Cliometrics and Basketball

Tim Donaghy was an NBA referee with 13 years of experience who resigned recently amid allegations that he had bet on basketball games, including games that he had refereed, over the past two years. Apparently, according to the stories, Donaghy is, or was, a compulsive gambler who allowed affiliates of the Gambino crime family to get their hooks into him when he amassed debts to them that he could not pay off; and he bet on basketball games that he officiated as a way to work off what he owed. The clear implication is that he officiated the game in such a way as to maximize the chances that his bets (and the bets of his Gambino friends) would win. The most likely mechanism for this would have been for him to bet that the total score in the game would be over the over/under line, then call more fouls than normal, which would increase the number of free throws in the game and consequently the score. Donaghy is apparently cooperating with the FBI, but the details of his cooperation, as well as his betting strategies and the games that he bet on, are not generally known yet and might never be.

This news is, of course, red meat for the sports press and for sports fans around the country. NBA officiating has long been the subject of widespread criticism. In particular, it has long been an article of faith that the league has forced officials to go easy on superstars and has fiddled with the assignments of referees for playoff games to increase the likelihood that playoff series will be long ones. The news that a referee was apparently corrupt has caused every sports department, sports columnist, and sports blogger searching through the games that that referee officiated for "proof" that he changed the games' outcome. In particular, all of them almost immediately seem to focus on Game 3 of the San Antonio-Phoenix series in this year's Western Conference finals. San Antonio won that game to take a 2-1 lead in the series and went on to win it. During the game and afterwards, Phoenix players, coaches, and fans howled about the officiating. It just so happens that Tim Donaghy was one of the referees. And so now we're treated to bleating from every corner about how the fix was in and Tim Donaghy stole a game for San Antonio that rightfully belonged to Phoenix. Exhibit A of this phenomenon is an ESPN.com column by Bill Simmons:

Before the Donaghy scandal broke, if you told me there was a compromised official working a 2007 playoff game and made me guess the game, I would have selected Game 3 of the Spurs-Suns series. There were some jaw-dropping calls throughout, specifically, the aforementioned Ginobili call and Bowen hacking Nash on a no-call drive that ABC replayed from its basket camera (leading to a technical from D'Antoni). Both times, Mike Breen felt obligated to break the unwritten code that play-by-play announcers -- don't challenge calls and openly questioned what had happened. The whole game was strange. Something seemed off about it.

At the time, I assumed the league had given us another "coincidence" where three subpar refs (and calling that crew "subpar" is being kind) were assigned to a Game 3 in which, for the interest of a long series, everyone was better off having the home team prevail ... just like I anticipated another "coincidence" in which one of the best referees would work Game 4 to give Phoenix a fair shake in a game that, statistically, they were more likely to win. After all, it's easier to win Game 4 on the road than Game 3, when the fans are pumped up and the home team is happy to be home. (Which is exactly how it played out. Steve Javie worked Game 4, a guy who Jeff Van Gundy deemed "the best ref in the league" during the Finals. Hmmmm.) Look, this could have been an elaborate series of connected flukes. I'm just telling you that none of it surprised me. Which is part of the problem.

Bill Simmons's schtick is that he's just a regular old sports fanatic who just happens to get paid to write a column, and you can see all of the attributes of the know-it-all know-nothings that make up so much of sports fandom here in this excerpt. He called it, you see. He knew that the fix was in on Game 3 right from the start, just as he knew that there was no way that the league would let the Suns lose Game 4 after the officiating travesty of Game 3. We won't examine all of the other things that he has known but later turn out to be inaccurate: sports fans love to make prognostications, but they never seem to remember the predictions that didn't come true.

Anyway, the subtext permeating Simmons's column, and the subtext permeating so much of what has been written about Donaghy and Game 3 is this: but for Donaghy's presence on the officiating crew and his corruption, the Suns would have won the game and might have won the series, thus changing NBA history forever! (Whatever happens in sport is always history, you see.) The problem with this is that we can never known what would have happened, and it's largely pointless to contemplate it. If past were not the past, the future would be different; that's all we can say. If Donaghy had not officiated Game 3, something about Game 3 would have been different. How, we can't say.

David Hackett Fischer calls the error that sports fans make here the fallacy of fictional questions (Historians' Fallacies: Toward a Logic of Historical Thought, pp. 15-21).

There is nothing necessarily fallacious in fictional constructs, as long as they are properly recognized for what they are and are clearly distinguished from empirical problems... Fictional questions can also be heuristically useful to historians, somewhat in the manner of metaphors and analogies, for the ideas and inferences which they help to suggest. But they prove nothing and can never be proved by an empirical method. All historical "evidence" for what might have happened if Booth had missed the mark is necessarily taken from the world in which he hit it. There is no way to escape this fundamental fact.

If foul trouble had not prevented Amare Stoudamire from playing more than 21 minutes in Game 3, undoubtedly the game would have been different; but it's impossible to determine what the difference might have been. Most people presume that this would have closed the margin between the Spurs and the Suns and made it more likely that the Suns would have won, but this is not necessarily the case. Too often, sports fans and sports columnists will pick out a few calls or coaching decisions that they regard as wrong-headed and concluded that their team would have won but for these bad calls or bad decisions. As Fischer writes in reference to real history, this is a fallacy. We can all agree that it if what has been written about Donaghy is true, it is terrible for the NBA and the game of basketball. Just don't begin to argue that Donaghy's corruption proves that the Spurs didn't deserve to win their series against the Suns.

(Oh, and about Cliometrics. Fischer talks about self-styled Cliometricians, who, at the time that Historians' Fallacies was written, were attempting to apply economic theory to fictional questions. I define Cliometrics as the attempted systemization of fictional questions.)