Sunday, February 7, 2016

Are there "shooter friendly" NBA arenas?

Baseball, in contrast to most every other major sport, allows each team significant leeway in designing their home venue. Both the length and height of home run fences varies from park to park. In addition, regional differences in air density and humidity can have a significant impact on how far a baseball travels in flight. 

As a result, there are what is known as "hitters parks" such as the Colorado Rockies' Coors Field, where the thin Denver air results in more than two runs per game on average. And there are "pitchers parks", like San Diego's Petco Park, with its dense, dry sea-level air and distant home run fences that lead to, on average, roughly one less run scored per game.

Does a similar phenomena exist in the NBA? Are there "shooters arenas"? Of course, the NBA maintains far more uniformity across its venues than the MLB. The dimensions of the court do not vary, the free throw line is always 15 feet from the backboard, and the three point line is the same distance everywhere (basketball brainteaser: If you were playing the Warriors and given the option of re-drawing the three point line, would you make the line closer, or further away?). 

The NBA also has strict rules on the equipment used in each arena. The ball itself must be inflated to between 7.5 and 8.5 psi, and the rims and backboards are required to meet precise specifications. Even the thread count of the net is regulated (no less than 30 thread, but no more than 120 thread). But despite all this, are there still measurable differences in shooting accuracy between venues? Differences that go beyond garden variety statistical variation?

Former NBA guard/forward (and current Phoenix Suns broadcaster) Eddie Johnson seems to think so. 

As the leading scorer in NBA history off the bench (19,202 points), Eddie's opinion carriers some weight. But he is no more immune to confirmation bias than the rest of us. If the Cavs arena truly has "soft rims", then does that show up in the shooting stats?

For this post, I am going to focus on free throw shooting, and whether certain venues lead to measurably better (or worse) percentages. There are too many confounding variables when looking at field goal shooting (team defense, shot selection, game situation, etc.). But free throws are the closest thing we get to a controlled experiment in the NBA. We will look at this in two different ways:

Impact on the Home Team

Measuring the impact on home teams is straightforward. For each season, we can split a team's overall free throw percentage between home attempts and away attempts. If the team's home venue has "soft rims", or other shooter advantages, one would expect a higher free throw percentage at home (above and beyond the relatively slight impact of home court advantage). For example, so far this season the Cavaliers are shooting 73.5% at home, and 71.7% on the road - which is directionally consistent with Eddie Johnson's tweet (note - the Cavaliers have played at the same arena since 1994, which slightly overlaps Johnson's 1981-1999 journeyman career).

Impact on the Away Team

Quantifying free throw percentage by venue for the away team is slightly more complicated. If we just aggregate away free throw percentage by venue, the result could be biased by the mix of teams that venue hosted. In other words, if a team tends to host better than average free throw shooters, that will skew the results. So, for each team, we will calculate an expected free throw percentage, based on their season total, and then compare that to the actual free throw percentage when visiting a particular venue.

For example, the expected free throw percentage of teams visiting the Cavaliers this season is 76.2%, somewhat above the league average. The actual free throw percentage for the Cavalier's visitors this season is 78.0%, once again consistent with Eddie Johnson's theory. But these results can be quite noisy season to season, so let's pull in as much data as we can on free throw accuracy.

The eye charts

There are two charts below which summarize free throw accuracy by venue for the past 20 NBA seasons. Each venue (labeled by the home team) has two rows: one for home team accuracy and one for away team accuracy. The percentage shows how much higher (or lower) free throw accuracy was at that venue. For example, the Brooklyn Nets are shooting 73.5% at home from the stripe this season, and 78.6% on the road, which shows up as a gap of -5.2% on the "home" row. The Nets opponents at the Barclay Center would be expected to shoot 75.3%, but there actual free throw percentage is 73.9%, which shows up as a gap of -1.3% on the "away" row.

There are two charts, but the numbers are exactly the same between the two. The only difference is that the first chart highlights where free throw percentages are higher than expected. If there are true "shooters arenas" then those advantages should confer to both home team and visitor alike. And those venues should show up as islands of dark ink for both rows.

Here is the chart, highlighted to show the venues that appear to favor shooters (direct link).

Eddie might be onto something. The Cavaliers show a fairly consistent bias to better free throw shooting at their venue, particularly in the mid to late nineties. The pattern dissipates somewhat in recent years though. The Wizards arena also show up with a lot of favorable percentages for both the Wizards and their opponents, although the current season results show no bias for either home or away team.

Are there arenas with "tight" rims? Or perhaps home teams that inflate basketballs to the higher end of the psi limits, leading to fewer shooter's bounces? Or could differences in air density, particularly in Denver and Salt Lake City, have a significant enough impact on a ball's trajectory to affect shot accuracy? Here is the same chart, highlighted to show poor shooting percentages (direct link).

Note that the Rockets show a sharp drop in free throw percentage starting in 2003, which lasted until about 2009. Not coincidentally perhaps, 2003 was the first year the Rockets began playing at the Toyota Center. Rockets forward Tracy McGrady actually went on record with his concerns about his team's home arena, speaking to the Houston Chronicle in 2008:
"I really feel a lot of guys are not comfortable playing in this arena," McGrady said. "I hear guys saying things about how they're not comfortable playing in the arena, how it's not a good shooting arena for whatever reason. "I feel the same way. I really feel the same way. It's not just our guys. It's guys around the league. They hate our arena. Who was the last player to score 40 in our arena?
Without venturing too far into tinfoil-hat territory, something seems to have been done around 2010, as the Toyota Center no longer shows the same anti-shooter bias it once did in its early years.


For the most part, the results here look fairly random season to season. With some 1,300 data points, there are bound to be pockets of outliers. But the Cavaliers and Rockets results do appear to be more than just statistical fluctuation (I might throw the Wizards in that pile too).

I would be curious to hear whether there are other "urban legends" circulating among the NBA regarding the various arenas and their "shooter-friendliness". I seem to recall Reggie Miller favored the Charlotte Hornets arena in his playing days, thinking its rim was more forgiving than most. It would be interesting to see if those legends line up with the data, or if they are just basketball old wives tales.

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