ESPN  

The scenario has been in a thousand crappy mob movies and after school specials: Star athlete gets in trouble with some bad people. Bad people offer the star player a way to get out of trouble, by manipulating a game he's playing in.

If he doesn't play along, he'll have his house fire-bombed or some such thing.

Tough situation right?

And one that, thankfully, could never happen to NBA players, who are rich as deities and could never really get in serious hock to bookies and mobsters.

Or so the assumption has long been.

But plenty of NBA players gamble on all kinds of things. Plenty spend more than they make or make bad financial decisions that cause them to end up not wealthy at all. 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.

An Undergraduate Report
Hold the phone: An undergraduate? Do we really have to listen to this?

Recently an alert TrueHoop reader (thanks, Seth) emailed me a link to the senior honors thesis of Stanford's Jonathan Gibbs. (Since then it has also been mentioned in an Op-Ed piece in Friday's New York Times, and it has been discussed briefly on several blogs.)

The paper is called "Point Shaving in the NBA: An Economic Analysis of the National Basketball Association's Point Spread Betting Market."

I read it. If you're not scared of academic talk, I recommend you do too.

To my untrained eye, it seems to be a rigorous and impressive case demonstrating, based on an analysis of 14 years of NBA games, that there are some oddities in the final scores of games that feature a heavy favorite.

Basically, heavy favorites are not beating the spread with the regularity you'd expect.

Gibbs explains: "I created a dataset containing data over the past 14 NBA seasons. Analyzing that data in a similar style to that of Wolfers [more on that later], yielded results consistent to what one would expect from point shaving: teams heavily favored fail to cover the spread a statistically significant amount of the time. ... As a huge basketball fan, it was my hope that I would find nothing. However, the data said otherwise."

Wow.

But, you know, does this whipper-snapper Gibbs know what he's talking about? Is there any chance anyone who matters at the NBA will even make it through the paper's 59 pages? Should I even be writing about it on ESPN.com?

Only if the paper is deemed credible by people with more clout than Gibbs, right? I asked some of the most respected names in the field to assess the paper, and they all agreed the work appears to be solid.

Experts Chime In
The University of Pennsylvania's Justin Wolfers, author of that memorable referee racial bias study, and a highly regarded assistant professor at the University of Pennsylvania's Wharton School, praised the paper as clever and well executed. Having spent a couple of hours assessing it, Wolfers was impressed, intrigued, and inclined to believe the paper's findings. "This paper was never designed," he says, "as proof positive that there is point shaving in the NBA. But what the paper found is certainly consistent with point shaving, and perhaps even suggestive of it."

I discussed the paper with one of Gibbs' supervisors, Stanford Assistant Professor Nick Bloom. Bloom declared that this paper got the highest grade in the class. He acknowledged that he had not audited all of the source data, but had seen the work grow over the course of time -- Gibbs made three seperate presentations along the way -- and believed the process to have been legitimate and well thought out. He also pointed out that there was no pressure to achieve stunning results, as other students who found essentially nothing exciting at all, but did great work, also got top grades. Bloom says that while this paper is not first-hand witness to crime, it should be thought of as "a weakly smoking gun."

California State University, Bakersfield Associate Professor of Economics David Berri (lead author of the "Wages of Wins") read the paper and declared it persuasive: "I am willing to say, having read the paper over, that there is something going on here. I am somewhat surprised an undergraduate could pull this off. My sense is that [one of the Gibbs' advisers at Stanford] Roger Noll, who is a very good economist (with an expertise in sports), helped a bit." (UPDATE: Berri just blogged about this study.)

University of North Carolina at Greensboro Assistant Professor of Economics Dan Rosenbaum, (who also works at times for the Cleveland Cavaliers, as well as the White House Council of Economic Advisers, but speaks here as a professor) examined the paper and says: "This is a credible paper. Despite being just an undergraduate, Gibbs has (a) put together data linking point spreads with outcomes for 15,859 games between the 1993-94 and 2006-07 seasons and additional within game information from 6,415 games from the 2001-02 through 2006-07 seasons, (b) efficiently reviewed the economics literature on sports betting, and (c) performed a careful and skillful econometric analysis. Overall, with some additional work this paper probably is good enough to be publishable in a good economics journal. It is one of the more impressive sports economics papers that I have come across lately. The main results are that strong favorites fail to cover as often as expected, leading to Gibbs arguing that players may be 'point shaving.' I don't find the final conclusion totally convincing -- you'd probably have to have massive point-shaving going on to make that evident in a statistical analysis -- but it's not something you can dismiss out of hand."

Point Shaving 101
Let's get into what the paper actually says.

First of all, history and other research shows that if you're going to shave points in basketball, the easiest way to do it is to get a player or coach on a heavy favorite to see to it that his team fails to beat a massive point spread. Hypothetically, if the favored team is expected to win by 12.5 points, and in the closing minutes they are up 15, a player might help see to it that the other teams gets a couple of easy buckets. Coaches might do that by fielding a squad in the closing minutes that was weak, tired, or mismatched with the opponents.

Gamblers in cahoots with the crooked player or coach would be betting large amounts on the underdog to beat the spread, and win maybe not every time -- it's an imperfect science -- but more than their fair share of the time.

You wouldn't pay a guy to see to it that his team beat the spread, because that's too hard, and depends on the effort of all the other players on the floor. Point being: on a court where everyone is trying their hardest to win, you can just decide, for a stretch of a game, to be worse than the other team, but you can't necessarily decide to be better.

Similarly, you wouldn't pay a guy to shave points in a close game, because for a bunch of reasons -- financial and otherwise -- the vast majority of players and coaches want to win, and not playing 100% at the end of close games, and risking a loss, is not in most players' DNA. (This is why Wolfers suggests, as a way to defeat any crooked influence of gamblers, banning betting on things that aren't important to the game, while allowing even more betting on things that are meaningful like which team will win.)

Betting Lines: Usually Amazingly Accurate
NBA betting lines are set by oddsmakers at the open of business, and then fluctuate throughout the day as bettors place bets. The point spread is moved to keep an equal amount of money bet on the underdog and the favorite. A five-point favorite in the morning may be a six-point favorite by sundown, for instance. If the casino has as many winners as losers, the house is really not gambling at all. They are merely taking money from one group, the losers, and handing it to the other group, the winners. The trick is, however, that the casino (or bookie) takes a cut of all winnings. Nice work if you can get it, right?

Gibbs and others have found that the legal sports betting market in Las Vegas (estimated to be a tiny minority of total sports betting, but nonetheless helpful as a method to learn about the trend), were practically perfect in achieving accurate lines. Over the nearly 16,000 games in the study, teams beat the spread almost exactly half the time (7,802 compared to 7,855). That tells you this system is extremely efficient, and sports books are doing a perfect job of making money from gamblers without having to worry about who's going to win or lose this or that game.

Suspicious Signs
Gibbs and others have looked just at the games where point shaving would seem to be most likely -- the games with spreads of 12.5 points or more -- and a really weird thing became clear. Suddenly the betting lines were not accurate. Favorites fell way short of the spread at a normal rate, and beat it by a long shot at a normal rate. But if the score was close to the spread -- in short, if it was a game that would be easy to shave points in the final minutes -- then the favorite fell short of the spread more often than they beat it at a significant rate.

That means that if the spread closed at, say, 13, the favorite tended to win by something like 11 or 12 more often than they won by 14 or 15.

The same was not true in games with small spreads. And the bigger the spread, the more likely the favorite would not beat it.

If players or coaches were point shaving, that's what it might look like. But there could be other causes, too. Correlation is not causation, as they say.

What Caused That?
At this point, nobody knows. Most of the experts I talked to say this could be a random statistical anomaly.

Of course, one theory is that it could be caused by a player or players on the winning team finding themselves on the floor as the game teeters around the betting line -- an easy opportunity -- and playing in a way to please gamblers who bet on the underdog. They might profit from this by betting on these games themselves, or they could be acting in concert with bookies or mobsters. (Most likely candidates: players in debt to bad people. And remember, unlike referees, players are allowed to gamble, and many do.)

And while the number of games involved is small -- Gibbs says five games a year could explain the statistics in his charts -- the effect is not nothing. Gibbs and others have found that if you bet on home underdogs every time they face a 12.5 or greater point spread, you would win so much more than you lost that it would even cover the percentage (or "vig," short for vigorish) that goes to the bookie or casino.

Suddenly, the efficient market of sports betting has a big chink in its armor, and it's not easy to understand why.

Could a Referee Be to Blame?
In a moment of referee controversy, it's fair to assess whether or not a referee like Tim Donaghy could be responsible for this same effect.

In a conversation about Gibbs' Stanford paper, Wolfers makes an interesting point: If you were a crooked referee, it would be just as easy for you to make one team or another score more. You could manipulate games essentially any way you wanted: to make bets on the favorite or the underdog winners, or indeed to make the game's total points scored higher than they ought to be thanks to lots of free throws. A referee, however, would have no obvious reason to manipulate games in a way that made heavy favorites, specifically, fall short of the point spread. That's the kind of poing shaving that would likely be done by people on the favored team. So if this data suggests any kind of point shaving, it would appear to be point shaving by a player or coach, not a referee.

2006 Study Found Similar Evidence in the NCAA
Gibbs says he started his paper following in the footsteps of Justin Wolfers, who last year examined historical NCAA scores and found that things got a little fishy around the point spread in a way that was consistent with players on heavily favored teams seeing to it that their teams fell just short of the point spread. In this way, the 2006 NCAA study and this 2007 NBA study are extremely similar. David Leonhardt of The New York Times did a nice job explaining the trend the first time around:

"It's the favorites with the big spreads," Kenny White, an influential Las Vegas oddsmaker, said, "that have the biggest advantage to be able to do something."

Past scandals also suggest that is how it works. When Stevin Smith was fixing games at Arizona State in the 1990's to erase some big gambling debts, he hit some big shots and helped his team win games. But he backed off just a little on defense to make sure his opponents covered the spread.

"I made myself feel better by always saying that I wasn't making my team lose, just helping myself out of a bad situation," Mr. Smith later wrote in Sports Illustrated.

This is precisely the pattern Mr. Wolfers believes that he has found. Smaller favorites -- teams favored by 12 or fewer points -- beat the spread almost exactly 50 percent of the time, showing how good those odds makers are at their jobs. But heavy favorites cover in only 47 percent of their games. There is little chance that the difference is due to randomness.

This is not persuasive by itself, because there are some obvious explanations besides point shaving. Heavy favorites may remove their best players at the end of the game, for instance, or simply slack off, not caring what their winning margin is.

But here's Mr. Wolfers's smoking gun: this slacking off seems to happen only when a game is decided by something close to the point spread. Heavy favorites actually blow away the spread just as often as everyone else. But they win by barely more than the spread a lot less often than slight favorites do.

There is a strange dearth of games in which 12-point favorites win by, say, 13 or 16 points. And there are a lot of games that they win by 11 points or slightly less. There is just no good explanation for this.

What's Next?
Is there point shaving in the NBA? Nobody knows that at this point. But I do know that we should stop assuming there isn't. It's only practical to keep an eye on it, especially in an era when the league is already steadfastly committed to ending any influence bookies and mobsters might have had on the outcome of games.

If the league is being honest about leaving no stone unturned in ferreting out the influence of gambling on the game, this is information you can use. It would seem to make sense to:

• Keep an eye on games, past and present, when heavy favorites fall just short of the spread. Do certain players or coaches seem to be involved in a strange number of those games? Gibbs says he hasn't looked into that, but says it would be pretty easy for someone to do so.
• Consider working with forensic economists regularly to assess game data for these and other kinds of red flags.