Playmaker Rating is a fairly simple basketball metric that is quite easy to calculate.
The formula is as follows:
PlayRtg = USG*(PPG+2.26*APG-TPG)/(FGA+0.44*FTA+APG+TPG) where USG = Usage Rate, APG = Assists Per Game, PPG = Points Per Game, TPG = Turnovers Per Game, FGA = Field Goal Attempts Per Game, FTA = Free Throw Attempts Per Game
But how did I come up with it?
It all started following a debate I had with a friend concerning the merits of assist-to-turnover ratio (specifically concerning Russell Westbrook). He argued that it was a basic, simplistic way of analyzing point guard's playmaking abilities. Obviously, a good point guard would have a higher assist-to-turnover ratio because they'd generate more assists than turnovers.
Sure, I'm fine with that. But the stat can get better, and that's where our opinions diverged. He agreed that other things were more telling but didn't think it was necessary.
That's what I'm not fine with.
Playmaking, even for point guards, involves more than just finding open teammates. After all, if your point guard can score in the flow of the offense, isn't that just as valuable as accumulating another assist? To analyze a player's true playmaking ability, scoring needs to be taken into account.
Let's look at the numerator first. Basketball players can do three things to end a possession when they have the ball: score, assist or turn it over. Obviously, points and assists are positive while turnovers are negative.
Points per game needs no coefficient in front because the difference between two-pointers and three-pointers is contained within the stat.
I chose not to put a modifier in front of turnovers per game because a turnover leads to an extra possession for the opposing teams and over the last few seasons, the league average has typically been 1.0 points per possession if you round to the nearest tenth. Essentially, a turnover costs the offensive team a single point on average, and thus there is no need for a coefficient.
So, why the 2.26 in front of assists per game? Put quite simply, not every assist is worth exactly two points of offense. Quite a few assists lead to made three-pointers by teammates.
To find out exactly how often this was the case, I turned to HoopData.com, a site that breaks down where on-court field goals are made and which ones are assisted.
During the 2011-12 season, 15.6 shots per game have been made at the rim, and 52.8 percent of them have been the direct results of assists, indicating that 8.23 assists per game are generated by shots made at the rim. From three to nine feet away, there are 4.1 made shots per game and 39.9 percent of them are assisted, producing another 1.63 assists per game from this area.
From 10 to 15 feet away from the hoop, there are 2.8 makes per game, and 42.8 percent of them are assisted: another 1.20 assists per game. From 16 to 23 feet, there are 7.6 makes, and 59.4 percent of them are assisted: 4.51 more assists per game.
Finally, from behind the three-point arc, there are 6.4 makes per game, and 84.2 percent of them are the result of passes from teammates. That means that 5.39 assists per game lead to three points instead of two.
Adding it all up, there are 20.96 assists per game by the average team in the NBA. 15.57 of them result in two-point shots, leading to 31.14 points per game. The remaining 5.39 come on three-pointers and thus lead to 16.17 points per game. Adding those two numbers up, we see that those 20.96 assists per game lead, on average, to 47.31 points per game.
Simple division therefore tells us that each assist is worth 2.26 points (technically 2.25716) if the sample size is large enough.
Now of course, I would have a terrible statistical mind if I was content to only use data from half of an NBA season. To verify, I went back and checked the results of the 2010-11, 2009-10 and 2008-09 seasons.
Using the same methodology, I found that each assist was worth 2.26 points (technically 2.6002) in 2010-11, 2.25 points (technically 2.2548) in 2009-10 and 2.27 points (technically 2.27129) in 2008-09.
At this point, I was content to accept 2.26 as a valid multiplier for assists per game in the PlayRtg formula.
The last part of the numerator is usage rate.
Incorporating involvement into the formula is necessary because players who are on the court more deserve to be rewarded more for their greater level of positive contributions. Ideally, I would have a modified form of usage rate—one that counted assists as "uses"—to insert into the equation, but that doesn't exist so simple usage rate will have to suffice.
It's one thing to shoot a high percentage in limited action, but another thing entirely to do so while remaining heavily involved in the offense.
Now, as for the denominator of the formula, it is simply a modified version of the formula for individual possessions. The following is taken from an article of mine that explains a number of advanced stats:
There are three ways that a player can be involved in the end result of a possession. They can attempt a field goal (regardless of whether it's a two-pointer or a three-pointer), they can end up on the foul line, or they can turn the ball over. However, simply summing those three results does not provide the number of possessions because shooters can attempt either one, two or three free throws on any given possession.
Box scores don't explain how many shots a player was fouled on, so we have no idea of knowing which fouls resulted in and-1 (for example) without looking through historical play-by-play data.
Just trust me on this one (I've read the studies and they're too complicated to explain in a short space) and accept the fact that the 0.44 multiplier is the best way of estimating the total number of possessions a player is involved in.
The only difference between the denominator of my formula and the equation for possessions is the incorporation of assists. Because we're analyzing the possessions in which a player passes, as well as the ones in which they shoot, the addition is necessary.
It's worth noting that this stat was originally developed to apply to the NBA. It still works for NCAA basketball, but the modifiers are slightly different than they would be otherwise.
-The above description is an updated and modified form of the original explanation, which can be found here.