Tim Donaghy's tale of Dick Bavetta

Tim Donaghy's "Blowing the Whistle" implicates several NBA game officials for having extra-curricular agendas while they're refereeing. Most of those ethical breaches can be fairly classified as favoritism to one team over the other based on a personal relationship or vendetta.

With veteran official Dick Bavetta, the charge is much different.

Donaghy portrays Bavetta as a genial NBA veteran and faithful company man who wants to facilitate a quality entertainment product every night. Since fans generally find a close game more compelling, Bavetta made a deliberate effort to keep the contest competitive, according to Donaghy.

Early in the book, Donaghy tells the story of being at his brother’s birthday party while there’s a Bavetta-officiated game on television:

“Watch,” I told my brother. “Anytime Bavetta referees, you’ll rarely see a blowout. When a team gets up by 20, he starts blowing the whistle like crazy.” And sure enough, that’s what happened -- one team got way ahead before Bavetta whistled the other team back into contention.

According to Donaghy, Bavetta’s tendency for keeping games close made him a favorite of the League. It also gave Donaghy an opportunity to capitalize:

From my earliest involvement with Bavetta, I learned that he likes to keep games close, and that when a team gets down by double-digit points, he helps the players save face. He accomplishes this act of mercy by quietly, and frequently, blowing the whistle on the team that’s having the better night. Team fouls suddenly become one-sided between the contestants, and the score begins to tighten up. That’s the way Dick Bavetta referees a game -- and everyone in the league knew it.

Aware of this propensity, Donaghy says he would often take the underdog when Bavetta was assigned to a game, and cash in as a result.

Since Donaghy maintains he made 70 percent or better on his money while leveraging these kinds of biases, we turned to economist Joe Price and his colleague Henry Tappen, who have performed extensive research on referee bias in the NBA. Price used his data sets to examine Donaghy’s claim that Bavetta systematically kept games close.

The results: Far from making 70 percent, that strategy would have lost you 12 percent of your money. In other words, choosing at random would have given you a better chance at success.

Anyone who consistently bet the “big underdog” (a team receiving seven points or more in the closing betting line) in Bavetta refereed games between the beginning of the 2003-04 season (when Donaghy says he began betting on NBA games) to the conclusion of the 2006-07 games (soon after which Donaghy confessed his actions to the feds) would have lost his shirt.

When confronted with this statistic by Henry Abbott, Donaghy balked. "I looked for spreads in games -- Bavetta games -- that were double-digit spreads," Donaghy said. "I'm telling you that, quite often, Dick Bavetta in the fourth quarter of games when the [lead] was 20 point or more, changed his style of officiating to where those games became closer. He would instruct other referees to change their style, too. He'd say, 'Let's not embarrass anyone. Get the marginal calls at one end, but not down at the other end of the floor.'"

Bavetta officiated 42 games between the beginning of the 2003-04 season and the end of the 2006-07 season where the closing betting line was 10 points or greater. The big underdogs in those contests went 17-25 against the spread -- a winning percentage of 40.1 percent. In other words, teams that were expected to be beaten badly were far more likely to be embarrassed when Bavetta was on the floor.

Joe Price, professor of economics at Brigham Young University, sifted through all the data. Price has studied gambling for a long time, and he regards a team receiving seven points or greater a big underdog. This generous interpretation of "big underdog" not only makes Donaghy's claim look better, but it also provides a bigger, more dependable data set.

To a get full understanding of Price’s findings and their implications, we asked Price to go over the data with us and explain how he reached his conclusions. You can view all the data on Price's website.

First off, how did you come to have all this data?

The data was originally collected as part of research that Justin Wolfers and I did on racial bias in the NBA. We collected the box-score and play-by-play data from basketball-reference.com and ESPN.com. The betting data came from covers.com.

So let’s look at this in the most practical context: Would betting on the underdog in games where the spread was seven or more points and Bavetta was the official have been a profitable strategy?

If you had bet on the underdog all of the games in which Bavetta was an official and in which one of the teams was favored to win by seven or more points, your bet would have paid off only 46.2 percent of the games. This would have caused you to, on average, lose about 11.8 percent of the money that you bet, on average.

As you and your research assistant, Henry Tappen, delved into the research, when did the red flags begin to appear?

First of all, some of the basic things that you’d expect to observe if Bavetta liked to keep games close or favor the underdog simply don’t play out in the data. For example, the final score margin in Bavetta games is slightly larger, on average, than non-Bavetta games (10.8 versus 10.4 points) and big underdogs (favored to lose by seven points or greater) are less likely to win when Bavetta is one of the officials (17.3 percent vs. 19.7 percent).

One facet of the game where referees have tremendous discretion is foul calls. Was Bavetta more likely to whistle favorites for more fouls, as Donaghy claims?

There is evidence in the data that referees have a tendency to show a little favoritism to big underdogs -- but Bavetta less than your average referee. These differences, however, are not statistically significant.

How conclusive is the evidence?

One of the challenges of assessing individual referee behavior in the NBA is that the publicly available data (such as the box-score or play-by-play data) does not indicate which referee made which call. The work that Justin Wolfers and I did on referee bias was based on the racial mix of the referee crew, so that wasn’t a problem. All the same, examining the behavior of one referee is challenging.

However, the real issue with the Donaghy allegation is whether you could use the information about whether Bavetta was officiating to predict the outcome of the game. Our analysis of the data provides no evidence that this is true. One thing to note is that there is a lot of variation in the final point margin at the end of games. There are certainly games officiated by Bavetta where the final score was close and games officiated by Bavetta in which the underdog beats the spread. But these things are, on average, more likely to occur in the games in which he is not one of the officials.

We're talking about 325 games officiated by Dick Bavetta. Despite the findings, is it possible that Donaghy could've identified specific trends within those games that would have allowed him to come out ahead?

It is possible, but unlikely. In order for us to test for effects on a subset of games, Donaghy would have to be more specific about which Bavetta games we should bet on. We did a simple experiment in which we tested what would have happened if you had bet on the underdog in the 104 games that one team was favored to win by more than seven points and Bavetta was the referee. Again, we found that, using that strategy, your bet would have paid off only 46.2 percent of the time, and you would have lost 11.8 percent of the money on average. This is compared to winning your bet 52.3 percent if you had bet on the underdog in games in which Bavetta was not the official.

As a behavioral economist and a fan of the NBA, how do you make sense of all this?

There is a long history of people making faulty inference based on small samples. One example is the “hot hand” phenomenon. When we see a player make three shots in a row, we often think to ourselves that he is “on fire.” For a player that makes half his shots, however, we would expect that, by random chance, about 12.5 percent of any random set of three consecutive shots would have all three shots made.

One the other hand, some patterns in referee behavior (such as racial bias) can only be detected by analyzing large sets of observations. With a limited set of observations, people often mistakenly see patterns and fail to detect true patterns.

Correction: The original publication of this post stated "Bavetta officiated 69 games between the beginning of the 2003-04 season and the end of the 2006-07 season where the closing betting line was 10 points or greater. The big underdogs in those contests went 25-44 against the spread -- a winning percentage of 36.2 percent." In fact, those 69 games extended through the 2007-08 season. As corrected above, Bavetta officiated only 42 games with closing betting lines of 10 points or greater from the start of the 2003-04 season to the conclusion of the 2006-07 season, with the big underdogs covering the spread only 40.1 percent of the time.