As Moneyball has shown, sabermetrics and advanced statistics have become a big part in evaluating athletes, teams and matchups in all sports. So something new for this season is going to be a closer look at how those statistics are calculated, what exactly they mean, and just how our dear Cavs stack up against them.
I will be your guide throughout this process. In the real world, I am an engineer by training, and know a little bit about numbers and what to do with them. I’ve been both a Cavs and basketball fan for some time, and hope to use my skills and this column for the greater good. So let’s do some math.
Player Efficiency Rating (PER) is one of the more commonly quoted sabermetrics. It is the brainchild of John Hollinger, and tries to sum up an NBA player’s overall usefulness in a single number – the higher the better. It’s easy to look at players like Kyrie Irving (PER 21.5 last year) and Donald Sloan (PER 9.0) and tell which is the better player, but what about Tristan Thompson (13.4) and Alonzo Gee (13.2)? Do their similar PERs indicate equality?
What does the similar PER mean for players who play different positions and vastly different styles? Before delving into those questions, let’s take a look at how PER is determined. The short story is that calculating a player’s PER happens in two steps. Step one is calculating an individual PER, which in broad terms consists of the following:
iPER= (stuff that happens on the court) / minutes
Secondly, the individual PER is put through a mathematical ringer to get the true PER:
PER=iPER*(lgPace/tmPace) * (15/(league avg.iPER))
This does two things – it normalizes for league pace, allowing for comparisons between players on fast paced teams (Sacramento led the league last year with 97.4 possessions per game) and slower teams (New Orleans brings up the rear at 90.6), and also normalizes PER such that the league average is always 15. This can make it pretty clear in one number who might be struggling for minutes, and who might be knocking on the MVP door. The higher the PER, the more effective a player is while on the floor.
Let’s take another look at the top bit. The entire formula is a bit winded, but here are some highlights to help understand the theory behind it. When you get down to it, anything that happens on the court affects a player’s PER. Essentially, these are positive actions (FGs made, assists, steals, blocks, rebounds, blocks, free throws) and negative actions (missed FGs, turnovers, fouls). Traditionally, the problem of combining these stats is this: how does one equate a field goal to a rebound? Or a steal? In order to understand how PER attempts to do this, it is necessary to define the Value of a Possession (VOP):
VOP=lgPts / (lgFgA-lgORB+lgTO+.44lgFtA)
This is a measure of, on average, how many points are scored on a possession by any given team in the NBA. The numerator is the total number of points scored in the league; while the denominator works out to the total number of league possessions (that last bit says that, statistically speaking, a free throw is worth 44% of a possession). With that out of the way, you can start to see the pieces fall into place.
A steal is the generation of an extra possession – multiply the number of steals by the VOP; you get the theoretical average number of points generated off steals. A turnover is the opposite – it’s the loss of a possession and by multiplying the number of TOs by the VOP, you get the theoretical average number of points lost to TOs. Similar tricks can be done with missed shots, rebounds, etc. So that is the short version of PER.
It looks at everything that happens on the court, and equates it by calculating the additional possessions and points generated by those events. As a first shot analysis tool, it’s not bad, but because it combines so many stats, it does lack depth. We saw one of the issues above – how does this help compare players at different positions? Throughout the season, we will look to answer that question and more with alternative numbers that present a more complete picture of the Cavs and their players.