My name is Jonathan Gibbs, and I was asked by Chris Masse to give a little insight into the paper I wrote for my economics honors thesis at Stanford University, which was recently referenced by Justin Wolfers in his NY Times op-ed piece. I undertook this project during September 2006 to study the NBA’s point spread betting market looking for the possibility of manipulation.

I started my project looking at the relevant previous economic analyses of the NBA betting market. There were two key papers that I used as the basis for my research to build upon. The first paper, written by Gandar, Dare, Brown and Zuber (1998) in The Journal of Finance, described the fundamental properties of the NBA betting market, in essence showing that it doubled as a prediction market. They wrote that “in almost all instances bettors are able to move lines by a magnitude sufficient to remove opening line biases by the close of betting,” (p. 396-397) and that “informed traders are both present and influential in this market” (p. 398). Simply put, the twelve hours the market is open between when the opening betting lines are posted and when the game tips-off closing the market, is sufficient time to significantly improve forecasts.

The second paper, written by Paul and Weinbach (2005) in The Journal of Sports Economics, describes a persistent inefficiency in the betting market. Using six years of data, they were able to show that large favorites fail to cover the spread a statistically significant amount of the time, rejecting the null hypothesis of an efficient market. Furthermore, they were able to reject the null hypothesis of no profitability for betting large home underdogs.

Together these two papers seemed contradictory as one states the market consists of informed traders betting lines to efficient prices, while the other proves that simple profitable betting rules exist across multiple seasons. My hypothesis was that point shaving could explain these contradictory notions.

To test this, I collected two data sets. The first took game results and betting lines from 15,859 games from the past fourteen seasons. I tested this data in manners similar to that of Gandar et al., yielding similar results to substantiate my data set. I then used similar techniques to those of Wolfers (2006) in which he examined the NCAA basketball betting market. Specifically, I segmented the data according to the size of the betting line and used a density function to graph the relative occurrence rates of betting spread forecast errors. This visually showed that different sized betting spreads have different forecast errors that occur more regularly. Notably, teams favored by small spreads (0-6) are more likely to just cover the spread relative to just failing to cover the spread. Teams favored by medium spreads (6.5-12) are equally likely to cover versus not cover the spread. While teams favored by large spreads (12.5+) are more likely to just fail to cover the spread relative to just covering the spread.

Since it does not matter by how much a team does or does not cover the spread, solely whether they do or do not, this information is immaterial for small and medium sized spread games as the market is able to efficiently equate covering and non-covering games. However, it is notable for large spread games because a market inefficiency has been shown to exist. The data suggested approximately five games per season are influenced by point shaving.

However, as I had not created an explicit structural model to estimate point shaving’s incidence, in an effort to substantiate this estimation, I collected a second data set containing the point differentials at the 5, 4, 3, 2, and 1 minute marks for 6,415 games from the past six seasons. The thinking is that the easiest time for a player, coach, or referee to shave points is during the final minutes of a game, after the outcome has been decided when only the final margin can be affected.

I used Probit and OLS regression to analyze this data. The results of the Probit models showed that when controlling for margin relative to the spread in the final few minutes of the game, that as the spread increases, the probability of the favored team covering that spread decreases. Specifically, teams favored by 10 or more points are statistically less likely to cover the spread when controlling for the margin at the end of the game when compared with teams favored by smaller amounts.

Furthermore, the OLS regression results showed that large spread games actually have the greatest amount by which they are expected to exceed the spread. This implies that teams favored by large spreads either just barely fail to cover the spread or destroy it. Together, these results are consistent with a trade-off existing with the NBA betting market trying to account for disparate talent levels between teams while controlling for the possibility of point shaving.

The key point from this second data set is that while the point spread should be strongly correlated with each game’s result, it is a prediction market after all, its setting is having causative effects. The setting of the point spread is inducing games to end up on one side more often than the other, due to the betting market’s non-linear payout structure altering incentives.

This post is quite long, and if you’ve read to here, I thank you. If you are interested in reading my unpublished undergraduate thesis in its entirety, it can be found here. I am interested to hear what you think and welcome comments, thoughts, and suggestions.

Thank you,
Jonathan Gibbs
jgibbs52 _) at _) gmail _) dot _) com