Sunday, December 13, 2009

Did Tim Donaghy really win 70% of his bets against the spread?

According to disgraced NBA referee Tim Donaghy’s new book, Donaghy won 70 to 80 percent of his NBA bets. (The link is to an excellent article by TrueHoop's Henry Abbott, which I recommend highly.)

70 to 80 percent is huge: these were bets against the spread, so you’d have expected that Donaghy's winning percentage would only be around 50 percent, unless he had some kind of edge.

What was his edge? Did he fix the outcomes of games with biased refereeing? Donaghy says no: the way he won so many games was by knowing which *other* referees were biased. Not corruptly biased, mind you, sometimes just unconciously biased. He says,

"I listened to the directives from the NBA office, I considered the vendettas and grudges referees had against certain players or coaches, and I focused in on the special relationships that routinely influenced the action on the court. Throw in some quirks and predictable tendencies of veteran referees and the recipe was complete. All I had to do was call it in and let the law of averages take over. During the regular season, I was right on the money seven out of 10 times. There was even a streak when I simply couldn’t miss, picking 15 winners out of 16 games. No one on the planet could be that lucky. Of course, luck had little to do with it."

Does that make sense? I don't think it does. I don't think that even perfect knowledge of the tendencies of referees can get you a winning percentage of .700.

According to basketball researcher Wayne Winston, a reasonable pythagorean exponent for basketball is 14. (That's from his book "Mathletics," which I've been planning to review for a while now -- I'll do it this week, I swear.) To increase your winning percentage from .500 to .700, then, requires an extra 6% of points, or about 6 points in a 100-point game.

Six points is huge. It's twice what home field advantage is worth. If you assume that teams score an average one point per possession when they're not fouled, but 1.5 points per two-shot foul, it would take 24 extra foul shots (12 fouls) in a game to account for six points.

Teams shoot about 25 foul shots a game on average. 24 extra foul shots would basically double the number of foul calls per game. If you assume that each of the three referees call 8 foul shots each, one biased referee would have to call *four times as many* foul shots for one team to raise its winning percentage to .700.

Of course, the biased ref could also *refrain* from calling foul shots for the other team ... but, with only 8 shots called per game per ref, there's a natural limit to what you can *not* call.

It just doesn't seem at all plausible that one "vendetta" or "special relationship" could have such a large effect. Especially considering that the examples Donaghy provides are pretty weak. For instance:

"Referee Joe Crawford had a grandson who idolized [Allen] Iverson," writes Donaghy. "I once saw Crawford bring the boy out of the stands and onto the floor during warm-ups to meet the superstar. Iverson and Crawford’s grandson were standing there, shaking hands, smiling, talking about all kinds of things. If Joe Crawford was on the court, I was pretty sure Iverson’s team would win or at least cover the spread."

Doesn't that sound pretty much impossible? First, could any professional referee call an extra 24 foul shots a game for Allen Iverson without drawing some kind of attention? And, second, isn't it completely implausible that anyone could rise to the ranks of NBA referee with judgment so bad that he would be *that biased* in favor of his grandson's idol?

Anyway, we don't have to take Donaghy's word for it: we can check the records. Actually, ESPN's Abbott already checked. It turns out that Donaghy's accusations are completely false. With Crawford refereeing, Iverson's teams went 5-9 against the spread. That's .357, not .700.

Abbott checks a few other of Donaghy's claims, and references others who have done similar checks. The bottom line: absolutely no evidence of any bias at all, much less the kind of bias that would let you pick 70% winners.

That leaves at least three possibilities:

1. Donaghy was not specific enough in describing the circumstances in which he knew he had a .700 chance of winning. Maybe, for instance, that only happened when Joe Crawford's grandson was actually at the game, rather than watching at home.

2. There was other information Donaghy used to make his picks, not just his knowledge of referee bias. As he said: "There were other factors that came into play. Inside information about injuries. Home game or away game. Home crowd. Many more factors to take into consideration."

3. Donaghy himself rigged the games in order to win his bets.

4. Donaghy didn't actually win 70% of his bets.

Number 1 still doesn't seem very plausible: as I argued, it's very hard for a referee to make a team lose 20% of the games it otherwise would have won, and make it look natural. This is especially the case if the grudge the referee holds is against a player, and not a team: can anyone really cause Allen Iverson to lose 6 points a game, without making it obvious?

Number 2 is implausible too: there are thousands of bookies and gamblers analyzing basketball much more thoroughly than Donaghy did. If most of the information he claims to have used was public, the betting line would have adjusted for those factors already.

Number 3 is implausible, for similar reasons. Actually, it's a bit more plausible than number 1, because, for one thing, Donaghy would care about the team, not any individual player, so he could spread out his biased calls. Secondly, he could concentrate his fixes in close games, so that it may not take 6 points a game, but perhaps only 1 or 2 points in a game that's tied in the last minute.

But, to me, Number 4 is the most plausible. It does require you to assume that Donaghy and the FBI are incorrect about the results of the wagers: but if Donaghy can be so wrong about the results of his strategies (which can be verified), why can't he also be wrong about the results of his bets (which cannot)?

Anyway, there would be easier ways to figure this stuff out, if there were a list of games that Donaghy bet on. Just check those games, and the betting lines, and see if there was anything unusual there, either by Donaghy himself, or the other referees at the game. But, according to the article, there is no such list. It seems like the NBA and FBI are taking Donaghy's word for how big his bets were ($2000 each) and how many he made (more than 125 over four seasons).

In that case, isn't it more plausible that the $100,000 Donaghy made came from sources other than winning 70% of his $2,000 bets? Maybe he won the lottery, or he was peddling confidential information about Tiger Woods, or he was selling illegal MRIs to Canadian patients with sore knees. Any of those seem more plausible than being able to go .700 against the spread.

In any case, I'd be willing to put Donaghy to the test. He says he can pick 70% winners. I think he can pick 50% winners. Let's set the bar at 60%. I'm willing to bet him even money that he can't go better than .600 in his choice of 30 NBA games this season.

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At Sunday, December 13, 2009 9:31:00 PM, Anonymous Dan said...

I don't think he has the access to the inside information he says he used to have when he was betting. He also can't help fix games himself anymore. So the 70% success rate he claimed he used to have wouldn't be that high anymore, regardless of whether or not he's lying. If the 70% claim was true in the first place, it's probably closer to 60% now anyway (more or less).

Even if his "true" game-calling ability was 70% back in the day, it's doubtful he'd take you up on your current offer, knowing that his "true" ability has declined due to a lack of inside information and influence on the outcome.

At Sunday, December 13, 2009 10:28:00 PM, Anonymous Anonymous said...

You're overestimating how many calls it would take to get to 6 points.

A possession is worth about one point. So a phantom travel or offensive foul is worth a point

A phantom shooting foul is worth (FG%*FT% + 1-FG%(2*FT%))-FG%. If you plug in 35% for FG% (the hypothetical population of shots you can call a phantom foul on is much more difficult than average), then these calls are worth about a point and a quarter.

I do agree with you that Donaghy's claims are incredulous.

The idea that he only made 100k picking 70% winners over 4 years defies belief. If I started with 10K and could pick 70%, it wouldn't take me 100 games to hit a million even if I was being conservative with my bankroll.

At Sunday, December 13, 2009 11:13:00 PM, Anonymous Anonymous said...

Do we know exactly how many NBA games he bet? What are the chances he just hit a lucky streak at some point during his betting days, which then gave him an overconfidence in his own abilities as a bettor (regardless of his actual lifetime record). I think it's entirely plausible he had a 70% streak in there somewhere and simply chose to forget about the games he lost.

At Sunday, December 13, 2009 11:55:00 PM, Blogger Phil Birnbaum said...

Dan: point taken.

Anon 1: OK, that makes sense. So we're talking 5 or 6 extra fouls a game, not 12, if the fouls are chosen judiciously. That's still a lot, considering the average is 8 a game.

Anon 2: The article says the bets were typically $2000, the total winnings were $100,000, and the winning percentage was .700. That means $250,000 was bet: $175,000 on winning bets, and $75,000 on losing bets. That's 125 bets over four seasons.

At Monday, December 14, 2009 11:29:00 AM, Anonymous Anonymous said...

In interivews, Donaghy has claimed 70 to 80 percent without ever making it sound like it was a specific winning percentage. He has also claimed that his winning percentage in games he worked was "identical" compared with games he did not work. Both of these statements suggest to me that he is giving only a rough estimate of his success and is not citing a specific number.

I'm guessing that most compulsive gamblers exaggerate their success rates (perhaps even subconsciously) in order to justify to themselves that they should continue playing. They likely make all sorts of excuses why their losses don't count. For example, Donaghy may have had a string of losses betting on a supposed tendency of a particular referee and then used those results to conclude that the particular tendency didn't actually exist. He might claim that his system has"learned" and that the resulting games of "confirmed" tendencies represent a winning strategy. But he's probably just misinterpreting random sequences.

I think it's quite plausible that Donaghy truly believes his inside information gave him the ability to win at a 70% clip. I'm not sure the FBI investigation really confirmed his winning percentage, it only concluded that it believed Donaghy was being truthful in a general sense. I do believe Donaghy is being a bit disingenous by repeatedly hanging his hat on the 70 to 80 percent line in order to support just about every other claim he makes about the NBA as if the FBI has confirmed all these claims.

At Monday, December 14, 2009 11:34:00 AM, Blogger Phil Birnbaum said...

Anonymous 11:29:

Absolutely makes sense. But you'd think Donaghy would have a pretty good idea of whether he won or lost overall, and about how much, right? It's hard to believe you've made $100K when you're actually losing, isn't it?

At Monday, December 14, 2009 1:29:00 PM, Anonymous Anonymous said...

I believe Donaghy admitted to participating in many different forms of gambling: sports, roulette, card games, etc. He very well might have come out ahead but may have been sloppy in keeping track of the exact details. I'm no expert on gambling addiction, but it seems plausible that he was fooling himself about how much he was really winning, among other things.

At Monday, December 14, 2009 4:04:00 PM, Blogger Wheell said...

If you want to see Donaghy go 70% check the games he officiated where the over-under moved 3 or more points and see how well the steamed side did against the closing number.


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