Analysis of Fouls and Markets - Redux

I felt pretty smug.  To recap: BrooklynFan asked in a post-game thread a question pertaining to a subject that aroused my curiosity: do refs favor the large-market teams? Answering this question would require research and statistical analysis (both of which I enjoy doing, sadistically enough).  So, I dug up the numbers, crunched them, and posted my findings all wrapped up with a neat, little bow.  Multiple recs and kudos from the StR community later, like I said – I was feeling pretty smug.

So smug, in fact, that when MustangMBS, while complimentary of my work, wondered in the comments if further analysis would be helpful to see if there was any correlation between foul differential and a given team’s star power, or perhaps home court advantage – well, I rather arrogantly declined.  Not necessary, I said, we all know that big-name players and home teams get preferential treatment.  To which Mustang politely asked me to prove it, or shove it.  (I’m paraphrasing here.  Please bear with me.)

So, I did.  It took a lot more time and effort than my initial analysis – compiling and organizing data for all 516 games played through Wednesday night as well as rosters for each NBA team is much harder than researching team stats for just the 30 individual teams.  But boy, am I glad I did.  (I think.)

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First, let’s address the star power concept.  Do refs give preferential treatment to stars, or to teams with stars on them?

To begin my research, I decided to use the oft-quoted PER.  Now, I know that PER has its detractors; but as far as I know, it’s the best statistical measurement of a player’s all-around performance.  The assumption is that a high level of performance equals a high level of star power.  Not exactly scientific, but in scanning the list of top-50 players ranked by PER I feel the assumption is pretty solid.

Of course, it’s still a team game.  So I calculated the average PER for each team’s full roster (!!) for comparison with each team’s Fouls per Game differential.  The results are below. 

Not a whole lot of definition to that scattergram, I’d say.  It looks just about what you’d expect a "no correlation" graph to look.

But something just didn’t seem right to me.  Is it really fair to define star power as the average of all 13 players on the roster, including the never-see-daylight scrubs at the end of the bench?  Perhaps it would be better to examine the top 50 PER players individually.

The problem is, how do you calculate Fouls per Game differential for individual players?  We only have statistics on number of fouls committed by individual players; nobody keeps track of how many times a player gets fouled.  Well, you can count free throws… but does that really tell you how many times a player is fouled?  What about and-one foul shots?  (One foul, one shot.)  How do you know if a player took any technical free throws?  (No fouls, one shot).  Non-shooting fouls?  (One foul, no shots).  There are too many variables to rely on foul shots as a barometer, in my opinion.

Still, there could be some inherent value in examining the half of the equation that we do know – fouls committed by each star player.  So, I gathered all the pertinent data, adjusted for minutes played (fouls committed per 48 minutes), and charted against PER.  Here’s what the machine spit out:

Hmmmm… now we’re getting somewhere.  It seems that there is a fairly defined correlation – among the top 50 PER players in the league right now, anyways – between individual star power and whistle friendliness.  Again, we’re looking at the fouls-committed side of the equation only.

Some comments:

• The league average for fouls-per-48 is 4.29.
• Of the top 50 PER players, the median fouls-per-48 rate is 3.95, and the mean is 3.91.
• Only one top-10 PER player exceeds the league average – Carmelo Anthony at 4.34.
• In all, only 18 of the top 50 PER players exceed the league average.  Of these, only two (!!) play PG, SG, or SF (Corey Maggette and Luke Ridnour).  The rest are all big men who, by nature of their size and their position, often defend the paint.  A high-than-average foul rate for these players makes sense.
• Oh, and that one outlier?  The statistically excellent player who commits over 8 fouls per 48 minutes?  The youngest old man in the world.

Okay – we can infer a bias in favor of top-performing players based on the above, but how does that play out at all in how refs call games overall (if at all)?  To try to figure this one out, I had to find a way to collectively measure each team’s individual top performers.  So, I calculated each team’s cumulative PER for the top 50 players in the league (to remove the scrubs from the mix) and charted against each team’s Fouls per Game differential:

There we go.  It seems fairly clear that teams that have the stars (higher cumulative top-50 PER) tend to have a higher FPG differential.  At least statistically speaking, they do tend to receive kinder treatment from the referees.

Now, I’m not going to get on any soapboxes and rail against disparate treatment based on "stardom".  It’s been argued back and forth, not just by StR commenters, but pretty much all over the interweb, ad nauseum.  Personally, I can see both sides of the coin.  I understand the requirement for equal treatment of all players on the floor in order to preserve the purity of the game and the integrity of the results.  At the same time, basketball is not simply sport, it is also entertainment and big business.  Stars are the entertainment draw, and people pay to watch them perform; it behooves the league to not deprive its customers of the entertainment experience they paid good money to watch.

I’m not here to editorialize, just to report.  And in this reporter’s opinion, there’s no doubt (never has been, really) that stars get preferential treatment by the refs.  It’s just that now I have some stats to prove it.

Before we leave the topic of star power, there’s one more chart I’d like to share:

This is a scattergram of each team’s total top-50 PER against market size.  Like it or not, large-market teams tend have a distinct advantage in statistical talent level.  6 of the top 7 "star power" teams are in large markets – the only exception being the Nuggets (ranked second).  As I’ve shown above, these teams stand a better chance of receiving a friendlier whistle.  But, that doesn’t necessarily mean that they have an advantage when it comes to winning games – these top 6 large-market teams by top-50 PER include both the Warriors and the 76ers.  Heh.

Again, I’m not going to get on a soapbox.  This is a matter of economics.  Large-market organizations will be in a much better position to attract top-level talent based on their higher revenue streams (broader customer base) as well as on intangibles (ability to meet certain top players’ lifestyle expectations, etc.).  This sucks for us Kings fans, but that doesn’t mean that small-market teams cannot attract and retain stars and compete at a high level against the big boys.  See: Kings from 8 years ago, or Spurs for the last decade, or Portland’s incredible string of consecutive playoff appearances from a while back.

One last thought.  Some commenters wondered if player or team popularity might contribute to friendlier whistles.  I wrestled with this one for a while, but ultimately decided that I would measure individual players by their on-court performance, not by their popularity with fans.  After all, who doesn’t wag their head at the all-star voting results?

That doesn’t mean I didn’t do any research.  The best measurement I could think of for player or team popularity is their merchantability (yes, it’s a real word!  I saw it in a legal document yesterday and just couldn’t wait to use it…).  That is to say, how much merchandise revenue each player or team generates.

First of all, the most current data that I could find is from January of last year – almost a year old.  What I found is a ranking of top ten NBA teams by merchandise sales, and a ranking of the top 15 players by the same yardstick.  Not exactly large sample sizes from which to draw any real deductions.  Also, there appears to be a strong correlation between the two lists – the only top-ten selling team that did not have a top-fifteen player was San Antonio, ranked 10th.  And, a couple of the top-selling players have changed teams in the past year – AI is no longer in Detroit, and Shaq is not in Phoenix.

So basically, I looked into it, but couldn’t really get any traction in the analytics.  If someone has any other data sources or ideas, I welcome your comments.

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Okay, now on to the home-court discussion.

This is the one that took a lot of time and effort to produce, since I had to manually cull data for each of the 516 games played through January 6th.

And, without further ado, here’s what the numbers say, in chart format as opposed to graph format, with my comments below.

First, a quick explanation of how to read the chart.  Home market is in the rows, and away market is in the columns.  The values are home team FPG differential – basically, you can look at it as the home court advantage as measured by the number of foul calls the home team gets as opposed to the away team.

Now, let’s note the obvious.  There is a home court advantage, after all.  Over the course of the first 516 games of the year, that advantage has been to the tune of 0.88 fouls per game.

Next, let’s translate that into something meaningful: points.  If we assume that 80% of fouls committed are shooting fouls, there is a 75% success rate on free throw conversion, and 20% of shooting fouls result in only one foul shot in an and-one situation (I don’t have any statistics to back up any of these assumptions, but they feel about right to me), then we arrive at about a 1.25:1 point-to-foul ratio – which means that 0.88 fouls per game equals 1.10 points per game.  So any given team can expect a statistical advantage of just over a point every time they host a game.

Interesting, but not surprising.

Now, let’s look at how the different market sizes stack up.

Large-market teams have a home-court advantage of 0.87 fouls – right in line with the league average.  Interestingly enough, the mid-market teams have the strongest home-court advantage, at 1.20 fouls – which translates to an advantage of 1.49 points per game.  And small-market home teams only have an advantage of 0.58 fouls, or 0.73 points per game.

Hmmmmm….

Next, let’s look at how different market sizes fare on the road.  Large-market teams only give up 0.64 fouls to their hosting team, while mid-market and small-market teams face an uphill foul battle of 1.05 and 0.93 fouls, respectively.  Converted into points, this means that large-­market visiting teams are spotting their hosts 0.81 points, while mid- and small-market teams are giving up a higher-than-average advantage when they go on the road (1.31 and 1.17 points, respectively).

The plot thickens…

Now, let’s drill down a little deeper into the matrix, starting with large-market teams.  When they host another large-market team, the home court advantage is 1.00 FPG (1.25 PPG) – fairly close to league average.  Surprisingly, large-market teams are actually hold no statistical home-court advantage against mid-market teams; in fact, they give away 0.17 FPG (0.21 PPG) to the visitors.  However, they more than make up for it when hosting small-market teams, averaging a 1.83 PPG advantage, which equates to 2.28 points.

I’ll let that sink in for a moment.  When a large-market team hosts a small-market team, their home-court advantage is more than double the league average.  Double.  The.  League.  Average.

Now let’s look at it from the perspective of the small-market as the home team.  When hosting another small-market team, their home court advantage is virtually nil (0.17 FPG, or 0.21 PPG).  Their biggest advantage is in hosting mid-market teams, when their advantage is 1.13 PPG (1.41 PPG).  And when the large-market boys come to town, a small-market team’s advantage is a paltry 0.38 FPG (0.47 PPG). 

I’ll repeat for emphasis.  When a small-market team hosts a large-market team, their home court advantage is less than half the league average.  Half.  The.  League.  Average.

It would be foolish to focus only on the small-market vs. large-market numbers, and ignore the other matchup combinations.  Especially with the mid-market teams – their numbers are rather extreme.  The highest home-court advantage of all is when a mid-market team hosts another mid-market team (2.20 FPG / 2.75 PPG).  And the smallest home court advantage of all, as mentioned above, is large-market teams actually giving fouls (and points) to their mid-market visitors.  And when a small-market team matches up with a small-market team, the home-court advantage is even smaller than when hosting a large-market team.

This kind of volatility in the numbers makes me hesitant to definitively stick a flag in the ground and proclaim that small-market teams get screwed by the refs.  To really make any sort of definitive conclusion, I’d want to perform the same sort of analysis on, say, the past ten years’ worth of NBA games.  But I really don’t have the time to compile all of that data for analysis.  It took me way too much time to just analyze the first 35+/- games of a single season!  But, if there were some folks who want to help me gather said data, I’d be very curious how the results shake out.

So there it is.  Not what I’d call a smoking gun, but deep down, something in my gut just feels… strange… about these numbers.  Paranoid?  Maybe.  I don’t know, really.  I feel like I’ve spent way too much time reviewing, analyzing, and thinking about this data recently – so much so that I may have lost some perspective.  Hopefully, that’s where the rest of the StR community will chime in.  I look forward to your feedback!!

One more thing… in case you’re interested, here is the home-court advantage chart by team.  If you take the time to look at and think about these numbers, I’d be interested in your observations.  I know I have some of my own (cough cough L*kers cough Knicks cough), but I’d be interested in what jumps out at the rest of you.

Cheers!

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UPDATE

Per Mustang's request, here's a graph showing home court advantage against win percentage.  It's quite clear that top-tier (playoff) teams tend to have a stronger home court advantage.