The following is the letter I intend to send to the L.A. Times regarding their piece earlier this month on the Puckett case. Any comments/critiques are welcome.

Dear Mr. Felch and Ms. Dolan:

I read with interest your May 3, 2008 article on crime-solving and DNA evidence, particularly in old cases where only partial matches are possible. In the case of murder trial of John Puckett, there was significant discussion of the debate over whether the odds of Puckett’s innocence were 1 in 1.1 million, as the prosecutor maintained, or 1 in 3, as the defense did. In fact, both numbers are almost certainly wrong.

Oddly enough, the reason why both numbers are wrong was made clear in a Times article that ran only three days later, which was co-authored by one of you. In that May 6 article, you rightly noted the problems inherent in the “prosecutor’s fallacy,” where the odds of an event occurring prospectively are mistaken for the odds that it has occurred, after the fact. To give an obvious illustration, the odds of anyone being struck by lightning in his lifetime are 3,000 to 1, and the odds of it happening on any given day are much more remote than that. However, once you encounter a corpse on an open field shortly following an electrical storm, the odds that he was struck by lightning grow exponentially. The reason is akin to the common joke “the odds of X are slim to none, and Slim just left town.” Before the incident, the odds that this unfortunate soul would be zapped were roughly 3,000 to 1, but after the fact, the vast majority of those other 3,000 would have resulted in him not ending up dead on the field, and can therefore be said to have “left town.” At this point, the only odds left to consider are those relating to alternative scenarios that also would have left the guy dead in the field.

Similarly, we know going into a cold database search like Puckett’s that there is a 1 in 3 chance that someone’s profile will randomly match to the killer’s (or conversely, a 2 in 3 chance that no one will), and a 1 in n chance that the killer himself will be in the profile, generating a not so random match of his own (and conversely, an (n – 1) in n chance the killer will not be in the database). If the search generates exactly one match, as it did in Puckett’s case, we can say with certainty that there was either a random match or a true one, but not both. These two possibilities can be described as follows, with G (guilt) indicating a true match and I (innocence) indicating a random one:

P(G) = 2/3 x 1/n
P(I) = 1/3 x (n – 1)/n

Which is more likely? That depends on the value of n. If the value happens to be 2, i.e., there was a 50-50 chance of Diana Sylvester’s killer being in the database, then the probabilities are as follows:

P(G) = 2/3 x 1/2 = 2/6
P(I) = 1/3 x (2 – 1)/2 = 1/6

The probabilities don’t add up to 1 but that’s OK; the other 3/6 represents the scenarios that “left town,” i.e., would have resulted in either no hits or more than 1. After confining ourselves to the 3 in 6 scenarios consistent with the single match we got, we are left with essentially 2 to 1 odds (or 1 in 3 chances) against Puckett having been an innocent who was randomly chosen. If the odds of the killer being in the database are higher than that, then we can be more confident of Puckett’s guilt, but not necessarily to an extent that would satisfy reasonable doubt. But if the original odds of the killer being in the database were 1 in 3, the same as the original odds of a random match, then innocence and guilt are equally probable. And if the odds are lower than 1 in 3 – not implausible given that they weren’t maintaining a sex criminal database at all in 1972 – then it is actually more likely that Puckett was a false match than a true one.

The bottom line is this: until we can find a reliable method of computing the likelihood that a given killer will or will not be in the database, it is impossible to tell what the odds are that a given match was obtained randomly or not. This may not matter in cases of full DNA matches, where the prosecutor’s fallacy makes the odds of an innocent match seem like a trillion to one when in fact, they are “only” a billion to one, or worst, “only” a million if the odds of the killer being in the database were unusually low. But it makes a huge difference in cases like Puckett’s, where the odds against a false match were only 2 to 1, and we have no idea at all what the odds of a true match were.

UPDATE: Before I had the opportunity to send the message, I got cc’ed in a message from Jason Felch that was the subject of Patterico’s post today. I ended up sending this message instead:
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Here in the Triad, more than a few cars have license plates beginning with the letters commonly referred to as Whiskey, Tango and Foxtrot. Mine don’t, alas, but I’ll consider trading in for plates that do if Alan Dreher, of Kathryn Johnston infamy, ends up as our new police chief. Jeebus. One wonders what the The Waters Consulting Group, who conducted the search on behalf of the City Council, has been smoking. The smart money says it’s something a bit more potent than Winstons or Salems.

UPDATE: While the consultants may have partaken in substances of dubious legality, it looks like the City Council stuck with the legal brands that made our city famous, and opted for former Cary Police Chief Scott Cunningham instead. Perhaps an additional silver lining to the fact that Dreher was a contender in the first place (here this time, and in Charlotte before) is that he applied for both positions knowing his career in Atlanta had reached a dead end? One can only hope, but regardless of the reason, Dreher is Atlanta’s problem, not ours.

John Hawkins has a pair of confused posts in which he claims he can no longer support John McCain’s candidacy because McCain “lied” about his newfound respect for the need to secure the border before introducing any de facto amnesty programs for those already here. This would be interesting if McCain had actually come out and said “screw border security, amnesty away!” What he actually said was a bit more … um … subtle than that:

He added: “I believe we have to secure our borders, and I think most Americans agree with that, because it’s a matter of national security. But we must enact comprehensive immigration reform. We must make it a top agenda item if we don’t do it before, and we probably won’t, a little straight talk, as of January 2009.”

Mr. McCain asked others on the panels for suggestions about how to “better mobilize American public opinion” behind the notion of comprehensive immigration reform.

In other words, candidate McCain has flipped alll the way from “Yes, I favor comprehensive immigration reform but we need to secure the border first” to “Yes, we need to secure the border first, but I favor comprehensive immigration reform.” Lest his readers mistake this for a distinction sans difference, Hawkins non-explains:
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American Airlines has announced its plans to charge a $15 fee to check bags on its flights. That was the last straw. From now on, rather than flying American every time they happen to offer the most convenient, lowest-priced flight to wherever I’m going, I’m only going to fly American when they offer the most convenient flight and beat the competition’s price by at least $15.

Rumor has it that John McCain has whittled his list of potential running-mates down to three. If the rumors are correct (or more precisely, if the inferences are correct that McCain’s inviting these three to choose a running mate between them), then we have two reasons to rejoice:

1. Bobby Jindal is among them.
2. Mike (P)huckabee isn’t.

One blogger I did not meet at the convention but did learn about from others there is Papa Delta Bravo, whose blog will soon be joining my blogroll. Check it out.

All ballots should give voters the option of either voting for their favorite candidate or against their least-favorite. Every vote against a candidate cancels out one vote for that candidate. If no candidate garners a majority of the net positive votes, a run-off will be held among the candidates who ended up with positive vote totals.

Discuss.

I didn’t blog much about the convention while it was in practice, but the reason is I was too busy hanging with a lot of really cool people. It was good to see Uncle and David Kopel again, and to meet Bitter Bitch, Sebastian, Robb Allen, Joe Huffman, Kevin Baker, Mike W., Thirdpower, the Rustmeister, the Squeakmeistermistress, TD, Caleb, Murdoc, Sailor Curt, Tam (whom some evil NRA staff member attempted to turn into a witch), U.S. Citizen, Michael Bane, David Hardy, David Young, Alan Gottlieb, ParatrooperJJ and some others whose names escape me at the moment. If you are among them, please identify yourself in the comments and I’ll add you to the list with my apologies.

I suck with a camera, so if you’re hoping for good gun pr0n you’ll need to follow the above links, but from my perspective, here are the high/lowlights of the conventions:

• No good deed goes unpunished. Bitter Bitch, to whom we all owe a colossal debt of gratitude for organizing the event and convincing so many gunbloggers to come in the first place, broke her foot before the convention even began.
• Chris Cox added insult to said injury by publicly threatening to deprive Ms. Bitch of her constitutional right to a secret ballot and “show the country how Bitter votes.”
• On Friday, if I hadn’t been such a dumbass and had paid closer attention to Bitter’s posts, I’d have known that I qualified for a media credential, which I would need to attend McCain’s speech. I’d have also known about the firearms law seminar, which I would have preregistered for and attended. Woulda, coulda shoulda.
• On Friday night, I finally did pull my head out of my butt and join up with the bloggers in time for us all to briefly leave the South for dinner and drinks in the Midwest. That was kinda cool, conceptually speaking, but cooler still was having the tab for the drinks picked up by Michael Bane. Thanks, Michael! I love ya man!
• After dinner, we returned to the South and had Jack and Coke, Jack and Dr. Pepper, Vodka and Coke, and whatever other alcoholic crap we could mix with whatever other fizzy bubbly stuff was on hand. US Citizen got thoroughly plastered. Uncle got mildly inebriated, which is saying a lot given that it takes a lot of alcohol to affect him much at all. Either that, or a small amount of alcohol turns him into a wise-ass, which distinguishes his drunk personality from its sober counterpart … how, exactly?
• During that session, either before or after he converted from a sober wise-ass to a moderately inebriated one, Uncle advised us that his teeth are like a bunch of little vaginas.
• Also during that session, which I’ll call “in vino wiseassitas,” several of us started speculating about what anti-gun conventions are like. I asked what the exhibits would be. Robb asked if they had an anti-gun range. Heh.
• A bunch of other really cool stuff happened during in vino wiseassitas. For some reason I don’t remember any of it, but I’ve heard it was really cool.
• At the banquet last night, Louisiana Governor Bobby Jindal gave an awesome speech, leading one of my fellow bloggers to suggest that McCain should name him as his VP, get elected, and then keel over in 2010. I was deeply offended by this vile suggestion, so I pointed out that for Jindal to serve 10 years rather than 7, McCain would have to wait until at least 2011 before keeling over. Err, I mean, I pointed out that it is terribly untoward to say that about anyone, especially the least vile Democrat in the race, so wouldn’t it be better for McCain to serve just one term and hand the reins over the Jindal after that? Yeah, that was what I said.
• Also at last night’s banquet, Glenn Beck gave a great speech, in which he compared the three individuals who have any chance of being President to the Three Stooges.
• Today a group of Truthers showed up to heckle Oliver North and Ted Nugent. More here.

I was traveling when the California Supreme Court joined its Masshole counterpart in ruling that the drafters of their respective constitutions really meant to guarantee a right to gay marriage, even if none of them knew that, so I didn’t get a chance to blog about it until yesterday, and thought it best to say less rather than more until I’d had a chance to peruse the lengthy decision. Now, I have, so here goes.

My first thought upon hearing that the decision was 4-3 (also mirroring Massachusetts’s experience) was “Oh crap, I knew that that silver lining of Janice Rogers Brown going federal had a cloud attached to it somewhere.” That thought turned out to be (mostly) wrong, as the Governator’s sole appointee, Carol Corrigan was among the dissenters. Thus, Brown confirmation or no, the decision would have 4-3, regardless. However, it would have been a more solid 4-3 split than the case we actually got, which I would argue is more of a 5-2 split on the core issue of whether gays have a “constitutional” right to marry other gays, while only 4 of the prevailing 5 agree that it has to be called marriage. In other words, today’s CA is 4-3 in Massachusetts’s camp, but 5-2 in New Jersey’s.

One aspect of the majority opinion I found amusing was the part that went into detail about how it does not establish a right to “gay marriage” as such, just a right to marriage generally, which just happens to extend to gays but not to polygamists, cousin-humpers, or anyone else who lacks the legal ability to exercise his allegedly constitutional right to “join in marriage with the person of one’s choice.” Footnote 52 insists that this decision absolutely, positively will not lead to a new right to marry one’s brother, but offers no reasons to support this conclusion beyond the usual “ick” factors the Perez court might just as easily offered up against gay marriage.

Lastly, for whatever good it does, Thursday’s decision should put to rest once and for all the uncommonly silly theory that Proposition 22 only applied to out of state marriages. On that issue the ruling was 7-0.

Word has it that the Winston-Salem Warthogs are looking for a new team name. I think “Cancer Sticks” would fit the bill quite nicely, but no one I know in the area seems to agree.