To Secondary Assist or not to Secondary Assist

Just over five years ago Eric Tulsky, who now works for the Carolina Hurricanes, published this article on assists. As you can see, he advocates dropping the secondary assist due to the amount of randomness in it (to be fair, I don't know his stance after publishing that). This is an older article, so I feel like I must as well update the numbers and the analysis and see what we find.

So I'm going to be using numbers from the past six years (2010-2016). I'm just going to do a simple year over year analysis like Eric did, but I'll split up between forwards and defensemen (I tried splitting up forwards between center and wingers but there was virtually no difference). Also the minimum amount players needed to have qualified for the analysis was 400 minutes for both years.

Repeatability

n	Position	A160	A260	A60
1402	Forwards	0.36	0.19	0.43
836	Defensemen	0.20	0.03	0.24

Here are the correlation coefficients for each metric. And I would say this all makes sense. First assists for both are more reliable than secondary assists. More so for forwards than for defensemen, for whom it's almost virtually random. And this is reflected in the total assists numbers. For defensemen it's only slightly higher than first assists. For forwards we see a a little bit more there. 

Of course this isn't it. Let's split up between players who stayed on the same team versus those who switched teams. As Eric T. noted, teammates play a role in assists, so numbers on players who change teams might be closer to the truth. So let's see:

n	Repeatability	A160	A260	A60
1020	Forwards-same	0.36	0.21	0.44
382	Forwards-Diff.	0.32	0.10	0.35
	Difference	-0.04	-0.11	-0.09
604	Defensemen-same	0.24	0.12	0.26
232	Defensemen-Diff.	0.06	0.02	0.11
	Difference	-0.18	-0.10	-0.15

And you can see that in all categories, players who stayed on the same team showed better persistence. Let's look at forwards: For forwards, first assists goes slightly down. But you really see it in secondary assists, where it takes a bit of a tumble. And this of course results in assists as a whole grading out worse for forwards who change teams. Defensemen, on the other hand, really have their numbers lose a lot. Secondary assists are virtually random when changing teams. And surprisingly first assists take a big hit too. I really didn't expect that much of a difference. 

One final thing though, let's look at what better predicts next years A60. First assists or total assists.

n	Predictivity	A160	A60
1020	Forwards-same	0.40	0.44
382	Forwards-Diff.	0.33	0.35
1402	All Forwards	0.39	0.43
604	Defensemen-same	0.27	0.26
232	Defensemen-Diff.	0.08	0.11
836	All Defensemen	0.23	0.24

As you would imagine total assists edges out first assists in all cases except, oddly, defensemen who stay on the same team. I won't put much thought into that, it's nothing. Also, the edge in each case is really small. I would imagine that this being only one year worth of data contributes to this. As you would imagine, after getting a few years of playing time we can make a better estimate of secondary assists.

Conclusion

The numbers here are, overall, close to the one's shown by Eric T. five years back. And I think the best bet when looking at assists is focusing primarily on primary assists. But secondary assists still matter a little. One year of assists tells us more than primary assists. Not by much, but there is something. And given a few years, we'll get a better judge of a players secondary assist "talent". Just looking at the leaderboards for secondary assist over the past few years will tell you that it means something. Secondary assists may contain a lot of randomness, but they still matter. The gain over primary assists is minimal, but they shouldn't just be discarded as noise (just mostly noise).

**All data courtesy of Corsica.hockey


***Update:

This is a good article on secondary assist-http://fivethirtyeight.com/features/some-nhl-stars-get-more-assists-at-home-than-they-deserve/. The next step would probably be adjusting for rink bias. Also this

@tangotiger SD of z-scores is 1.02, histogram suggests moderate skew/shift right pic.twitter.com/E2bf1jQYCH

— Michael Lopez (@StatsbyLopez) April 22, 2016

 is a good chart showing how small the spread of talent is in secondary assists. Even though it would have been better to do a separate chart for forwards and defensemen.