Social psychologists have long noted an interesting phenomenon in humans when it comes to giving credit or laying blame. To explain this pattern known as the correspondence bias , psychologists use the terms situational attribution and dispositional attribution in describing how we tend to do certain types of mental accounting. Consider someone you like or respect: if that person is criticized for some perceived error, you are more likely to attribute the error to outside (or situational) forces than to more innate characteristics (or disposition) of the individual. Bobby Cox gets an unfair rap as a manager. If it weren't for some bad luck with the umpiring and base-running in 1991, and the misfortune of running into the historically great Yankees later that decade, he'd have several World Series titles. Similarly, if we perceive an error from someone we don't like or respect, we're more likely to give less weight to circumstances and attribute the error to the person's disposition: Cox won fourteen division titles in a row and only managed to win one World Series. Whiffing on that many opportunities shows that he generally didn't have the stuff of a great manager.
Now let's examine the other side of the coin. If someone we like or respect does something good, we're more likely to give the individual a disproportionate share of the credit: Greg McElroy was a great college quarterback at Alabama. A team can't go undefeated in the SEC and win a national title with a mediocre quarterback. But what if we don't like or respect the subject as much? When that person does something good, we're more likely to seek out some environmental factor(s) to explain things: It doesn't take much talent to be highly successful handing off to Mark Ingram and throwing to Julio Jones. A lot of players could have won a title with that surrounding cast.
There were two particular halves of play in this year's Men's NCAA Basketball Tournament that led me to consider how correspondence bias can impact perceptions of basketball officials. After one half of the first game, the general crowd reaction was that the officiating crew had been terrible. At half-time of a game played the following day, the consensus was that those officials had been quite good, if not excellent. As I pondered the highly disparate judgments of the two crews, what struck me was the tight relationship between those perceptions and the corresponding quality of play in each first-half.
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The first half of the East Regional Final between Ohio State and Syracuse was, to say the least, unattractive; the teams combined to shoot about 35% from the field, making twenty of fifty-seven attempts. While the officials only called seventeen personal fouls in the half (not an extraordinary number), judging from the reactions of fans and national commentators on Twitter, the referees had been as much a part of the game as the players.
Contrast this with the first half of the Midwest Regional Final in St. Louis, in which Kansas and North Carolina shot 67%(!) from the field, making 34 of their 51 combined attempts. The referees in that game seemed like they were just along for the entertaining ride, mostly content just to let the players get up and down the court and make shots. And yet they called sixteen total fouls, only one fewer than the supposedly highly-involved crew in Boston the prior afternoon. With the fouls counts so close, what explains that perception gap?
Sure, there were some missed calls in the first half in Boston, but the first twenty minutes in St. Louis wasn't perfectly refereed either. A key starter ended up with two first-half fouls in Boston via at least one questionable call; but that was true in St. Louis as well (Sullinger and Withey, respectively). And while some would point to the unfortunate sequence in Boston that included a missed block/charge play followed by a bench technical-the type of sequence that didn't occur between Kansas and UNC-I don't think that's enough to fully explain the wildly different reactions.
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Though some coaches may not want it, most players and referees love games with good flow-more possessions with fewer fouls and other interruptions. The first half of KU-UNC game seemed to have really good flow, yet it had essentially the same number of fouls as the first half of the other game that had virtually no flow. Part of the solution to this puzzle is that we felt like we were getting to see more actual basketball between whistles in St. Louis than in Boston.  Kansas and UNC were getting up and down the floor faster and more often than Syracuse and OSU, so it felt like the whistles weren't interrupting the game as often.
It's easy to look at the referees when ascribing responsibility for poor flow, but is that always a fair place to look? Let's go back to the puzzle and re-frame it: on a fouls-per-minute basis, the two halves had essentially equal referee involvement.  This means that if our eyes were right, we need a better measure of "referee involvement" than fouls-per-minute. We can improve on that metric when we bring into the analysis a game's number of possessions, or tempo. The first half in Boston saw 17 fouls called on 65 total possessions, while in St. Louis there were 16 fouls on 74 total possessions. So fouls-per-possession gives us, at least for two particular games, a measure of referee-involvement that squares reasonably well with our perceptions.
Of course the above discussion doesn't tell us whether the crew in Boston was too involved in that game, or whether the crew in St. Louis involved themselves at a more appropriate rate. The only way to assess that would be for a tournament officiating supervisor to do a play-by-play breakdown of each game and compare the accuracy rates. The attempt here is not to re-litigate individual plays in either game, but rather to use the discussion of correspondence bias to raise the reader's consciousness as to the factors influencing the rate of foul calls in a game. Sometimes officials call too many fouls, sometimes too few. But there's evidence to support the idea that players and coaches exert influence on officials that's often overlooked.
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One could argue that the Boston game felt choppier because the officials were so involved. But that notion seems incomplete for a couple of reasons. The first goes back to shooting: when both teams are shooting well there's simply not going to be as much for officials to do. A made shot means there's virtually no chance of a loose-ball foul, and completely eliminates the chance of a foul on an extra shot attempt following an offensive rebound. The fact that Syracuse and Ohio State shot so poorly virtually guaranteed that we'd feel like a lot of fouls were being called.
The other aspect of the East Regional Final that undercuts the idea that the officials were too whistle-happy was the game's pace. While poor shooting by two teams should generally lead to more fouls on a per-possession basis, teams can still "smooth out" the game by getting up and down the court quickly. The more transition situations there are in a game, the more widely dispersed players will tend to be on the floor. And when the floor is spread (this idea applies in half-court settings as well) there will be fewer opportunities for the kinds of contact that lead to fouls. Due to what I'll call this spacing effect, increases in tempo should result in a decrease in per-possession fouls. The East Regional final was played at a significantly slower pace than was its counterpart in the Midwest, and as the theory would predict, more fouls were called per possession.
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But of course the real test of these ideas isn't whether they fit with two particular games, but whether they show up in trends over much larger samples. Again, these arguments point toward an inverse relationship between FG% and fouls/possession and, and also between tempo and fouls/possession. Thanks to Jon Pence, creator of www.SCACChoops.com, we have a good sample on which to test these ideas.  Jon generously agreed to pull data from every ACC game over the last five seasons to see if there was anything to the patterns predicted by this intuition. There's a lot of work left to be done in this area, but the general ideas do seem to be borne out on the court.
The first figure shows a slightly inverse relationship between TotFG% and fouls/possession. This fits with the argument above: when teams are shooting well there is significantly less need for officials to actively manage the game. An alternative reading of this trend would be that FG% tends to increase in more loosely called games. The logic there would probably be that foul calls tamp down the pace of the game, and even if some fouls go uncalled-even on illegal contact leading directly to some missed FGAs-overall shooting would tend to improve due to improved average shot-quality that comes with higher tempo. This is one of the areas that certainly deserve more exploration, e.g. we might look at possible links between offensive efficiency and fouls/poss, offensive efficiency and tempo, etc. But for now my hunch is still that fouls/poss is more dependent on shooting than the other way around.
Figure 2
                                                                          
In the second figure we see that fouls/possession indeed moves opposite tempo.  This fits with the possibility of a spacing effect, i.e. better average spacing should lead to fewer fouls called on a per possession basis. An alternative conclusion would be what I'm calling the quick-shot effect. The logic here would be that higher-tempo games see teams shooting the ball in fewer highly contested situations, even when offensive spacing hasn't really been affected by the pace. In practice this would mean that teams aren't generally pushing tempo by running so much as by taking shots earlier in the shot clock outside of transition/secondary-break offense.
In addition to the general weakness of such a strategy, two trends in the data indicate against this possibility. The first is the tendency (seen in Figure 2) of teams to take a higher percentage of two-point shots as tempo increases.  If more "quick" shots (as opposed to actual speedier turnarounds, shots in transition, etc.) were driving increases in tempo, one would expect the percentage of three-point shots to rise as tempo rises, since it's generally easier to get an open perimeter shot early in the shot clock than it is to get an early, open shot from inside the arc. The other trend supporting the existence of a spacing effect is that FG% tends to increase with tempo. If shots taken earlier in the shot clock are more often just quicker, as opposed to actually better/more open (the quick-shot-effect scenario), the decreased quality of those shots should lower teams' total FG%, something we don't generally find in the data.
There's a lot more research still to be done in this area. These links need to be analyzed more deeply, and additional connections need to be considered. But I hope this will spur some new discussions about how basketball analytics can be used to think about the role of referees in the game, and the influences that coaches and players have on how referees do their jobs.
The Playcaller welcomes all questions and comments, and can be reached at theplaycaller@gmail.com.
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