# NBA Finals: Is There a Heat-Refs Conspiracy?

Following in the footsteps of rigged lotteries and expelled superstars, the NBA conspiracy theory du jour holds that referees work their magic to help the Miami Heat win games. Paul George has griped about it and The Onion has spoofed it, but the theory’s doubters claim that the Heat deserve more calls because they attack the hoop more frequently. Who is right?

Before answering this question, it’s worth pointing out that both camps—the critics and defenders—have some backing to their ideas. If we use free throw attempts per field goal attempt as a measure of getting calls, the Heat do receive an above-average number of whistles on the offensive end, according to data from Basketball Reference. In the regular season, the Big 3 era Heat have gone to the line 0.317 times per field goal attempt, compared with the 5-year league average of 0.287. And, as the theory’s skeptics say, attacking the hoop is linked slightly but significantly with getting calls. Floor data from NBA.com show that, ignoring all other variables, teams that boost their proportion of shots from within five feet by one percent can expect an increase of 0.0034 free throws per shot.

To find out whether Miami takes an exceptional number of trips to the line while controlling for their propensity to attack, we’ll run a linear regression which will predict a team’s number of free throws per shot attempt. The first independent variable will be the team’s percentage of shots within 5 feet, which we’ve seen is linked with drawing fouls. The second will be fast break points per game because wide-open fast break opportunities count as close shots but are unlikely to be plays on which whistles are blown (barring a blatant foul), so we need to control for this factor. The third will be a dummy variable for each team, so the Miami indicator will equal 1 for the Heat and 0 for all other teams, the Atlanta indicator will equal 1 for the Hawks and 0 for all other teams, etc. If the Heat’s dummy variable is positive and significant, there must be something about the Heat that leads Miami to earn more calls than one might otherwise expect.

As it turns out, the regression does find a positive coefficient on the Miami indicator variable, meaning that there’s something about the Heat which leads them to receive more shooting foul calls than you’d otherwise expect. The coefficient isn’t significant, however, and other teams’ coefficients are larger. The Thunder, Nets, and Nuggets all outperform their free throw expectation by more than the Heat do, as indicated by the larger coefficients on their indicator variables.

On the other end of the spectrum, the Sixers and Warriors underperform their free throw expectation more than other teams. And unlike the teams at the top of this measure, these two teams have significant negative indicator coefficients.

Overall, the data suggest that the Heat probably do have something going for them other than attacking the basket. But so do other teams, which casts serious doubt upon the “home cooking” conspiracy. There’s a positive correlation (of about 0.23) between free throws above/below expectation and winning percentage over the past 5 seasons. With this in mind, a likely explanation is that good teams are also good at getting to the line. As Kirk Goldsberry has noted, Miami has three of the five most efficient scorers within eight feet of the basket. It could be that teams like the Heat take smart shots that force their opponents to foul in desperation. It’s also possible that good teams shoot more free throws due to clock-stopping fouls at the end of games. Ultimately, either drawing fouls is just one more thing that good teams are good at, or the conspiracy runs deeper than we initially feared.