Have you seen The Cheatwave here on ESPN.com? Click around. Lots of interesting stuff.
And a great time to talk again about point shaving in the NBA.
Last week I published a pretty lengthy story about the work of a Stanford undergraduate that finds something a little funny about NBA scores. As I wrote then:
Is it conceivable that there are NBA players manipulating games to make money or get out of trouble? Do we have to worry about more than just the referees?
Finding out would be an extremely tough multi-stage process. A good first step would be to take a serious look at the final score of NBA games, to see if there was any indication that the betting line was influencing the final scores of games.
If you have read "Freakonomics" then you know about this newish brand of research. With modern computing tools and masses of data "forensic economists" can poke around and identify trends and biases that may not have been evident before. These numbers often challenge conventional wisdom, but when done well have proven reliable again and again. It's a hot new tool for uncovering various crimes, and in one famous instance led to a major shakeup in the mutual fund industry.
That kind of research would be unlikely to be able to prove anything. But it would give you an idea if point shaving by NBA players (or, indeed coaches) was even something worth keeping on the radar.
As his honors senior thesis, a star undergraduate at Stanford decided to do that research.
And what he found was that in the NBA, it would be a big mistake to assume that there is not point shaving by players or coaches, because the betting line certainly does seem to be having a suspicious effect on the final winning margin in certain games.
There's way more to that post, including a look at the findings, and testimony from a number of top statistical experts. In a follow-up, we hear from the author of the paper, Jonathan Gibbs.
Reader reaction was across the board. It's clear that a lot of people took the time to really understand some pretty complex research and most of them liked it.
Many objected to the findings for one reason or another. The gist of Gibbs' findings were that heavy favorites fell just short of the betting line more often than you would expect, statistically. A lot of people found that unremarkable, and point common gambling knowledge that underdogs are better bets in general, because underinformed gamblers skew the market toward favorites.
I bundled the various objections into one email (I didn't include every criticism -- many were redundant) that I sent to Gibbs and one of his advisers for this project at Stanford, noted economics expert Roger Noll, to see if they could help us understand better.
Professor Noll was nice enough to respond.
Commenter: There is no logical reason for the premise that a pointspread of 12 should have as many games land on 10 or 11 as would land on 13 or 14. In fact, a number of 12 is adjusted to compensate for the public inclination to bet on favorites. As a general rule of thumb, a pointspread of 12 would be 10 or 10.5 if not for gamblers' biases. ... I think if you asked people who have made their living in the pointspread industry will tell you any data that shows large underdogs cover more than 50 percent of the time is dog bites man. Once the double digit favorites cover at a disproportionate rate, you have man bites dog. In 2005, favorites covered at a high rate in the NFL and the bookmakers got slaughtered.
Noll: Much research in the past shows that betting is actually quite efficient -- with a handful of notable exceptions (see a nice article by John Trijonis in Engineering and Science, the Caltech alumni magazine, a couple of years ago). The reason is that sophisticated betters, when observing a spread that is that far out of whack, jump in and drive the spread back down.
It takes ALL people to be stupid (not just some) to cause a bias. See P. T. Barnum!
That is why cases of bias are hard to find, although some people are very good at finding the few cases that exist, and make money doing so. But they can not continue to make money if they publish their results, because that causes betting to switch to correct the bias! (That is the point of the Trijonis article.)
On balance, the betting on NBA games appears to be efficient -- that is, the favorite wins very close to half the time. Given this fact, NBA betting does not appear to be biased in favor of favorites.
The underlying statistical idea here is that the point spread of basketball games is a random event in which the expected spread equals the point spread, and the chance of an actual spread that is one point above the betting spread is exactly equal to the chance that the actual spread is one point below the betting spread.
The hypothesis that is tested is whether this is true.
For games in which the spread is low, it turns out that the hypothesis is true -- if the spread is 4, the favorite wins by five points as often as the favorite wins by three points. But if the spread is 12, the favorite wins by 11 points more frequently than the favorite wins by 13 points.
Thus, any criticism of Jonathan's analysis has to explain why his results are true for big spreads but not for small spreads.
The garbage-time hypothesis does not explain skewness in the distribution. Obviously, garbage time affects the ultimate spread, and a coach can control the spread by putting in the scrubs earlier or later.
One way that Jonathan's results might come about is that coaches base decisions about when to put in the scrubs on the point spread with a couple of minutes to go. If they are not involved in shaving, their only concern is to guarantee a win and give their best players a rest.
Thus, garbage time would cause the ultimate spread to be lower, but there is no reason to believe if skews the spreads very near the betting spread -- but not when the winner is ahead by a lot more than the betting spread!
That is, if a team is favored by 12, it is as likely to win by 20 as to win by 4. Only margins near 12 are affected. Garbage time can not explain this -- unless the coach systematically puts his scrubs in earlier if his team is up 14 than if if his team is up 20 AND the opposing coach does not respond with his own scrubs. (If this were the case, the coach of the favorite would be the source of shaving!)
Commenter: In games that end near the point spread, 12.5 point favorites fall short of covering the spread a statistically significant percentage of the time. You (or this undergraduate) argue that players can't add points, they can only shave them, which is sensible enough. It's easier to make a turnover than to score a basket. Fine. But why wouldn't these conspirators cover their tracks and pay players or coaches on the team that is favored to lose to shave points? Why not throw a little money to a backup point guard on a bad team and have him "accidentally" pass the ball out of bounds a few times late in the game if a favorite is just short of covering?
Noll: I agree with the logic in that a bad team can dump a few points as easily as a good team. If shaving were equally likely for both, then the distribution of outcomes would not be skewed, and the last few minutes of every game in which the spread was more than ten points often would see nothing but turnovers and bricks!
The empirical results say that this is not the case, so the issue is how to explain the empirical results.
I think the best answer is that if a team is behind by 12 points with two minutes to go, the probability it will win is low but not zero. If it shaves points, the probability is zero. If a team is ahead by 12 points and intentionally misses a basket, its probability of winning falls, but only very slightly -- after all, it is the better team both in general and that night. Thus, the favorite has less to lose, and so should be more willing to shave.
