Disproving Ref Preference in PFs (Or Not)

Warning:  The below is miles of text with no cute graphics and may represent the misalignment of Mercury in retrograde which typically sends my Virgoan brain into dormancy, but I have endeavored anyway.  I have endeavored to share some of my own delvings into the question of ref foul call preference.  Good, Bad, or Ugly?  You tell me.

First off, I have to give lots of credit to doogman77 who posted some very interesting research on the number of fouls called and whether or not there are differences in calls for different teams was due to a small versus large markets.  That started me digging and pondering the best way to look at the data on fouls that is reported for each team and for the games.


It was pretty straightforward to look at the Kings team stats and see that the Kings foul other teams an average of 22.7 times a game and get fouled an average of 20.8 times.  This is a difference of +1.9 player fouls (PF), meaning they foul other teams 1.9 more times than they get fouled.  This number does not, however, tell use much about any underlying patterns.  We know that there have been games against teams like the Fakers and Mavs where pretty big differences in fouls existed, but trying to get a handle on the numbers is somewhat difficult because any one game doesn’t provide enough information to use as evidence and many teams foul and get fouled at very different rates. 


Because of the difference in the average number of fouls per team I could not just be total or average PFs and get something meaningful.  To do that we would have to include or address the average rate that a team fouls and gets fouled in any kind of analysis because each teams fouls and gets fouled at different rates.  The Kings are +1.9, but a lot of teams are lower.


Team stats give the average player fouls (PF) called against a team per game and the average number of PFs called against their opponents.  I started looking at these numbers and found that most teams don’t have a wide difference in these averages.  For many teams the difference between these two numbers (Team average PFs minus Opponents average PFs) is just a small fraction of a foul.  For example, the Bulls average is about 19.7 PFs and their opponents average 20.3 PFs for a difference of .6 fouls.  Meaning their opponents foul them about .6 more times a game than they get fouled.   


I decided to look at these team averages and compare them to the differences in the PFs per game. Data can usually be broken down to show some interesting findings.  The question was whether or not the differences between these team PF averages and the differences in the game PFs would show anything significant.   


I compiled all the data, PF averages for each team the Kings have played, and all the totals of PFs called in each of the games.  I took the differences in averages (Team average PF minus Opponents average PF) and substracted that from the same difference in the number of fouls called in each game (Team PFs minus Kings PFs).  I did this to determine how wide a disparity existed between the average differences in fouls called and the difference in individual games.  For example, the Bulls have an average difference of .6 fouls, but during the November 21st game they had 20 PFs called against them and the Kings had 22 PFs.  The difference in fouls was 2 PFs for that game, but they already average .6 more PFs.  So I subtracted that from the game PFs (2 PFs minus .6 PFs for a total difference of 1.4 PFs). 


My reasoning for doing this was to control for the differences in the number of times teams foul and how often they, on average, get fouled.  Probably sounds like numbers geek speak, but let me explain.  If the Kings were to foul a team 3 more times than they got fouled in a game that might be considered a pretty large difference, but it wouldn’t be if that other team usually got fouled that much more each game.   It might even look bad if they fouled a team 2 more times, but would actually be the opposite if the team averaged 3 more times per game.  If this is all still just geek speak I apologize. 


I took the average PFs per team, the counts of PFs for each game, compile them into one data set, got the difference in the two numbers, and broke out these differences into some categories to see what I could see.  My thoughts were along the lines we have discussed.  That some teams (those more successful, preferred, or more popular teams) would have a fewer number of fouls against them and more fouls called against the Kings and that the differentials in these numbers would be higher than their team averages. 


I decided to go with dividing the games into two groups to get at this in a way everybody would understand and that was objective, those games played against playoff teams and non-playoff teams.  I selected those teams currently 8th or better in their respective conferences as playoff teams.  My plan was to break out the groups and see if there are differences.  If there is no difference between the PFs called between the two groups after accounting for the average rate of fouls for each team then that would show that there was really no support for any claim that foul preference exists. 


I compared the differences in team average fouls to the game PF numbers and lo and behold I have some serious differences.  The differentials were much higher for playoff teams than for non-playoff teams.  The differences between fouls against all teams in all games was 1.33 more PFs for the Kings (+1.33), but against playoff teams this broke out as +2.64 PFs and against non-playoff teams as only -.07 PFs.  Meaning the Kings lose the PF contest against playoff teams and actually win by a small margin against the non-playoff teams. 


Please keep in mind that this is a reduced number than the actual difference in the number of PFs.  Playoff teams on average have an +.68 foul advantage overall.  The actual average of PFs against playoff teams for the Kings is a difference of +3.31.  I am reducing the +3.31 PF by the playoff team average of PFs, +.68.  If there was no real difference between the two sets of numbers then that would pretty much disprove that any foul preference exists.  That said, the differences don’t prove “preference”, just that more fouls are called.  Which we kind of knew already, but it is good to have a better grip on it.  


So this differential of +2.64 PFs exists after taking away the team average PFs from the game PF averages.  What does it mean? Does it mean that there is a preference given to these playoff teams or are they just that much better?  That is probably arguable.  Causality is a tricky beast.    


One of the things much discussed StR is that Home court gives some advantage in the number of fouls called.  It seems like a widely held opinion that the Home team is more likely to win the foul differential contest if there are fans booing bad call.  I decided to check out the differences in Home versus Road games and the differential grew wider against playoff teams.  From +2.64 PFs overall against playoff teams, it went up to +3.77 PFs for Road games and dropped down to +1.76 PFs at Home games.  That is a large drop from Road to Home games, 2 fouls.  So, this means that on average the Home court advantage cancels out a lot of the advantages that playoff level teams get in fouls called, though they still have the advantage, and that they get an even greater advantage on their Home court. 


The question really is of causality.  These differences could all be written off as due to better teams getting fouled less by teams with younger or less talent, but there was little to no difference in the average differentials overall for non-playoff teams or for their Home versus Road games and shouldn’t teams level of play stay the same on the Road or are Home teams just playing that much better?  It could be argued that a Home advantage should exist in PFs for all teams… Again, it is really arguable to determine what causes the difference, but I did not disprove foul preference and that is something. 


There is clearly a difference after accounting for team average PFs and that difference only exists for playoff level teams.  If there had been little to no difference then that would have disproved foul preference exists.  In stats sometimes it more important to not be able to disprove something than it is to prove something.   



To say you can know something as fact from stats is a good way to start an argument.  People devote huge amounts of time arguing over the most minute bias or differences in methodologies.  There is a limited amount of data used here.  We only have the games this season and that is one issue…  We CAN’T use last years data for obvious reasons and so we have to go with what we have and make the most of it.  We can say that we did not disprove ref preference, but beyond that it may not be about what we can know as FACT.  It might, instead, be more about what we can approximate given our existing data. 


I think the comparison of the averages and the differentials between the team PF averages and game PF numbers means we can approximate a few things for the Kings.  That better teams get more PFs called their way and fewer against them. Numerically we can say that they have a PF advantage as that is shown to be true even after accounting for the average number of playoff team’s PFs (I know small sample, but again we got what we got).  So, we can estimate or approximate that the Kings have to score higher against these teams, especially on the Road, than other teams in order to win because of this disadvantage.  They would probably need to score approximately 6 points higher, on average, against these teams, with 8 points higher on the Road and 4 points higher at Home to make up the difference in the number of PFs called.



We can question whether or not the difference in PFs can be attributed to ref preference or to just better teams playing better.  We can question if this will be the same at the end of the season, but that will be a different team with KMart back, I hope, and may not apply.  In the case of games the PF differentials and how much is determined by good versus bad play may be something that can be analyzed by looking at the other game indicators of good play. 


Is the opposing team scoring a high percentage on their shots?  If so then that might indicate they are just playing better than the Kings and likely not getting bailed out by PFs, but what if the opposite is found?  I know that at least one of the recent games against the Fakers was truly not good for them.  They shot a horrible percentage and lost on all but one of the indicators of good play yet got a huge disparity of PFs, but then they were at Home…  It might be worth pursuing.



Upon reflection on the above and in consideration of the King’s recent games, I am (still) of the opinion that the Kings have to not only play against the opposing team, but also have to play against the refs (I know it is kind of weird to say it that way).  The refs are often calling games against the Kings and in some games seem, to me, to be the opposing team’s sixth man.  They don’t call many of the games against certain teams evenly or even handedly and there are too many calls that are impacting the game, again my opinion here. 


The Kings were the absolute worst team last year and are clearly, IMO again opinion, getting zero respect from the refs.  They are giving breaks to superstars with no calls and calling phantom fouls against Kings who don’t even touch, or barely touch, these Dons of the NBA.  The foul disparity has been quite high.  Too high.



That is all I got.  I have to come up for air and resume my life.  Immersing one’s self in number can be good, but it requires a focus I need to apply to other things right now.  So, I hope this is informative.  That is my intent and that my mono-focus addressed this well enough. 

(This is a FanPost from a member of the Sactown Royalty community. The views expressed come from the member, and not Sactown Royalty staff.)

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