# Introduction to Advanced Hockey Statistics: Corsi Number

Before I begin, I want to point out that I am by no means an expert in this and some of you might already know all this and more. However, since we have never really discussed advanced hockey statistics on this blog, I thought that an introduction to the various metrics would be useful. All data used in this site is from Behind The Net, an excellent source for hockey statistics.

Beyond goals and assists, how do we know if a player is 'doing well'? Since 1967, the NHL has been tracking plus minus, which is essential a difference of goals scored and goals against while a player is on the ice, not counting power play goals. However, this isn't always the best indicator of performance, especially because of its dependence on goaltending.

An alternate to plus minus is what is called a Corsi number. It can be summarized as the difference in shots attempted by the player's team and the shots attempted against the player's team. While it can be done for all situations, typically Corsi Numbers are only used for 5 on 5 play. All of the Corsi Number calculations in this article will be for 5 on 5 play.
Corsi Number = (Shots on Target For + Missed Shots For + Blocked Shots Against ) - (Shots on Target Against + Missed Shots Against + Blocked Shots For)

This is essentially measuring puck possession. Not only does it consider shots that hit the target, but also shots that went wide or high, or shots attempted that were blocked. This is because even if the shot was missed or blocked, the team still had possession in order to be able to attempt a shot on goal. An alternate to Corsi Number is a Fenwick Number, which doesn't consider blocked shots. I prefer the Corsi number because from an offensive point of view, it represents gaining possession in the zone and at least creating enough space to attempt a shot. From a defensive point of view, even if the shot was blocked, the need to block the shot was created and thus I view this as a negative event from a possession point of view.

Now obviously the better teams in the league will generally dominate play and you would expect this metric to be dominated by the league's best clubs. To account for this, a new Relative Corsi Number is calculated as follows:
Relative Corsi Number = Corsi Number of player - Corsi Number of Team when player not on ice

All of these metrics are scaled to a per 60 minute basis when considering aggregates. Click after the jump for an example as well as more definitions and an analysis of the 2010-2011 Senators.

Let's do an example and calculate Erik Karlsson's Relative Corsi from the 2010-2011 Senators. All the data is per 60 minutes.

• Karlsson was on the ice for 2.04 goals for, 3.04 goals against, 29.0 saves for, 29.1 saves against, 11.6 missed shots for, 10.3 missed shots against, 16.0 blocked shots against and 12.9 blocked shots for. Note that saves for are shots on target that weren't goals, so Karlsson was on the ice for 29.0 + 2.04 = 31.04 shots on target.
• So, his Corsi Number = (2.04 + 29.0 + 11.6 + 16.0) - (3.04 + 29.1 + 10.3 + 12.9) = 3.3 or without rounding individual components, Karlsson actually has a Corsi Number of 3.27
• When Karlsson isn't on the ice, the Senators score 1.98 goals for, 2.70 goals against, 26.3 saves for, 25.9 saves against, 10.7 missed shots for, 11.4 missed shots against, 12.4 blocked shots against and 13.2 blocked shots for.
• Karlsson's Relative Corsi Number = 3.27 - [ (1.98 + 26.3 + 10.7 + 12.4) - (2.70 + 25.9 + 11.4 + 13.2) ] = 3.27 - (-1.82) = 5.09 or 5.1.
• So what does this mean? It is saying that for every 60 minutes that Erik Karlsson plays 5 on 5 versus every 60 minutes that he doesn't play, the Senators will be better off by a net 5.1 shots attempted./

How does this compare with the Senators other defencemen (only considering 40+ games and finishing the season with Ottawa, sorry Chris Campoli).

 Rank Players Relative Corsi Number 1 Matt Carkner +6.8 2 Erik Karlsson +5.1 3 Filip Kuba -0.2 4 Sergei Gonchar -2.7 5 Brian Lee -5.2 6 Chris Phillips -11.0

A few things that probably jump out:

• Erik Karlsson and Matt Carkner are the only players with a positive number.
• Filip Kuba wasn't that bad, being almost even.
• Chris Phillips was in last place at -11.0./

Of course some players start in the defensive zone more often than the defensive, and thus this would bias their shot totals. One possible adjustment is outlined by Jlikens here, where each net offensive zone start is worth 0.8 shots and each defensive zone start is worth -0.8 shots. A neutral zone start is well, neutral. Now, I will state, while a Corsi Number has a clear definition, this adjustment for zone starts is experimental. Nevertheless, using the approach above yields:

Zone Adjusted Relative Corsi Number = Relative Corsi + [ 60 * (defensive zone starts - offensive zone starts) / (total 5 on 5 ice time in minutes) ]

After adjusted for this, the defenceman are ranked as follows:

 Rank Players Corsi Rel D-Zone Starts O-Zone Starts Ice Time Zone adj. Corsi Rel 1 Matt Carkner +6.8 163 163 637.6 +6.8 2 Erik Karlsson +5.1 297 396 1322.55 +1.5 3 Filip Kuba -0.2 250 301 998.08 -2.7 4 Sergei Gonchar -2.7 288 326 1137.77 -4.3 5 Brian Lee -5.2 182 174 738.45 -4.7 6 Chris Phillips -11 400 369 1404.03 -9.9

Technically, I think it might be necessary to calculate the zone starts when the player is not on the ice as well, and recalculate the Corsi Off-Ice Number based on the weighted ice time, however it is not possible for me to do this without the microdata.

The biggest drop here was Erik Karlsson, who had 57% of his non-neutral zone face-offs in the offensive zone. It is important to note that the order stays mostly the same, except that Carkner is further ahead of Karlsson. The Senators are still almost 10 shots worse off for every 60 minutes that Chris Phillips is on the ice for. So what kind of competition did they play against? To determine that, we define another metric, known as the Relative Corsi Quality of Competition, or Cori Rel QoC.

Corsi Rel QoC is the weighted Relative Corsi Number of a player's opponents.

For example, if a player plays 30% of the time against five players with a relative corsi of +1.5, 35% of the time against five players with a relative corsi number of +0.2, and 35% of the time against five players with a relative corsi number of -2.1 then:

Corsi Rel QoC = (0.3 * 5 * 1.5) + (0.35 * 5 * 0.2) + (0.35 * (5 * (-2.1)) = -1.075 (This is incorrect, thanks to Grant Jenkings for pointing this out)

Corsi Rel QoC = (0.3 * 1.5) + (0.35 * 0.2) + (0.35 * (-2.1)) = -0.215

This is how the Senators defencemen ranked:

 Rank Players Corsi Rel QoC 1 Chris Phillips +0.847 2 Filip Kuba +0.528 3 Erik Karlsson +0.491 4 Sergei Gonchar +0.161 5 Brian Lee +0.149 6 Matt Carkner -1.211

As expected, Chris Phillips faced the toughest competition. However, compared to the rest of the league, Phillips faced only the 29th toughest competition among NHL defencemen with 40+ games, implying that the Senators did not match up against the opponent's best lines as often as the other teams. Nicklas Lidstrom led the NHL with a Corsi Rel QoC of 1.807. Matt Carkner's Corsi Rel QoC of -1.211 was the fourth easiest among NHL defencemen, explaining his very high rating from earlier.

My conclusions from this as follows:

• Erik Karlsson did very well against slightly above average competition. While his defence may have been lacking at times, his offence more than made up for it. Karlsson with another year of experience should start pushing near the elite status of defencemen in the league.
• Filip Kuba was not as bad as Senators fans have made him out to be. He was by no means spectacular, but look for him to improve this year.
• Matt Carkner was given very easy and simple tasks, and he did them very, very well.
• Chris Phillips isn't being used against the opponents top lines as often as he was the year before. In 2009-2010, Phillips faced the 11th toughest competition with Corsi Rel QoC of 1.341, while teammate Anton Volchenkov was 7th at 1.400. I think Phillips will improve this year, but it might be worth considering to not play him against the top pairing all the time. Having said that, who else can do it?

However, Phillips was on a really bad team, so let's see how this compares to the other non-playoff teams in the Eastern Conference.

 Rank Players Team Zone Adj Corsi Rel Corsi Rel QoC Competition Rank 1 Travis Hamonic NYI +9.7 +0.729 7 2 Henrik Tallinder NJ +7.7 +0.636 11 3 Tobias Enstrom ATL +4.5 +0.417 14 4 Mike Weaver FLA +4.4 +1.381 2 5 Andrew MacDonald NYI +4.4 +0.379 5 6 Jason Garrison FLA +3.3 +1.412 1 7 Joe Corvo CAR +1.3 +0.646 10 8 Dion Phaneuf TOR -1.2 +0.724 8 9 Filip Kuba OTT -2.7 +0.528 13 10 Tim Gleason CAR -7.3 +0.705 9 11 Zach Bogosian ATL -7.7 +0.556 12 12 Chris Phillips OTT -9.9 +0.847 4 13 Keith Aulie TOR -12.2 +1.119 3 14 Anssi Salmela NJ -15.3 +0.736 6

• There are two ways to take this, the first is that the only two players below Phillips had played 0 and 64 career NHL games coming into the season. On the other hand, Phillips still faced the fourth toughest competition among non-playoff teams.
• Filip Kuba faced the second easiest competition (among the top two defenders) from non-playoff teams but still managed to be only ninth.
• While I don't know these teams intimately, not many of them seem to use a true 'shutdown' pair, instead playing their best overall defencemen against the top lines.
• What were the Leafs thinking playing a rookie defenceman against the toughest competition?

Statistics aren't everything and there is certainly a place for intangibles such as character or leadership. However, many other characteristics such as being 'clutch' can also be quantified and over the course of this season, we will analyze additional situation based metrics. I feel Corsi is a good metric for measuring net possession, whether it be how often a team gets into shooting position or prevents its opposition from doing so. As shown above though, it is important to look at a Corsi number in context and what it represents, as well as keeping in mind things like zone starts as well as the quality of competition.

Next week, I will have a similar article on the Senators forwards. Hint: Jason Spezza was very good and Daniel Alfredsson was not very good.

For more detailed information, please regularly check out Behind the Net, Arctic Ice Hockey, and Copper and Blue.

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Erik Condra
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