What is the objective value of an assist?

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For anyone that has ever seen Gretzky thread a pass over to Jari Kurri, it is obvious that passing is vital to offensive production, but how does it compare to actually putting the puck in the net? And what about the guy that is passing to the guy making the pass, how does he fit to all of this? Surely he is important as well; he gets a whole point for his troubles.

Since the 40’s, the NHL and NHL fans have at least implicitly accepted the notion that goals are equal to first assists and they in turn are equal to second assists. But as I discussed in an earlier post, because there are 1.7 assists per goal (in today’s NHL), using points as a proxy for offensive skill suggests that more than 60% of the offense is created by the two passers, leaving only 30 some for the goal scorer. This does not pass the sniff test. How often when you watch a hockey game do you even remember what the second assist looked like? Sure, sometimes there is a really nice breakout pass from the d-man, and the odd time someone quarterbacks the puck in the offensive zone to create a good scoring chance, but in general, second assists are not noteworthy and relatively not that important.

Some fancy stats, like Goals Created or Goals Versus Threshold (Gvt), have looked at making minor modifications to the 1:1:1 weighting system, but using little more than elementary reasoning to back their findings. Goals Created arrives at the conclusion assists are worth half a goal and Gvt comes up with 66%, but once again mostly using intuition.

Following Alan Ryder’s logic, I arrived at 1 : 0.5 : 0.25 as the proper weighting, but I’d like to put it to the test.

To better attack this question, leaving rhetoric aside, I decided to construct an experiment using persistence to measure the actual value of goals and assists.

Methodology

First, I found all players that played more than 300 even strength minutes in all five seasons from 2007-2012, in total just over 300 NHL players. Then, I calculated a sort of goals created per 60 stat for 2007-2010, and tried to see how well it predicted the same stat for the two seasons between 2010 and 2012. The caveat being, however, that instead of coming up with a reasonable sounding weighting and then testing the persistence, I would vary the weighting to try and find an optimum. My assumption, therefore, is that the better the persistence of a particular weighting, the closer it is to reflecting some sort of true offensive productivity.

*Note: As per Rob Vollman’s finding of predictability, in constructing the goals created stat I weighted the seasons 1:2:4, with the 4 weighted season being the most recent, 2009-2010.

Finding the value of a first assist:

I started with the following formula shell.

Experimental Goals Created = (Goals + (First Assists *(number between 0 and 100)) + (Second Assists *(0))

To control for usage and context I found the varied goals created stat per 60 minutes of even strength time on ice.

I calculated the goals created stat with first assists weighted 0%, then 5%, then 10%, and so on to 100, all the while keeping second assists at 0%. At each step I did a regression to see how well the first three years correlated with the final two and noted the r-squared value.

Here is the graph of the r-square values.

r-square 07-12 first assists

If we look at the curve, we see when first assists and second assists were weighted 0% (i.e, when we were just testing how persistent goals per 60 minutes played was), the persistence was around 72%. At the peak when first assists were valued at 54% of a goal the same figure shot up over 5% to almost 77%. This value is significantly higher compared to the persistence normally found with just goals or points individually, and suggests that a stat valuing goals: first assists: second assists at 1: 0.54 : 0 is a better indicator of offense than goals or points alone.

Now that I found a maximum, I could fix first assists at 54% and see if I could further bolster the persistence of the stat with the introduction of second assists, repeating the same methodology.

r-square 07-12 second

First thing to note is that yes, it is possible to increase the persistence, but only very slightly (note the scale on the y-axis). Second, second assists peaked in persistence around 19%.

So to answer the question, what is the value of an assist we arrive at 54% for first assists and 19% for second assists.

Just to be sure though, I repeated the experiment with using the seasons 2009-2014 and found similar results.

r-square 09-14 first

First assists in this sample peaked at around 56%, suggesting 54% to be a very reasonable weighting. Note: this weighting still increased persistence approximately 5%, but from 69% to 74%

r-square 09-14 second

Second assists proved to be more of a problem. This sample suggests that the optimal weighting should be at 11% and not 19% (in absolute terms however, there is very little difference between 0% and 30%). I believe there are several reasons for this. First, because 2012-2013 was a lock-out year the sample is reduced and more noise was introduced in the system. This partly explains the discrepancy we found with first assists as well, 56% versus 54%.

Second, it is a reflection on the nature of second assists. We should note that the data is rougher (as in not as statistically smooth) for second assists compared to the first assist graphs, and that the impact is significantly smaller. This, combined with the high variation of the two samples, echoes Eric T.’s conclusion that second assists may not be all that reflective of offensive talent at all. He showed that for forwards that changed teams season to season, there is almost no persistence at all with second assists, meaning that teammates, teams, and other transient factors were more responsible for second assists than any discernable skill.

So, how much is an assist worth. Well first assists are worth approximately 55% of a goal, and second assists are worth less than 19%. If I was to make a formula, I think until further proof manifests, it would be prudent to value them at 10% or less at least when evaluating a forwards offensive production.

I don’t think this means ditch the stat altogether. I think the stat may still prove interesting when evaluating defensemen and possibly even for approximating other passing skills, maybe offensive possession or neutral zone efficiency (not that I have any real inclination as to how this might be true). Information is information and although, I agree that we should not pretend that second assists are an indicator of any definite offensive skill, but they may prove useful one day.

Goals : First Assists : Second Assists

1 : 0.54 : < 0.19 (and tending towards 0 for forwards at least)

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