PLAY: A Playmaking Metric, Part 1 – Intro

I wanted to share a recent project I did with friends and colleagues Chris Weld and Chris Arney titled "Quantifying playmaking ability in hockey".  The one sentence summary is that we developed a metric for quantifying playmaking ability in hockey that is better than assists in two quantifiable ways: (1) it is more consistent than assists, and (2) it is better than assists at predicting future assists.  

In this article, we'll give an overview of what we're doing, and the motivation behind it. 

One reason for the improvement is that our playmaking metric is based on both shots and goals.  Since shots are often more consistent than goals, and better predictors of future performance than goals, including shots helps a lot.  Assists, which are based only on goals, are subject to the same randomness as goals for small sample sizes.  Also, we have accounted for strength of teammates for our playmaking metric.

Using shots isn’t completely straightforward.  While assists count the number of a player’s passes that lead to a teammate’s goal, there is no analogous statistic that is tracked for shots.  We don’t know how many of a player’s passes lead directly to a teammate’s shot.  We note that Rob Vollman developed a way to estimate passes that lead to a teammate’s shot, and it works pretty well.    That article also has a good description and discussion of quantifying playmaking ability, and some interesting stuff about pass-to-shot ratios. 

In order to develop our playmaking metric, we first develop an “altruistic contribution” metric for players that is based on shots.  It is basically the difference in shots taken by a player’s teammates (excluding the player’s own shots) when he is on the ice versus off the ice.  It’s kind of like a shot-based WOWY that doesn’t include the player's own shots.  This is a different approach from Vollman’s, but I imagine this gives similar results to Vollman’s estimated passes.  We'd have to take only estimated passes at even strength, and then divide by playing time at even strength (our metric is a per 60 minute statistic).   I haven’t checked this though.

Then, we combine this altruistic contribution with assists to form the playmaking metric. So the metric is based on both goals and shots, and has the two advantages over assists mentioned in the first paragraph.  

We'll finish Part 1 by discussing "marginal contribution" which is the first step in computing PLAY. 
Next article, we’ll talk about some of the background required to compute the playmaking metric, and look at some pictures like this:

Then, we’ll talk about the playmaking metric itself.  

Marginal Contribution

We start by defining a player’s “marginal contribution”, or his total contribution to his team.  It is similar to WOWY or WOWY-like analysis, which have been discussed in these seven places, for example. Marginal contribution m is defined like this:

m = GFon – GFoff

GFon is the goals scored by the team when player A is on the ice.  GFoff is computed by taking the average GFon of all of A’s teammates during only the times in which they are not on the ice with A.  But this average is actually a weighted average… weighted by time on ice with player A.  Some people average like this, and some don’t.  We chose this method so the stats of players who hardly play with A have a weight near 0 and do not factor into the computation of GFoff. 

In any case, you can just pretend this is WOWY, however you have seen it calculated, or however you calculate it yourself, and you’ll get the basic idea.  In fact, let’s just call it WOWY for the rest of these articles instead of marginal contribution.  Also, remember we are only considering offense, and only considering 5-on-5 play.

We could have chosen other ways to define marginal contribution. For example, we could have used Adjusted Plus-Minus (APM).  I prefer APM over WOWY (admittedly, I’m biased), but WOWY is faster to compute, especially when we do pairs of players in the future, so we went with that instead. 

The next step is that this WOWY will be divided into competitive contribution and altruistic contribution.  We'll save this for next time.

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