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.

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 = GF

_{on}– GF_{off}
GF

_{on}is the goals scored by the team when player A is on the ice. GF_{off}is computed by taking the average GF_{on}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 GF_{off}.
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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