Review: zone start adjustments to shot differential

Eric T.
November 05 2012 07:26AM

Malhotra faceoff
Little known fact: Manny Malhotra personally funds 60% of the research into zone start adjustments
Photo by Matt Boulton

Note: In conjunction with the NHL Numbers reference library, we will occasionally be publishing review articles aimed at establishing the contemporary understanding of an area and highlighting opportunities for additional research.

Today is the five-year anniversary of what I believe is the first published list of how often players took offensive or defensive zone faceoffs, and with it in the comments came the question of how zone starts might affect their on-ice shot differential.

There have been a lot of attempts to answer that question over the last five years. In this review article, we will touch on some of them and then make our own recommendation.

The beginnings

The first look at quantifying the impact of attack zone faceoffs came from Vic Ferrari looking at how many goals follow within a minute of a 5v5 faceoff. Whether he restricted it to having all ten skaters still on the ice for the goal or whether he allowed most of them to change, either way about 2/3 of the goals were scored by the team that took the draw in the offensive end. This strongly supported the notion that a player's usage could have a significant impact on his results and opened the door to trying to quantify how large that impact could be.

In his next post on the topic, Vic reported that each defensive zone draw decreased a player's Fenwick shot differential by about 0.6 shots and calculated the first zone start-adjusted shot differentials, looking at the Oilers' adjusted Fenwick. Matt Fenwick used 0.6 shots per faceoff in looking at the Flames' adjusted Corsi. JLikens reasoned that since blocked shots represent about a quarter of the Corsi events, the 0.6 figure calculated for Fenwick (which excludes blocked shots) should probably swell to 0.8 for Corsi (which includes blocked shots), and he published a league-wide adjusted Corsi chart.

And from there, the idea took off. If you search Google for zone start adjusted Corsi, you will get literally hundreds, maybe thousands of results that use this approach.

It has always bugged me that we don't really know where the 0.6 figure came from; Vic just asserted it without any explanation. My guess was that he used the same methodology as in his previous post looking at goal rates, counting how many shots were taken between the faceoff and the player leaving the ice and averaging across each player-faceoff, but we don't really know.

One goal of these review articles is to highlight holes in the literature that bear further investigation. In most cases, that will be wrinkles that have not yet been explored. Here, I think simply reproducing and confirming Vic's work would be of value, since so much subsequent analysis has been based on it.

Alternative answers

Although the Ferrari/Likens approach is by far the most widespread, a number of other investigators have gotten involved.

Dirk Hoag used a regression of season totals, looking to see how many more shots went to the players who often started in the offensive zone. He found that each additional offensive zone start correlated with an extra 1.1 Corsi shots. I could imagine that this approach might overstate things slightly by assuming more causation than actually exists -- since more teams deploy their top-line in the offensive zone than in the defensive zone, the skill of those top-line players will make offensive zone starts look more beneficial than they really are. So this estimate might be a bit high, but serves as a reasonable upper bound.

The same issue plagues my own look at comparing players to similarly-deployed peers. In that approach, I looked at the Corsi or Corsi Rel of players with similar offensive zone starts as an empirical baseline for what we should expect of someone in that role. The result is similar in many ways to the direct correction, but like the regression approach it cannot distinguish correlation from causation -- Patrice Bergeron might have done way better than most players with 42% offensive zone starts, but that's at least partly because that isn't a list of top-tier comparables.

JaredL observed that teams get about 40 shot attempts per 60 minutes between an offensive zone faceoff and the first line change, and the advantage almost completely dissipates by the time a single player leaves the ice. He used this to make corrections for how a player was used, with less influence from usage than was observed in the other approaches. A reasonable approximation to his corrections had a player's Corsi/60 going up by about 0.18 shots for every percentage increase in offensive zone starts.

This approach reduces the concern about player usage considerably. There could still be some skew if the best players take a lot of offensive zone faceoffs, since they would tend to outplay the lesser opponents who take the defensive zone faceoff, and some of their superior skill would be lumped into the assessment of how valuable an offensive zone faceoff is. However, the skew would be confined to the fraction of a shot extra that they generate in that brief period, whereas using their whole-game statistics as Dirk and I did results in their superior play throughout the game all being factored into the importance of the faceoff.

Thus, Jared's approach is superior, and is similar to what I imagined Vic did. But to see whether his correction is the same as Vic's, we need to convert Jared's result to a shots-per-faceoff number.

There are two ways to do that. The first is to use Jared's approximation that a 1% increase in OZ% leads to a 0.18 increase in Corsi/60. The average player who plays a full season is on the ice for a little under 1200 minutes and gets about 700 attack zone faceoffs, so plugging through some arithmetic leads us to the conclusion that each extra offensive zone faceoff was worth about 0.25 shot attempts (1190 minutes * 0.18 shots per 60 = 3.6 extra shots; 1% increase in OZ% = 14 extra OZ starts; 3.6 / 14 is about 0.25).

Alternatively, we can work directly from the raw data. If almost all of the advantage comes from that period before a player leaves the ice, and we know the rate of shot generation during that period, we just need to know how long that period lasts to estimate the value of the faceoff. Since Jared reported that teams spend just over 900 minutes in that timeframe, and we know they take about 2200 attack zone faceoffs, again with a little arithmetic we can work out a benefit of about 0.27 shot attempts per faceoff (900 / 2200 = 0.4 minutes per faceoff; 40 shots per 60 post-faceoff minutes = 0.67 shots per minute; 0.4 * 0.67 = 0.27).

These numbers are much less than the figure of 0.8 shot attempts that grew from Vic's assessment. I had guessed that Vic's method was similar to Jared's, but the disparity in their results leaves me uncertain what Vic actually did. Let's look at some other methods for assessing the impact.

David Johnson showed that the impact on Fenwick can be almost completely negated if you throw out the first ten seconds after an attack zone faceoff. This also doesn't give us a direct comparison, but since he publishes stats with this correction on his website, we can work things out for ourselves.

We can pull the corrected Corsi from his site and pull the total Corsi and number of offensive or defensive zone faceoffs from behindthenet.ca. Subtracting the former from the latter gives an indication of how a player's Corsi changed as a result of this approach to zone start correction. A regression of this correction factor against the number of extra offensive zone starts the player had gives a slope of 0.35 shot attempts per faceoff, regardless of whether you include all players or just the full-time players. This is a bit higher than Jared's estimate despite using a similar approach, but they are in agreement that the widespread estimate of 0.8 shots is too high.

Yet another approach comes from our zone entry data. I have not published data on faceoffs since a midseason review, but one of the things zone entry data lets us do is count how many shots come between the faceoff and the first time the defense clears the puck. For the Flyers' games, that figure was 0.31 Fenwick shots; for the Wild's games it was 0.32. There could conceivably be an influence that extends beyond the clear, but in practice we see nearly equal results once the puck leaves the zone. So an offensive zone faceoff increases your Fenwick For by about 0.31-0.32 shots, which means it probably increases your Corsi For by about 0.4 shots.

Where we go from here

The next step would be to remove the last vestige of sampling bias from our analysis. The approaches that focus on the period immediately after the faceoff reduce the impact of teams' tendency to use their best forwards in the offensive zone, but certainly do not remove it altogether. An ideal study would go player by player and look at the difference between their average outcome after offensive zone faceoffs or defensive zone faceoffs. Averaging across players would remove the impact of player skill -- if a player did 0.6 shots better on the offensive zone start, this approach would not care whether he was a middling third-line forward who got +0.2 shots in the offensive zone and -0.4 in the defensive zone or a top-tier first-line forward who got +0.4 and -0.2.

Overall, no two estimates are in direct agreement, but the analyses that are known to derive from looking directly at the outcomes immediately following a faceoff converge in the range of 0.25 to 0.4 Corsi shots per faceoff -- one-third to one-half of the figure in widespread use. It is very likely that we have been overestimating the importance of faceoffs; they still represent a significant correction on shot differential, but perhaps not as large as has been previously assumed.

Previously from the reference library project

 

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Eric T. writes for NHL Numbers and Broad Street Hockey. His work generally focuses on analytical investigations and covers all phases of the game. You can find him on Twitter as @BSH_EricT.
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#1 Becanucks
November 05 2012, 01:24PM
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I think that part of the problem lies in purely linear correction, but I lack the time to try to adjust a saturated model... The Sedins aren't so bad as their adjusted Corsi would make us believe, but hey, what do I know, I'm a Canucks fan ;)

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#3 David Johnson
November 05 2012, 04:35PM
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@Eric T.

You have estimated that between a face off and the puck leaving the zone there are on average 0.4 shots attempts (corsi events) but can we conclude that this is the actual benefit of an offensive zone start? Shouldn't the benefit be increase in corsi events after an offensive zone face off above what we would expect during normal play (i.e. play not after an offensive zone face off)? If I have done my math right, a team is expected to get 0.014 corsi events per second during my zone start adjusted ice time (i.e. not including the 10 seconds after a zone face off), so if it takes 10 seconds on average to clear the zone, the benefit of an offensive zone face off is really 0.40 - 0.14 or 0.26 and not the 0.40 as you speculated.

I am just guessing on 10 seconds being the actual average time to clear the offensive zone but seems reasonable based on my 10 second nullifying zone start effects observation. If this is the case it brings you right in line with the conclusions you have drawn from JaredL's work.

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#5 David Johnson
November 05 2012, 09:49PM
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@Eric T.

Yes, I guess you are right.

I just did a regression similar to what you did with my 10 second stuff but I used a variety of different types of players over the past 5 seasons.

All Forwards >1000 minutes: Slope=0.26 r^2=0.50

All Defensemen >1000 minutes: Slope=0.33 r^2=0.57

All Goalies >1000 minutes: Slope=0.44 r^2=0.73

All players >1000 minutes: Slope=0.30 r^2=0.55

I am not sure what to make of the fact that the slope increases so much from forwards to defensemen to goalies with the r^2 increasing as well except maybe this addresses some of your "where do we go from here" comments. Defensemen are less likely to be line matched and less likely to be zone start biased than forwards and goalies are not line matched or zone start biased at all and as you move down the list you approach something closer to the true zone start effect.

What is interesting is the goalie slope of 0.44 is essentially derived from a team measure and this is very close to your 0.40 estimate which is also derived from a team measure. Makes me think somewhere around 0.40-0.45 is closer to the true effect. I am guessing the slope among forwards (and to a lesser extent defensemen) is lower because the top offensive players when they are put on the ice in the offensive zone face the top defensive players, and the top face off guys which is suppressing their offensive zone boost on an individual level.

Finally, like you I didn't find much difference when using regulars vs using everyone. Forwards >2500 minutes had a slope of 0.26 and a r^2 of 0.51 which is almost identical to forwards>1000 minutes (see above) and forwards>500 minutes (slope=0.26, slope=0.50).

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