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# The interesting way that the Corsi spread has tightened in the NHL

What does it tell us about the next frontier of hockey analytics?

### A look to the past

In a few places, I’ve seen the theory that as ideas like shot attempts become more engrained into NHL front offices, and players who tilt the ice in their team’s favour become appropriately valued, that the spread in shot attempt ratio across the league is becoming tighter and tighter. In other words, the gap between the best and worst Corsi teams is getting smaller. Certainly, there is some evidence for this claim.

### Spread of shot attempt ratio

Year Standard deviation of shot attempt ratio
Year Standard deviation of shot attempt ratio
2017/2018 2.45
2016/2017 2.38
2015/2016 2.79
2014/2015 4.08
2013/2014 3.82

This makes it seem pretty straightforward, and in some sense, it is. The spread has narrowed over the last five seasons, though it’s worth noting that the standard deviations recorded in each of the last three years are not significantly different from one another (in a statistical sense). It’s also important to look a little more deeply and examine why this measure of spread is getting smaller. The way we (or at least, I) tend to think of convergence is that everyone is uniformly moving closer to 50% shot attempt ratio, which represents true parity.

However, this isn’t necessarily the case. We can do something simple and heuristic to examine where the convergence is coming from. This is not fully robust, for a couple of reasons that I won’t bore you with, but I think it’s sufficient to get the point across. Below is a table that tracks how the top ranked, 5th, 10th, 15th, 20th, 25th, and last ranked team in shot attempt ratio has performed in that metric in each year.

### Tracking CF% of ranks over time

Rank 2013/2014 2014/2015 2015/2016 2016/2017 2017/2018
Rank 2013/2014 2014/2015 2015/2016 2016/2017 2017/2018
1 57.41 55.81 56.98 55.19 54.38
5 54.58 53.54 52.71 51.9 52.62
10 51.39 52.33 51.54 50.93 51.69
15 50.44 51.35 50.36 50.52 49.82
20 49.16 49.43 48.15 49.62 49.17
25 47.34 47.19 46.9 47.67 47.82
Last 40.15 36.28 44.08 44.17 44.95

If you’re more of a visual learner, I’ve got you covered.

There are a couple things I want to point out here. First off, note the scales. We’re talking about a pretty small shift, all things considered. This is perhaps the most important part of this graph! Secondly, note how over the last three seasons, the convergence is pretty muted.

The most obvious thing here is how much better the ‘worst’ teams are. Part of that is due to the Buffalo Sabres impressive commitment to making sure they got the best lottery odds in those seasons. But even excluding the Sabres, the two or three worst teams from 2013 to 2015 were far worse than they are now, at least by shot share. This is one area where the spread has definitely converged dramatically, whether it’s due to the reduced incentive for tanking (which took effect in the 2015/2016 season) or other reasons. On the other hand, the convergence of the top ranked team is not quite as dramatic. This is true even if you exclude the Sabres; the worst teams besides the Sabres in the early years are in the 42% range.

The 15th, 20th, and 25th ranked teams are essentially constant in performance across the entire sample range. The 10th ranked teams exhibit a little more variance, but the pattern seems idiosyncratic over the past three years, rather than persistent. Finally, the 5th ranked teams exhibit the same mild convergence as the top ranked teams, though they are largely constant over the last three seasons. You could run hypothesis tests comparing the ranks of teams across years, but you wouldn’t find anything contradicting the above paragraph - none of the visually uninteresting lines in the chart above are statistically significant.

I also want to point out that teams in the same year are not independent from one another. The worst ranked team is an opponent of the other teams, meaning other teams get to beat up on them. If the worst ranked team is especially bad, you’d expect the other teams to have slightly inflated shot shares as a result. What this means is that the convergence of bad teams towards 50% might also be partially responsible for the milder convergences we see near the top of the league. This could be an area for future study.

So, what’s the takeaway on the claim I started this off with. Well, shot attempt ratios have converged over the last five seasons. However, we’ve seen no obvious pattern in the last three seasons. As such, it’s not clear to me that this convergence is continuing.

The above figure tells us the relative frequencies of teams with various levels of shot share in each of the three most recent NHL seasons. Apart from 2016/2017 being incredibly tight (which probably helped generate this talk about the narrowing of the spread of shot attempt ratios), there aren’t many significant differences. The following season was also similar in spread to 2015/2016. As such, it seems difficult to say with confidence that there is still a converging of shot attempt ratios across teams.

As to where it’s going from here? Well, this leads to my next thought.

### ... and now to the future

My guess (and this is very much a guess, not based on anything mathematical) is that we will see seasons fairly similar to the three that just passed in terms of the spread of shot share. This means that teams will be tight in terms of shot share. More and more, what I think teams will invest in, and where they can find huge returns is in the ability to manufacture higher efficiency shots (i.e. shot quality). A sustainable edge in shooting percentage can go a very long way. While it’s generally accepted that most players do not exert significant control over their own (or linemates’) shooting percentage, there are some that do. I think they’ll become even more valuable in a post-2016 world where the spread of shot share is smaller than it was during the Enlightenment Era of 2007 - 2015. This is where we are thankful for Auston Matthews.

More significantly, I think coaching will turn towards systems that generate more high quality chances, in a sustainable way. We’ve already seen teams like the Leafs completely remove point shots from their diet, and focus on working the puck into the slot more. This is an area where tracking data for both the players and the puck will be incredibly useful. What sequences lead to high-end chances (due to Ryan Stimson’s work on The Passing Project, we already have some idea)? What plays are being overused? These are the sorts of answers that I think we’ll have to generate next in order to get a better understanding of how teams are differentiating themselves. As soon as the NHL makes that data available, it will be an arms race, in the public sphere. Among NHL teams, it already should be.