Is PJ being historically underplayed? ... And can we prove it?
There's an inherent attachment to the idea that numbers are objective, scientific — more intellectual than the 'eye-test' used by the layman. But at least in respect to raw averages, this is rarely the case.1 The key is to use the right numbers, that can account for whatever variables there may be.
A stat for which this is crucial is per minute, which fans often use to compare players with different playing time. 'Per minute' usually fails for two reasons. First, players who don't play much are going to be skewed (extrapolating someone's numbers from 15 minutes to 25 isn't ridiculous, but 5 to 30 clearly would be). And second, some players may have respectable minutes per game, but they may always be in garbage time.
But if these variables can be accounted for, Statistic X per minute could tell us something.
Enter PJ Hairston, who seems to score at a rate outrageously high for someone with his playing time. But does it just seem that way?
The first thing you learn in Statistics is that a stat is just a number — conclusions or "meaning" has to be assigned. But what scientific statistics offers is the ability to tell if a number is significant, even if no one can agree on what the conclusion should be.
TBF.net crunched some numbers and found every ACC player's Points Scored Per Minute Played for those that averaged at least 12 minutes a game. Considering these players in theory had to play at least three full media timeouts, one can say they were playing a decent role on their team.2
In total, 103 players (as of Tuesday evening, January 29th) in the ACC fit the description. The top 10:
PJ Hairston is second in the ACC in Points Per Minute scored, second only to the nation's leading scorer in Virginia Tech's Erik Green. Naturally a counterpoint could be that this is because of UNC's pace, and with four Tar Heels in the top 10, one might have a point.
But not if you go deeper. The PPM doesn't mean much because no one uses it. How are you to know if Hairston's .61 is really that much more than Bullock's .49?
Sparing readers most of the technical garb, it's a simple Z-score. You find the average of our list of 103 PPMs, and then find the standard deviation (how far away a # is from that average). How far away a particular number is from that average in respect to those standard deviations tells you how significant a number is.
This is especially helpful when numbers you want to compare are small, or very close to each other. What we're about to show is that top 10 list above, but normalized with a "bell curve" you learned back in high school. Scores are from 0 to 1.0 (or 0 to 100), with a .5 (or 50) being average, and so on.
Green, Hairston and Brice Johnson aren't just higher than everyone else; they're WAY higher than everyone else (Hairston's score is 99%, with Green's essentially at 100%). When compared to the entire rest of the 103, PJ's playing time differential becomes even more striking. There are only two players in the top 15 below 25 minutes per game, Brice and PJ; both significantly lower than their peers.
The conclusion here is in the eye of the beholder. But as far as Statistics goes, it is an undisputable fact that PJ's playing time is a significant outlier in terms of every other player in the ACC in relation to their scoring.
And since the 2013 ACC may or may not be void of the league's usual superstars, let's look at how PJ compares to a few historic Tar Heel seasons. The following is PPM for the leading perimeter scorer on some past UNC teams:
Almost every one of those players was an All-American. Only one is struggling to get off the bench for more than half the game.3
To recap, Hairston's playing time is statistically, scientifically, borderline historically, significant in terms of how well he scores. Fact.
Now there's a quick-react contingent that asserts PJ's lack of playing time resides in his defense.4 But when you see how significant Hairston's scoring actually is, this argument erodes fast. In light of his offense, PJ would have to be really, really bad at defense to account for his playing time. This simply is not the case. To argue PJ's lack of PT is because of his inconsistencies is to argue there is another player in his place that doesn't have the same defects in some part of their game.5
It's also thrown around that PJ is not the most efficient scorer. This is partly true. But his true-shooting-FG% (which is actually not bad) is, again, nowhere near low enough to account for the discrepancy in playing time.6
If PJ Hairston played Rashad McCant's 2004 minutes,7 he would average just under 20 points per contest. Try to keep a straight face as you argue a would-be 20ppg scorer shouldn't play more than half the game because of the occasional lapse on defense; for an unranked team that struggles to consistently put the ball in the basket.
Obviously this is where the conversation turns mostly into OP-ED, but that's sort of the point. Conclusions are prescribed in every case with statistics. To be clear: the numbers don't necessarily 'prove' anything, but they certainly prove PJ's playing time is worth discussing.8 Something doesn't add up.
Why PJ isn't playing is anyone's guess. But, no doubt, people are guessing. And, no doubt, they will continue to.