Another shot quality article? Of Corsi did!

So there have been some misconceptions lately about shot quality, I figure, or what the “Corsi” statistic is meant to capture. The Toronto Maple Leafs are the absolute centre of the “quality or quantity” debate for shots and it’s become quite a story surrounding the Leafs. Every game the Leafs play, whether they win or lose, seems to be a victory for Team Regression or Team Traditionalism.

On Tuesday, a Toronto Star reporter echoed and endorsed the belief of Twitter user @erndog44: “advanced stats guys say Raymond’s bad angle shot in 1st period is equivalent to that shot Kessel just sniped”Chris Boyle has taken to Sportsnet introducing his “shot quality project,” and while I’m interested to see the results, I don’t think that there’s a way to quantify the value of every individual shot taken in the last six years that properly explains whether there are teams that can affect shot quality enough to win games.

Bill James once wrote that statistics have the power of language, but there’s some curious mistranslations when it comes to Corsi. It is simply shot attempts for minus shot attempts against, and the story Corsi tries to tell isn’t that “all shots are equal, shoot from anywhere and you will get a lot of success”. That would be a poor strategy. Corsi is an approximation of zone timeJP Nikota, a fellow Maple Leafs blogger, went through Toronto games last year with a stopwatch, recording the amount of time the Leafs spent in their end versus the opponents’s end, and wasn’t able to find anything worth telling us that we didn’t already learn from Corsi.


In 2011-2012, the starting goaltender with the highest save percentage at even strength was Jaroslav Halak. He stopped 93.8% of shots. On the penalty kill, Halak stopped 86.8% of shots. In the shootout, he stopped just 71.9%, and that was the high end.

Nobody that uses data in any serious way would not be able to tell you the easy conclusion to this: when forwards have more room to move, it is easier to score goals on the goaltender. Shots in space, such as breakaways or two-on-ones, have a much higher expectation of going in than an unscreened shot from the point. Nobody, not even the most ardent Sabremetrician (I feel the name can be easily converted to hockey parlance. Jim Corsi is, of course, a goalie coach with the Sabres) would deny that it’s easy for a forward to score on a breakaway than a point shot. 

So, shot quality matters, yes?

It does. It matters a lot. Shot quality is likely the single biggest difference between teams in an individual game. The problem is whether shot quality is repeatable. Things get hairier there.

Are there teams that can convincingly create breakaways more than another team? The Leafs, by my count, have scored 5 goals on odd-man rushes this season started in the neutral zone including two against Anaheim. That hasn’t been the biggest source of their offence. Passes and rebounds in the slot have. The physical act of shooting is not the only thing that affects shot quality. Think of all the things that have to go right for a player to generate a breakaway opportunity. He has to be in the right place at the right time, and the opposition all have to be lined up in the exact wrong place. You have a better chance to score, but no coach will tell you that his or her strategy is to get a breakaway every shift. It’s simply not repeatable.

Here is Tyler Bozak’s first goal of the season:

Quality shot, yes?

In that case the “puck luck” aspect of the breakaway isn’t the shot. It’s what led up to it. After losing the faceoff, Bozak went up to cover the point man Andrei Markov. Markov in his career has been one of the steadiest defencemen on the planet, and probably the reason why his partners Sheldon Souray and Mike Komisarek got big contracts elsewhere that they never lived up to.

Markov mishandles the puck and gives it away:

Sometimes you hear “99 times out of 100, so-and-so buries that chance”. In this case, 99 times out of 100, Markov doesn’t just lose control of the puck.


The way I’ve mapped it out mathematically:

  • Puck possession + Luck = Scoring Chances
  • Scoring Chances + Luck = Goals

Not every extended possession will result in a scoring chance. You need to hope that a puck bounces off a leg onto your stick, that a defenceman blows his coverage or that the goaltender gets a bead of sweat in his eye that momentarily distracts him. Goals are random events that result for several reasons, not always because an opponent generated a quality shot, and almost always because an opponent took a shot on net.

Look at this goal the Leafs conceded against Carolina.

The Hurricanes carry the puck into the zone:

Jiri Tlusty loses control when walking it in and Carl Gunnarsson attempts to clear the puck around the boards:

It’s cut off by Justin Faulk at the right point and he throws the puck on net:

This is funny. The puck hits Carl Gunnarsson in the leg. You can’t really see it, but you can tell by Faulk’s release that he didn’t shoot the puck particularly hard:

The puck bounces into an open area:

Right onto the stick of Eric Staal:

After the game, everybody wanted to discuss the goal that went in off of Jonathan Bernier for the winning goal. The freak goal. It made for a better story. I think the Staal goal is a better explanation of what happens when the hockey gods catch up to you, because it’s the sort of goal that happens dozens of times a year.

That shot by Faulk certainly doesn’t have the same expectation for a goal as Tyler Bozak’s breakaway, or Eric Staal’s shot from the high slot. It did, however, extend the Hurricanes’ possession for a tiny bit, enough for the Hurricanes to capitalize off of a good bounce.


In Fooled by Randomness Nassim Taleb brings up the monkeys-and-typewriters saying. “If one puts an infinite number of monkeys in front of (strongly built) typewriters, and lets them clap away, there is a certainty that one of them would come out with an exact version of the Iliad.” Taleb writes as a follow-up: “Now that we have found that hero among monkeys, would any reader invest his life’s savings on a bet that the monkey would write the Odyssey next?”

The Leafs are taking higher quality shots than their opponents right now. It helps that Phil Kessel, James van Riemsdyk, Joffrey Lupul and Nazem Kadri all play in their top six. It helps that they have offensive players that have slightly harder or more accurate shots that go in, and that all the players have the necessary speed to really open up the ice.

But will they continue to out-shoot their puck-possession problems? That’s a little dicier. It’s been successful for the last 58 games or so. That said, the amount of shooting percentage an individual team can repeat in the last few years is very low. Only a fraction of the percentage in one year can carry over to the next year.

What will be interesting is if Toronto indeed continues to shoot like this. Is it because the players are skilled? Is it because the system is designed to enhance the quality of opportunities? Have all the players gotten particularly lucky? Every explanation could be valid at this point, but the real question to me is where the team will be in March.

I think we have to wait until then to make judgments on how plainly right or wrong the analysts were and if the Leafs can continue to shoot higher than 10% at 5-on-5 (they’re at 9.42% so far) then we can dig further into figuring out what special potion the Leafs have that make them so successful. Basically, let’s see what happens when they try to write The Odyssey before we form conclusions about their play.


  • The problem I see here is that we have a statistical study of SH% or PDO that is valid normal distribution for an entire population.

    Where things are not clear is the application of the that study to an individual or subset of the population. Does an subset or individual regress to the mean of the entire population.

    As a poor analogy consider height of different populations. The entire population is on average 1.6m. If we take a small sample we might see the average height is 1.5m or 1.8m but with enough sample size the population will regress to the mean.

    Now here is the twist, if we only sample residents of Guatamala for example, the average height will be 1.4m and no amount of increasing sample size will regress the mean to global average 1.6m

    Now I have no idea if the leafs are able to consistently control shot quality. The problem we face here is that it is difficult to separate skill from luck for an individual team due to sample size limitation. And we actually require multiple seasons to gain confidence if for example the leafs or another team could control shot quality. And with changing personnel we have too many moving parts to make any valid statistical inference. That said, we shouldn’t “assume” that subsets of the population will regress to the mean of the global population.

    To summarize, the question to answer is under what conditions is it appropriate to apply the global average calculated for an entire population of PDO or SH% to an individual team. Always, sometimes and are their exceptions? The point being, is that if we don’t ask good questions, then our own bias from misapplication of statistic may produce misleading conclusions.

    These kind of difficult question gets closer to the crux of the debate.

    • This is a very valid point.

      Just commenting here because I think it is worth addressing and I could do it further in depth.

      Just to quickly comment on distributions, though. The human population and NHL PDO numbers are a little different. The human population on average may be a certain height, but from observation we can see people that are a foot taller than others and we don’t even blink.

      For PDO numbers? The observed talent of shooting and save percentages is minimal. We’re not so much looking at an average, but we’re looking at nearly every PDO number being within a certain range, and the PDO numbers outside the range wound up creeping inside. The talents weren’t repeatable.

  • MaxPower417

    One more detail there is much focus on the leafs above average SH% but most of the statistical work has been completed for PDO. That said, if the leafs SH% falls and regresses which I would not want to bet against, we should expect the leafs ES SV% to regress upwards as it is slightly below average to help offset the declining shooting percentage.

    And like I commented previously, the leafs above average PP/PK and SH% has only contributed to the leafs winning one more game (less then two points) then they should based on their current PDO. That is, they have not out performed expecations or been “lucky”.

    Said differently, the leafs have not benefited from luck as much as we may believe. So yes the team may very well regress in terms of SH% and PK% or PP% but provided they don’t face “bad luck” outlier event their is not much to support that the leafs points total will regress. Though until we get 20 games of data anything is in the realm of small sample size.

  • MaxPower417

    “What will be interesting is if Toronto indeed continues to shoot like this. Is it because the players are skilled?”

    Yes, I think that is what the Leafs are…lots of guys that are consistently high percentage shooters. Some had good numbers even before they became Leafs.

    Lupul is a career 11.7% and 14.9% as a Leaf. He also had a 15.9% year with the Ducks.

    Kessel is amazingly consistent at around 12.5% in the last 140 games.
    JVR is 11% career and 12.9% last year.
    Bozak is a career 15.9% over 248 games
    Kadri is a career 14.4% over 109 games.
    Even Mason Raymond is well above the average at 9.6% over 384 NHL games.

    The killer is Bolland, a career 14.5% over 342 games! When your third line center is shooting like that, you can have three lines with high percentages.

    Add in the fact that Carlyle doesn’t play his low percentage, 4th line guys in the third period and you have the potential for a consistently high team shooting percentage.

  • MaxPower417

    Good read Cam. Just to address the scenario above, I think people still need to realize that not all shots/corsi events are good decisions. Why waste a shot on not when far out, and no traffic is in front? That usually just results in giving the other team the puck, just like a dump in. Or, worst case, you end up providing the 2nd assist on a goal by the opposing team as seen Tuesday when Winnick missed the net and sprung jvr on a two on one with Kessel. The more teams start to lean on this method of tracking the puck possession of a player, players will start ro realize this and begin forcing shots that shouldn’t be taken, which is not a good strategy.

  • MaxPower417

    I liked this article. Very interesting stuff.

    I have to respond to one of your quotes though:

    You say “Is it because the players are skilled? Is it because the system is designed to enhance the quality of opportunities? Have all the players gotten particularly lucky? Every explanation could be valid at this point, but the real question to me is where the team will be in March.”

    To me, the notion that the third possibility is as valid as the others is simply impossible. There’s just no reason to think that good bounces and good fortune have been consistently doled out to multiple players on the Leafs over ~50+ games. I don’t see this explanation as being valid. Luck is neither consistent nor evenly distributed across individuals.

  • MaxPower417

    Actually, what Bill James said is this:

    “…baseball statistics, unlike the statistics in any other area, have acquired the powers of language.”

    The point he was making was that things like batting average and ERA (the “old” statistics) had acquired the powers of language by virtue of the fact that people had become familiar with the underlying concepts. James’ point was that most statistics could not be said to have acquired the powers of language.

  • MaxPower417

    So explain to me how the Leafs are 7-3 with this horrible system that Carlyle has implemented that messes with their Corsi, which is unthinkable. At what point are you going to bite the bullet and admit you’re wrong? I’ll check every 10 games or so.