# Nylon Calculus: Does the data offer any evidence of referee bias?

The foul is an incredibly important part of an NBA game, to the point that players are making entire careers on getting to the free throw line. Teams have taken advantage of the foul as well, both “situationally” or to cause havoc.

What about the referees? Much like players, referees have personalities that definitely have a mark on games. For example, Eric Dalen has been known to let the “players play,” in that he doesn’t take kindly to complaints about getting roughed up.

On the other hand, referees like the great Joey Crawford have their moments, but referees do work to command the floor in order to perfect the basketball product, per Monty McCutchen. So how do fouls, and a referee’s propensity to call them, actually affect the outcome of games? The graph below compares each teams fouls per game and win percentage from last season.

For teams, it’s obvious that committing fouls is a bad thing to do during games, but this graph serves as a pretense to analyzing league officials and their tendencies. Without delving too much into this, the trend stands where teams that foul more will tend to have poor winning percentages. There’s a lot that this graph leaves out, but you can get a glimpse into some team personalities. For example, the 76ers could be categorized as “aggressive” whereas the Phoenix Suns can be considered, fairly, “careless” when factoring winning percentage against fouls.

This first graph shows that the more fouls in a game called tends to give fans higher scoring games, but it’s a little misleading. For example, the difference between the average game officiated by Mike Callahan to that of Bennie Adams is only different by about five points, which is still only about 2.5 points for each home and away team.

Every season, 1,230 NBA games are played, and each game day at 9:00 a.m. ET, three officials are assigned to each game in the day, giving us 3,690 “officiated games” for the season. When reading the graphs, note that one officiated game can be governed by Nick Buchert, Zach Zarba, and Leroy Richardson, referees with pretty diverging fouls per game averages. Buchert’s average over the course of the season adds up to little more than 42 fouls per game, while Zarba’s typical officiated game stands at little under 38 fouls per game. In either case, understand that these varying groupings comprise the data shown in the graph above, in that a single game counts for both Zarba and Buchert. Also, note the range of points per game and fouls per game is relatively small in the grand scheme of things.

For what it’s worth, that particular game officiated by Buchert, Zarba, and Richardson was between the Phoenix Suns and the Milwaukee Bucks on 22 January 2018. Both teams combined for 214 points and amassed an astounding 48 personal fouls, which definitely fits the tune of a Nick Buchert officiated game.

In case you’re wondering, official Nick Buchert in the upper right of the graph did indeed officiate 62 games, while Eric Dalen in the lower left officiated 26 games. In this overview, Dalen had officiated the least amount of games, and I couldn’t possibly leave a legend off. I did end up leaving off a few officials that only refereed a handful of games.

A game that’s typically out of character for a Dalen officiated game is the Los Angeles Lakers and Washington Wizards game that took place on Nov. 9, where both teams combined for 50 fouls and 206 points. Most of the fouls were committed by the home team Wizards, and the first graph in the piece confirms that the Wizards tend to foul a bit more than other teams in the league on average.

This graph compares fouls per game to home team winning percentage, and you can see the correlation isn’t exactly strong. It can suggest that referees don’t considerably favor home teams over away teams in games, but the graph doesn’t lay weight to the type of fouls.

First, let’s consider free throw attempts per game and a team’s overall winning percentage.

It goes without saying that free throw attempts definitely help teams win games, and it looks like getting to the line about 21 times per game is kind of a sweet spot since 9 out of 12 teams in that range are playoff teams. Since this correlation is somewhat strong, we could probably predict that referees that call more fouls to get a single free throw attempt negatively affect teams. Conversely, the more free throw attempts there are per foul called made, then teams will tend to win.

Now, there isn’t a strong reason as to why I chose to look at the home team winning percentages other than the fact that it can be falsely perceived that referees might be favoring home teams. While the correlations look strong between fouls and winning percentage, the ranges of points in each game that these referees officiate are small (about 2.5 points for each team across 1,230 games, remember?).

Now we’re able to see a slightly stronger correlation by incorporating free throw attempts to home team fouls.

Having talked a little bit about Nick Buchert and his officiated games, his relative extremity for calling fouls is normalized by how many free throw attempts he tends to give out. While on average the home team will win about 67.5 percent of the time when officiated by Buchert, he’s not doling out fouls leading to free throw attempts like perhaps Mitchell Ervin and Jacyn Goble.

Jokingly, if a home team saw Eric Dalen walk through their own stadium doors then they shouldn’t expect much help getting to the free throw line. Although in that Lakers and Wizards game back in December, the Wizards got 20 free throw attempts on 19 Laker fouls which is definitely Dalen territory (1.05 FTA/pf), while the Lakers nabbed 41 attempts on 31 Wizard fouls (1.32 FTA/pf). One would think that this game is an easy one for the Lakers, but they lost.

In the Bucks and Suns game, however, Milwaukee was generously given 1.68 FTAs/foul as the home team compared to the Suns’ 0.91 FTAs/foul. Now both teams do foul more compared to the rest of the league per the first graph, but we can probably assume that a Buchert-led game could lead to more free throw attempts for the home team, although this game seems to be a bit of an extreme given where it would land on the x-axis.

Finally, we’ve arrived at the point where home team points are taken to account and are able to observe but a slightly stronger correlation. Here you can see referees like Buchert and Goble split a bit more from the pack due to higher home team points per game, but incorporating points on top of winning percentage don’t really draw any conclusions outside of categorizing these referee’s archetypes.

As in the video interview with Monty McCutchen linked at the beginning of this piece, not all referees are perfect (McCutchen and Jason Phillips both make the questionable call on Andre Iguodala in the video). While the correlations suggest that free throw attempts per fouls called suggest better winning percentages, I don’t think it outweighs the better shooting abilities of players in their own gym, or for any game in general. Plus would you really think the likes of these guys are colluding or forcing a game in their direction?

Next: Big men are getting under-valued in free agency

When the season comes rolling around the corner, watch for the NBA to release assignments on game day so you might get a sense of who’s officiating the game you want to watch. For example, if you want the best chance for a losing home squad you might want to see if Haywoode Workman is officiating that night. If you want to see the home squad run away with a game, you might catch the James Capers game.

All data presented here is from the 2017-18 season from Basketball-Reference.com.