Kieran Healy

Law vs Economics…

… UCLA vs Berkeley, Conservative vs Liberal, Eugene Volokh vs Brad DeLong. They go head-to-head over Bill Bennett. Brad thinks it absurd, as a matter of simple probability, that Bennett might have broken about even over the years. Eugene says the sources for the evidence might be untrustworthy:

Some casinos are estimating the total losses at over $8 million, but Bennett explicitly says otherwise; instead, he’s saying that he’s come out pretty close to even (whatever exactly that means), and thus … that the supposed casino estimates are mistaken or highly incomplete. This has little to do with statistics—it’s a question of fact. Bennett may be lying, but only if you think the casino estimates are sound, something that the article certainly doesn’t prove.

I don’t think Eugene is ignorant of statistics (his undergraduate degree is in math and computer science) but I’m not sure his response addresses Brad’s main point. Eugene correctly insists that we’re not fully sure Bennett lost $8 million, because that number is a possibly wrong estimate from the casinos. But Bennett didn’t just say “That estimate of my losses is incorrect” he said he had come out pretty close to even over the last 10 years. I find this claim absurd for the same reasons as Brad. No-one disputes that Bennett was a high-rolling, high-stakes slot-machine player for years. We know how slot machines work. They are set up to make a fixed profit over time. There is no uncertainty about their profitability. The house cannot lose in the long-run. It defies belief that a single player routinely playing the house’s slots for 10 years could break even. I can’t see a way around this, unless Bennett wants to say that by “breaking about even” he means “losing no more than the 2%-8% set by the machines,” and that seems a little disingenuous for such a virtuous guy. Brendan Koerner has more on this over at Slate.

Update: Eric Rescorla continues the conversation.

>>I don?t think Eugene is ignorant of statistics< <

Volokh writes that he is “agnostic” over whether Bennett or the casinos are telling the truth, and who can write that “Some casinos are estimating the total losses at over $8 million, but Bennett explicitly says otherwise; instead, he’s saying that he’s come out pretty close to even (whatever exactly that means), and thus (returning to the previous paragraph) that the supposed casino estimates are mistaken or highly incomplete. This has little to do with statistics—it’s a question of fact.”

From my perspective, it’s impossible to write a paragraph like this unless you are—in some powerful sense—ignorant of statistics. When the background probability of some state of affairs is overwhelmingly improbable, claims that the state of affairs actually took place need to be regarded with great skepticism, not taken at face value.

To dismiss the background probabilities and turn it into a simple “he said, he said” problem about which one should be “agnostic” is a major analytical mistake. It’s simply wrong: the equivalent of arguing that “all men are mortal,” and “Socrates is a man” implies that “all men are Socrates.”

Maybe I’m mistaken, but I was under the impression that the original article said that he had taken out $8 million in chips, which isn’t quite the same as losing $8 million. Or did I miss something?

Was everything he bet in slots? He’s also supposed to have bet video poker, which I’d imagine might not be as predictable as slots. And, did he pursue other forms of gaming besides slots and VP? Maybe how much he won or lost isn’t so predictable.

ALL problem gamblers think they’re breaking even. mostly likely because they’re counting on that next big score. bennett is deluded and debating the point is pointless.

Pardon me, but who really gives a s**t how much he lost or won? If he had come home with 8 million would that really change the argument from either side? The guy spent countless hours plugging money into slot machines, and indulging in a victimless vice which he himself initially justified using arguments that he had dismissed with Olympian contempt when applied to other vices (in other people). Isn’t that the point of the whole Bennett story?

Say Newsweek has it exactly wrong, Volokh has it exactly right, Bennett broke even, etc., etc. So what? The legitimate criticisms and legitimate defenses of Bennett are unchanged by the amount wagered or lost (or won).

Pardon me, but who really gives a s**t how much he lost or won? If he had come home with 8 million would that really change the argument from either side?

You’re right that this isn’t the main point, but bear in mind that it was Bennett himself who offered the “I broke even” as a defence.

Right – but “I broke even” is essentially a corrolary to the “I can handle it” argument of casual drug and alcohol users that Bennett has rejected elsewhere. The criticism to be levelled at Bennett is that he would make that argument at all.

I suppose you are right in that if he didn’t break even but said he did, he’s a liar, which is certainly an unambiguous breach of virtue. But it seems that the discussion has kind of changed from a discussion of the credibility of Bennett to a discussion of the credibility of his accusers, i.e. the journalists who broke the story. That’s too bad, because even if they got the numbers wrong, Bennett is still a hypocritical, self-serving windbag.

I have been, off and on, a slots player on those machines which can have an edge for the customer (overall, these machines still give the edge to the casino, just like all slot machines and video poker). I got to know many gamblers, both professional and amateur. One of the things you find is that most gamblers, even many professionals, regularly misstate their overall winnings. This is human nature; you tend to remember your wins and forget your losses. Gamblers do this all the time, although the smart pros always know pretty closely just how much they really are up or down—amateurs almost never do. It’s natural for Bennett to think he’s more or less broken even, but it’s so incredibly unlikely… well, I wouldn’t take that bet. Casinos love people like that though; that ability of humans to forget the bad and remember the good is the bread and butter of the casino business.

I don’t have any problem with DeLong going after Bennett, but I don’t understand why he’s so eager to go after Volokh. Volokh said that he was agnostic between the article’s claim that Bennett lost $8 million and Bennett’s claim that he’s “pretty close to even.” In context, “pretty close to even” can plausibly be read as a claim that Bennett lost some amount that’s (a) significantly less than $8 million, and (b) insignificant to Bennett, and that seems to be how Volokh read it. That isn’t evidence of innumeracy, but only that Volokh’s a judicious guy.

BTW, if the manager of a $1 billion portfolio had lost 2-4%, I don’t think anyone would call him a liar if he claimed to be “pretty close to even” even though he’d lost millions of dollars. That’s not a defense of Bennett, but Volokh’s getting a bum rap.

I think DeLong’s attack on Volokh was both unfair and in poor taste. Even under DeLong’s implied statistical model, the conclusion of the argument depends on the assumptions. DeLong assumes a house take of 10% (i.e., expected net winnings per trial 500 * house take) and a standard deviation of 1350 in per trial net winnings. DeLong’s numbers were correct for these parameter values. However, if the house take is smaller or if the standard deviation is larger, the probability of being within a wealthy former beaurocrat’s margin of “even” becomes nontrivial under plausible alternative assumptions. For instance, try the Central Limit Theorem argument out with a $500 stake, a house take of 0.02, 16,000 plays, and DeLong’s 1350 standard deviation; even at 160,000 plays, the probability is reasonably large with a house take of 0.02 and standard deviation of 2200.

I include some of examples and details here, including some arguments supporting a smaller take and larger standard deviation. It’s possible that DeLong has detailed knowledge of slots to support his assumptions, but he gave no indication of such. Without it, I do not see how the alternative assumptions are ruled out. That’s the key when taking the offensive as DeLong has: the burden is on him to discredit plausible alternatives that complicate his conclusions.

Volokh’s agnosticism was based on the uncertainty of whether the quoted losses include winnings. If not, then it is possible that Bennett put down $8 million in as few as 16,000 plays, so the distinction is relevant. (I realize that new information has come to light here, but I am taking on the argument at the time of the original discussion.) As such, Volokh could have been well aware of the Central Limit Theorem and simply made different guesses about the configuration.

As a statisician, I spend a part of every day talking people through statistical solecisms, but I also spend a part of every day learning subject matter from the scientists with whom I’m collaborating. If I approached the former with the attitude of disdain DeLong shows Volokh, I could only expect the same in return, and both sides would lose. It seems to me the same ethic should apply in the blogosphere as well.

Be kind, for everyone you meet is fighting a great battle.

Philo of Alexandria

Bill Bennett’s statistics

Time to join the free-for-all over whether or not Bill Bennett lost money. Kieran Healy is siding with Brad DeLong against Eugene Volokh over whether or not Bill Bennett lost money. Eugene’s argument: Well, let’s take a close look at…