort is back!

Jessica King, the dancer who beat Comfort out for a spot in the top 10, has been felled by an injury, making room for Comfort in the top 10.  Not only that, but Comfort will replace Jessica on the 50 city tour later this year.

What the hell happened? Did she get hit by a bus or something?

(Tee-hee-hee!)

The show's producer, big-toothed Brit Nigel Lythgoe, won't get specific about the injury that occurred, so allow me to engage in some wild speculation.

Jessica was inadvertently impregnated during last week's "Adam and Eve" routine with Will.


Debbie Allen knee-capped her for dragging her protege into the bottom 3.

My threatening e-mails finally got through their spam filter.

Whatever the reason, there is a more pressing question: does this mean I'm not bad luck anymore? Is the curse broken? There is only one way to find out: to the casinos!

(Oh, and PS: If you actually do care about important things going on in the world, read this post on the mortgage crisis by Jonathan Golob of The Stranger, aka Dear Science.  Could not have said it better myself.


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jesse
@ July 11, 2008


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What's the opposite of a lucky horseshoe? An unlucky cow-hat? That's what I am, an unlucky cow-hat.  My ability to lose and cause others around me to lose is legendary.  My own wife won't sit at the same table with me when we go to casinos - and considering how unlucky I am, why is it we keep ending up in casinos in the first place?

My bad luck is starting to stretch, and gain momentum, and touch things beyond the blackjack table.  If I root for you, or wish you well, run away, for I am the kiss of death.

First, despite (or because of) my endorsement, Jason Giambi and his ugly-beautiful mustache will not be going to the All-Star Game.  He lost the final vote to Evan Longoria-Parker of the Tampa Bay Rays, despite his complete lack of mustache.

But that wasn't the worst blow.  No, that came on Thursday, when Comfort was kicked off So You Think You Can Dance before she got into the top 12, which means America will be denied the chance to see her perform on the SYTYCD tour later this year.  But what's amazing is that my kiss of death endorsement didn't just make her lose, it actually made her deserve to lose.  She was terrible on Wednesday night. 



Oh, is there no respite from this terrible burden of mine!  And I don't even get to hook up with Maria Bello in the end.






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