Whatever your position is on the death penalty, you'll probably admit that the killing of an innocent man by the State would be a tragedy. If you are a regular reader, you'll no doubt be unsurprised to hear my position on the issue.

Let me pause briefly to comment on the irony that I expect there is great intersection between those that find the government incapable of providing health care (life) but perfectly capable of administering capital punishment (death). Moving on.

The horrible irony of the anti-death penalty movement is that the best thing that could happen for the cause is for a man who has been executed to be proven factually innocent after the fact (there's even been a movie about it. Seriously!) In the latest issue of The New Yorker, David Grann profiles what may be just such a case.

Do yourself a favor and read the whole thing. But whether or not the case of Cameron Todd Willingham turns out to be the case that changes the debate about capital punishment in this country, about certain things there can be no doubt. Probability dictates that the United States has unquestionably, at some time in its history, executed an innocent man.

There have been 1,173 executions since 1976. According to The Innocence Project, 242 people have been found to be wrongfully convicted through the application of DNA evidence. 17 of these people served time on death row.

Or, put another way: without the application of DNA evidence, 17 people would have been wrongfully executed since 1976. That's one every two years. However, innocence can only be proved in this method where DNA evidence exists, and is pivotal to the case. Without access to statistics, I will make a conservative estimate that 50% of capital murder cases do not involve DNA evidence.

If 50% of cases have no DNA evidence, that accounts for 595 executions without DNA. Furthermore, 17 exonerations out of 1190 cases represents a (astoundingly high) wrongful conviction rate of 1.43%. If the average wrongful conviction rate is 1.43%, what are the odds that out of 595 executions, 0 innocent men have been killed?

Think of each case like a coin flip, except instead of a 50/50 shot on each flip, the odds of heads are 1.43%, and the odds of tails are 98.57%. We have flipped the coin 595 times. What are the odds that we got tails every time?

Flip one time. The odds of tails are 98.57%. Flip again. The odds of this flip being tails are once again 98.57%, but there was only a 98.57% chance that you got to flip a second time without getting heads. Your total odds are (98.57% x 98.57% = 97.2%). If you flip 595 times, the formula is:

98.57%^595 = 0.02%

In other words, based on what we know about the wrongful conviction rate in cases where there is DNA evidence, if we assume half of all executions did not involve DNA, we can determine that the odds that no innocent man has yet been convicted is only two-tenths of one percent.

And it turns out that we've executed so many people that it almost doesn't matter what you make the odds. What if the wrongful conviction rate is only half of one percent, and the number of cases not involving DNA is only 20%?

99.5%^298 = 22.5%

22.5%. A shockingly low number. And this is only considering cases since 1976, when capital punishment was re-instituted after a four year hiatus. And after capital punishment was limited by a Supreme Court decision to murder cases only. And after all the technological advances in criminal investigations (I mean, have you seen CSI?) The odds are much lower than this. The odds are, essentially, zero.

In the New Yorker article, Justice Antonin Scalia is quoted as saying:

[There has not been] "a single case--not one--in which it is clear that a person was executed for a crime he did not commit. If such an event had occurred in recent years, we would not have to hunt for it; the innocent's name would be shouted from the rooftops."

To pivot the argument on the existence of a single case where a man's innocence can be factually proven is to miss the point entirely, and to fail to understand probabilities. Whatever your final thoughts are on the case of Cameron Todd Willingham or the justification of the death penalty, this fact remains: it is a mathematical certainty that, if an innocent man has not yet already been killed by the death penalty, it is simply a matter of time.