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## Friday, 24 July 2020

### Counterpasses and Rebounds - The Five Goalie Outcomes

We’re used to looking at what goalies do in terms of only two outcomes: did the puck go in or not? Every save is a victory and every goal a defeat. That’s too simplistic because there are things that a goalie can do to either prevent additional shots once a shot has been taken or to punish offensive teams for taking shots. It may even be possible to reduce the quality of shots before they are taken.
In this article, we will consider the first two cases: mitigation and counterpasses.

Preliminaries
From the Sportlogiq event data of ~4000 events/game (passes, receptions, loose puck recoveries (LPRs), zone entries, etc.) we derive  ~450 possessions/game based on the markers 'isPossessionEvent' and 'isDefensiveEvent' already in the event data. If a team performs a possession event, that team has possession; if a team performs a defensive event, we know that the other team has possession. Then we look at the first and last events from each possession, and mark each one as a transition. We're specifically interested in 'shot-to-X' transitions.
We count a defensive rebound as a shot-to-lpr transition - where one team ended their possession with a shot, and the other team started their possession with a loose puck recovery (LPR).
LPRs count as possession events. At the recovery event is when we start the clock on possession length.
Whistles. Any stoppage in play is a break in possession. We count shot-to-faceoff transitions as goalie stoppages. (goal-to-faceoff is counted separately)

We count offensive rebounds as any rebound that keeps possession in the offense. So that's any time there are multiple shots for the offense in a possession, and any time that a shot happened but was not the final event of a possession.Also apart from either rebound is the counterpass, which is where the goalie definitively gains control of the puck and passes it to a teammate. (i.e. shot-to-pass transitions between possessions)

The Five Outcomes
First, let’s consider some preliminaries about shooting.
In the 3,000 games of the 2017-18, 2018-19, and start of 2019-20 regular seasons in regulation time, teams experienced the following (including empty netters, excluding blocked and missed shots)
Table 1: Shots, shot attempts, and goals.
 Home Away Total Shots on Net / game 32.82 31.68 64.50 Shot Attempts / game 63.49 61.20 124.69 Goals / game 3.09 2.81 5.90 Goals / Shot 9.41% 8.87% 9.15% Goals / Attempt 4.87% 4.59% 4.73% Shots / Attempt 51.69% 51.77% 51.72%
We know that about 52% of shot attempts become actual shots on net, whereas the rest are either deflected by other players or misses (as in, they wouldn’t have been goals even without a goalie). We also know that 9.15% of shots score, but otherwise we’ve simplified the other 90.85% of shots as ‘not goals’. The event data also has records of things like loose-puck-recoveries (lpr), passes, and zone entries which we use to break down those saves into four categories based on what happened after the save.  Loosely best to worst, these are:

1. counterpass: The goalie immediately takes control of the puck and passes it to a teammate.

1. Stoppage: The goalie immediately covers the puck or otherwise creates a stoppage in play.

1. Rebound to defense: The goalie never controls the puck, but deflects it such that offensive possession ends.

1. Rebound to offense: The goalie never controls the puck, and it is deflected back into offensive possession.

Using these goalie outcomes, there are three natural  ways to count "rebound share" without including goals.

Method 1: (def rebounds) / (def rebounds + off rebounds)
Method 2: (def rebounds + counterpasses) / (def rebounds + off rebounds + counterpasses)
Method 3: (def rebounds + counterpasses + 0.5*stoppages) / (def rebounds + off rebounds + counterpasses + stoppages)

Method 1 only considers shots for which the puck was never considered to be in possession of the goalie, and takes the proportion of those that were recovered by teammates.

Method 2 also includes counterpasses as if they were good rebounds. The outcome of counterpass is similar to the defensive rebound in that the defending team receives the puck, the goalie has a more deliberate contribution as well as tactical choice of the receiving player.

Method 3 takes Method 2 and also includes stoppages as half a ‘good’ rebound and half a ‘bad’ rebound, based on the assumption that each faceoff is a 50-50 coin toss. Even for cases where one team is significantly better or worse at faceoffs than the other, that ability shouldn’t be attributed to the goalie when they stop play.

For the 64 goalies that have faced at least 1000 shots in our data the measures from all three of these methods are strongly correlated with each other (Pearson r = 0.934 to 0.999), and all three have negligible correlation with save percentage (Pearson r = 0.060 to 0.068). Unless otherwise specified, rebound share is calculated using Method 3.

Examining shot outcomes as five possibilities instead of two gives us the following table. Notice that we’re not considering shot attempts throughout most of what follows, that’s because we’re trying to focus on events that can be directly attributed to goaltending.

Table 2: The five outcomes, home and away
 Per Game \ Goalie Home Away Total % of Total Shots on Net 31.68 32.82 64.50 100% counterpasses 1.66 1.57 3.24 5.01% Stoppages 8.90 9.13 18.04 27.97% Rebound Defence 8.58 8.84 17.41 26.99% Rebound Offence 9.72 10.19 19.90 30.85% Goals 2.81 3.09 5.90 9.15%

What do we learn from this?

* The home team faces 3.5% fewer shots than the away team. Similarly, they produce 2.5% fewer stoppages and 3.9% fewer rebounds.

* The home team produces 5.7% more counterpasses, or about 9% more counterpasses per shot, than the visitors. That can be explained in breakdown by manpower situation in the next table.

* The home team also scores 10% more goals than the visitors, but that’s covered in plenty of places elsewhere. Why not 3.5% more? Probably because they’re ahead more, and teams that are ahead take fewer, but higher quality shots. That part of shooting behaviour is covered in Hockey Abstract 2014.

* Counterpasses are rare. They’re rarer than goals, and a typical netminder manages to pull off an average of about 1.6 of them per game.

* Ignoring counterpasses, rebounds are split 53-47 in favour of the attacking team. That’s not dominance, but it’s not a statistical artifact either; there are more than 40,000 rebounds per season.

* Assuming faceoffs are 50/50, the average shot rewards the attacking team with 9.15% of a goal and costs them (27.97/2 + 9.15/2 + 26.99 + 5.01) = 50.56% of a possession.

What we did NOT learn is the context in which goalie actions like counterpasses and rebounds happen.
Context could be numerical advantage or disadvantage (i.e. the manpower situation), score situation, or distance to the net. We’ll slice the data each of those three ways in order. Other parts of context we’ll ignore for this analysis include whether attacks are part of a top line, whether there was a defender near enough to apply pressure, and whether Carey Price is using his Jedi powers tonight.

 Some say Price can see around corners and into the future.

Let’s break down rebounds and counterpasses by numerical advantage.
Intuitively, we might expect that teams on the power play should be able to collect a greater share of the rebounds because they have more players to pick up the puck after a shot. We might also expect the defending team to collect more of their rebounds because shorthanded teams on the attack is a rarity; it usually means something has gone wrong like a breakaway, but Table 3 tells a different story.

Table 3: The five outcomes by number of skaters
 Defender Situation Neutral PKill PPlay Total Shots 158766 28628 5972 counterpasses 7372 (4.64% of shots) 426 (1.49%) 1907 (31.93%) Stoppages 46348 (29.19%) 6897 (24.09%) 841 (14.08%) Goals 13320 (8.39%) 3796 (13.26%) 564 (9.44%) Total Rebounds 91706 17510 2659 Attacker Won 47511 (51.81% of rebounds) 11227 (64.12%) 934 (35.13%) Defender Won 44195 (48.19%) 6283 (35.88%) 1725 (64.87%)
When the defending team is on the powerplay and somehow still needs to rebound, it goes to a defender almost two-thirds of the time. We might remember the shorthanded breakaways more, but most shots are part of a time-killing strategy to make a line change.
When the defending team is at even strength, 4.6% of shots get converted to counterpasses. That changes dramatically depending on the numerical situation. When the goalie is on the penalty kill, that drops to a third the neutral rate, and when the goalie is on the power play, the rate increases to seven times the neutral rate. That reveals some of the nature of counterpasses: a lot of them are happening in response to the attacking team trying to ice the puck. Technically an icing still counts as a shot if it would have become a goal without goalie intervention, so a lot of these ‘counterpasses’ are merely low-pressure passes back to a skater during a line change.
Next, consider those 1.6 counterpasses per game. If every goalie was equally good at producing counterpasses (and faced an equal number of shots per game) then the number of counters per game should follow a Poisson distribution. Does it?
According to Table 4, the distribution table of counterpasses, there’s a clearly detectable difference between the uniform-goalies ideal of a Poisson distribution. On its own, that only means that goalies, are not clones of each other. Digging deeper, there are fewer 2-counterpass games and more 0-, 5-, and 6-counterpass games than clone-goalies would produce. In other words, there are fewer games in the middle and more at the extremes than simple statistics can explain.

Table 4: Table of distribution of number of counterpasses.

 counterpasses Number of Games % of total Expected Poisson 0 1064 21.87 1016.6 1 1609 32.17 1619.8 2 1204 24.07 1290.5 3 649 12.97 685.4 4 282 5.64 273.0 5 118 2.36 87.0 6 37 0.74 23.1 7 7 0.14 5.3 8 1 0.02 1.0 9 (or more) 1 0.02 0.2
Chi-Squared: 37.54 on df = 8, p < .00001  (Setting the cutoff at 9+)
Chi-Squared: 33.39 on df = 5, p < .00001  (Setting the cutoff at 6+)

#### Split by goalie

That’s a hint that some goalies are genuinely better at punishing a shot with a quick pass to a teammate than others. Who might these Frank Castles between the pipes be? This next table gives the 10 best and worst counterpassers among those 64 goalies that have faced 1000 shots in the study period.

Table 5: Best and worst counterpassers.
 Goalie Shots Faced counterpass % Goal % / SVG Mackenzie Blackwood 1119 7.33 8.85 / .9115 Jimmy Howard 3662 6.20 8.36 / .9164 Anders Nilsson 1820 6.10 8.57 / .9143 Craig Anderson 3558 6.07 9.58 / .9042 Aaron Dell 1978 5.97 9.76 / .9024 ... ... ... ... Corey Crawford 2827 3.68 8.95 / .9105 Laurent Brossoit 1200 3.42 9.75 / .9025 Cam Ward 2488 3.30 9.24 / .9074 Scott Darling 1675 3.16 6.93 / .9307 Anton Forsberg 1116 3.14 8.06 / .9194
Table 5: Best and worst counterpassers.
Let’s examine rebound share (using Method 3) and break down the results by individual goalie. In the 3 seasons we’re using, there are 64 goalies that have faced 1000 or more shots, which we’ll use an arbitrary cut-off finding the best and worst rebounders to avoid goalies that were only in net a handful of times. What can we say about these results?
Can we say anything about this? Specifically, are the differences between players’ rebound share large enough not to be noise? The weighted (by shots faced) mean of rebound share among these 64 goalies is .5092. The next table shows the number of standard errors (the z-scores) above or below that global mean each goalie is, using the standard error estimated from their rebound share and shots faced.
Using Method 2, we see a few goalies that are more than 4 standard errors above the global mean, which we wouldn’t otherwise expect to see in a dataset this small. Method 3 tends to compress rebound share towards 50% because it assigns half a defensive rebound and half an offensive rebound to each stoppage in play based on the assumption that stoppages matter and that the average team wins a faceoff 50% of the time. Using Method 3, these differences are no longer unusual for randomly generated rebound shares.

Table 6: Best and worst rebounders.

 Goalie Shots Faced Rebound Share Method 2 Rebound Share Method 3 SE(share) Mackenzie Blackwood 1119 .553 .538 .0149 Jacob Markstrom 4161 .546 .532 .0077 Jimmy Howard 3662 .545 .531 .0082 Anders Nilsson 1820 .534 .525 .0117 Casey DeSmith 1366 .534 .524 .0135 ... ... ... Carter Hutton 2919 .488 .492 .0092 Jordan Binnington 1677 .488 .492 .0122 Robin Lehner 3160 .486 .491 .0089 Martin Jones 4469 .485 .489 .0074 Laurent Brossoit 1200 .448 .465 .0144

Markstrom and a few others are legitimately better than par at punishing shots against him. There’s only one goalie that’s notably worse than the average in rebound share. On the surface, it doesn’t look like there isn’t much of a range from the best and worst in terms of rebound share. There certainly isn’t enough of a difference to make an attacker think twice about shooting against one goalie but not another. If you consider loss-of-possession to be the ‘cost’ of a shot, then it’s 1.1 times as ‘expensive’ to shoot against Markstrom or Howard as it is against Lehner or Jones.
We have a measure of the ‘cost’ of a shot. In save percentage we already had the ‘benefit’ of a shot. We can now put these together to get a cost-benefit tradeoff: how many turnovers is it going to cost to get a goal against a certain goalie?

We compute
shots/goal = 1 / (1 - save percentage)
And
turnovers/goal = (rebound share) * (shots / goal)
and show the best and worst 5 in our dataset in the following table:
Table 7: Most and least 'punishing' goalies.

 Goalie Rebound Share Method 2 Rebound Share Method 3 Save% Shots / Goal Turnovers / Goal RB Method 2 Turnovers / Goal RB Method 3 Scott Darling .513 .509 .931 14.43 7.41 7.34 Carter Hutton .488 .492 .926 13.57 6.62 6.67 Jack Campbell .516 .511 .920 12.48 6.45 6.38 Carey Price .510 .507 .920 12.53 6.40 6.36 Jimmy Howard .545 .531 .916 11.96 6.52 6.35 ... ... ... ... ... ... ... Laurent Brossoit .448 .465 .903 10.25 4.60 4.77 Frederik Andersen .513 .509 .892 9.29 4.76 4.73 Braden Holtby .500 .500 .894 9.42 4.72 4.71 Andrei Vasilevskiy .510 .507 .889 8.97 4.58 4.55 Louis Domingue .517 .512 .886 8.80 4.54 4.50
Unsurprisingly, save percentage (or equivalently, shots per goal) is the dominant factor in determining turnovers per goal. Save percentage matters so much that Carter Hutton, who was near the bottom of rebound share, is near the top for turnovers per goal. Compared to save percentage, rebound share is like a tiebreaker between goalies with otherwise very similar saving ability. Jimmy Howard has a slightly lower save percentage than Jack Campbell and Carey Price, but manages to match them in turnovers per goal by having a very high rebound share.
The numbers in Table 7  may look a bit unimpressive given there are 200 possessions per side per game (if you include the really short ones), but these are turnovers that are directly attributable to the goalie: defensive rebounds, counterpasses, and (half of the) stoppages. They’re also the lion’s share of the most important turnovers during a game.
A graph between save percentage and turnovers per goal demonstrates how important save percentage is to this composite score.

 Figure 1
As an aside, note how much better shots/goal accentuates the differences between goalies than save percentage does.  In this table it’s clear that Scott Darling is almost twice as difficult to get past than Louis Domingue, whereas save percentage reveals a more arcane difference of .045.
While rebound share is much less important than save percentage, it shouldn’t just be ignored. It describes a completely different aspect of goalie performance than save percentage, as shown in Figure 1. Considering both save percentage and rebound share together gives more information that save percentage alone.
 Figure 2

How do these two measures compare to each other? In the following scatterplot, each dot is a goalie in our set, where the X axis is save percentage and the Y axis is counterpass %.
It’s not clear what we’re hoping to see here. A strong positive correlation would show that counterpass is closely related to save percentage, and thus also be an indicator of goalie quality, however redundant.
Instead, we see almost no correlation at all (Pearson r = 0.034). Independence means that CA% and SV% are two independent facets of goalie behaviour. At worst it suggests that CA% is a useless curiosity stat, but at best it implies that CA% is a new dimension to evaluate netminders, like pitch framing ability was for MLB catchers.

 Figure 3

Maybe individual differences are too noisy, let’s instead group goalies by number of games of played during the study period. There are 64 goalies with 1000 or more shots faced, so we'll split these in half. Since we're no longer looking at individual goalies, we'll expand our scope to everyone who played 10 or more games between the pipes.

 Rank 1-32 GP Rank 33-64 GP Rank 65-90 GP Number of games (range) 79-151 33-76 10-30 Number of games (mean) 115.4 54.9 17.2 Shots Faced / game 32.3 32.2 32.2 counterpasses / game 1.60 1.60 1.69 Goals Allowed / game 2.94 2.96 2.89 Save Percentage (mean) .909 .908 .910 Rebound share (Method 3) .506 .507 .504

The uniformity is surprizing. What isn't apparent from the table is how the rank 65-90 goalies in games played are twice as variable in goals allowed per game.

#### Split by Distance

As long as we’re looking at saves through a five-outcome lens, we should also recreate a classic analysis. The figure below is the smoothed percentage of shots that become goals from each of the locations in the offensive zone. Basically, the shorter of a straight line there is to the net, the better.
The horizontal and vertical dashed red lines represent the mean shooting percentage and mean distance to the net of each attempt, respectively.

 Figure 4

If a typical goalie lets in 8-10% of shots, then why is the success chance of a shot attempt around 6%? Because a large portion of shot attempts are either blocked by another skater, or they miss the net and wouldn’t be goals even if there was no goalie. Figure 5 shows the proportion of shot attempts that never reach the goalie or the net.
 Figure 5

How frequent are the other outcomes at different shooting distances? Counterpasses are rare at any distance, and the relationship between them and shooting distance is noisy. In Figure 6 the dashed lines are the proportion of shots that get counterpassed and the mean distance to the net.

 Figure 6
Likewise, in Figure 7, which shows  stoppage probability over distance, the horizontal dashed line is the marginal probability of shot attempt resulting in a stoppage of play at any distance. As a portion of shot attempts, goalie-induced stoppages in play are more-or-less constant, but as a portion of actual shots, that proportion climbs from 20% at point-blanc to about 50% at 60 feet (20 metres).
 Figure 7
There are fewer rebounds as you go because ever fewer of the shots ever reach the goalie in the first place. If we only look atshots (Figure 9) and not shot attempts (Figure 8), the picture is different. Notice that defensive rebounds are rarer than offensive ones because we’re not considering other ways the defending team gets the puck like counterpasses and faceoffs.

 Figure 8

 Figure 9

Combining these two, how does rebound share (Method 1) vary by distance? There’s a lot of noise and no obvious trend, as shown in Figure 10.
 Figure 10

#### Season-to-season consistency

Rebound share may be noisy, but is it at least consistent for a given goalie from season to season? According to the next figure, no. This implies that the stat isn’t just tied to the goalie but to the defense as a whole. The Pearson correlation between the 17-18 and 18-19 seasons and the 18-19 and 19-20 seasons are 0.079 and 0.256 respectively, as shown in Figure 11. The equivalent Spearman correlations, which are more robust to extreme values, are -0.003 and 0.189 respectively. Either way, there’s no clear carry-over from season to season.
 Figure 11
This isn't just a weakness of rebound share, it’s a feature of goalie evaluation. Save percentage suffers from the same inconsistencies, as shown in Figure 12. For save percentage over the same pairs of seasons, the Pearson correlations were 0.001 and 0.166 respectively. The Spearman correlations were 0.028 and 0.244 respectively.
 Figure 12