Non-Traditional Metrics Glossary: Corsi

VANCOUVER, CANADA - JANUARY 2: Henrik Sedin #33 of the Vancouver Canucks looks to pass the puck while being checked by Dan Boyle #22 of the San Jose Sharks during the third period in NHL action on January 02, 2012 at Rogers Arena in Vancouver, British Columbia, Canada. (Photo by Rich Lam/Getty Images)

We continue our offseason series that looks at some of the non-traditional statistics we sometimes use to evaluate players and teams here at Fear The Fin. Follow me over the jump for today's feature on Corsi.

What is it?

Corsi is a team's even-strength shot differential, or a team's even-strength shot differential with a specific player on the ice if we're applying it to an individual. Instead of only using shots on goal, in an effort to both increase sample size and provide a more complete measure of on-ice activity, analysts include all shot attempts when calculating Corsi. Goals, shots on goal, shots that miss the net and shots that are blocked all factor into a team or player's Corsi number. For example, at even-strength last season, the Sharks directed 4090 total shots at the opposition net and had 3799 shots directed at their own. That means they were a +291 Corsi team last year, although it's generally more common for a team's Corsi number to be described with a ratio or percentage. Since, in total, there were 7899 even-strength shot attempts (or "Corsi events") during Sharks games last season and San Jose generated 4090 of those, the Sharks are said to have been a (4090/7899) = 0.518 or 51.8% Corsi team in 2011-12. During even-strength play, they earned 51.8% of the shot attempts.

Similarly, when Joe Pavelski was on the ice at even-strength last season, the Sharks directed 1358 shots at the opposition net and had 1118 shots directed at their own. This means he was a +240 Corsi player, a 0.548 or 54.8% Corsi player if you choose to express it as a ratio or percentage (meaning the Sharks earned 54.8% of the shot attempts when Pavelski was on the ice) or, as is most commonly cited, he was a +12.32 Corsi player per 60 minutes, a result obtained from dividing Pavelski's Corsi number by his even-strength ice time. This is beneficial since it eliminates the variable of ice time from the equation and allows us to more easily compare players.

Why is it called that?

Corsi is named after Buffalo Sabres goaltending coach Jim Corsi, who first devised the stat as a way of measuring the amount of work his goalies faced. The basic idea behind it was that while missed and blocked shots may not have a chance of going in, they still force goaltenders to remain alert and positionally secure.

What does it tell us at the team level?

Corsi is most commonly used as a proxy for puck possession, specifically puck possession in the offensive zone. The guiding principle behind its utility is the obvious fact that the puck has to be somewhere at all times and Corsi is the best indicator available of where the puck is since teams can't record shot attempts unless they have it. From 1999 to 2002, it was a lot easier to determine where the puck spent time in any given game as the NHL tracked zone time as an official stat. For whatever reason (likely because it must have been pretty damn hard to track in real time) they stopped doing so but, unsurprisingly, Vic Ferrari showed that a team's Corsi number correlated very strongly to the percentage of time they spent in the offensive zone for the years in which both sets of data are available. Corsi is important because, as we learned last week, with a few exceptions there isn't a very large team-to-team spread in shooting and save percentage during 5v5 play in today's NHL. The most sustainable component of a team's results is its shot differential, as Ferrari showed here by demonstrating that a team's 5v5 shooting percentage in one randomly chosen half of their schedule had no correlation to their shooting percentage in the remaining half, their save percentage in one half had a slightly positive correlation to that in the other half but that was far and away trumped by the repeatability of shot differential.

The main thing that needs to be accounted for before ascribing a team's talent level to their Corsi ratio is what's usually referred to as "score effects." Score effects describe the overwhelming tendency for NHL teams to play more conservatively with either a big lead or any type of third period lead, generally yielding the neutral zone with greater frequency and thereby allowing more shots. For example, although this uses Fenwick instead of Corsi (Fenwick, which we'll discuss later in this series, is just Corsi without blocked shots), only Pittsburgh, Detroit, Boston and Los Angeles outshot their opponents at even-strength last season when they were up by a goal and only Detroit outshot their opponents when they were up by two goals. Similarly, only Nashville failed to outshoot their opponents when they were down by a single marker and only Edmonton failed to do so when down by two. You can see score effects in action with this graphical depiction of a 5-3 Sharks win over Chicago last February via Behind the Net:

Shots_2011_20815_php_medium

The vertical blue lines represent Sharks goals while the vertical brown lines are goals scored by Chicago. The horizontal lines represent the respective teams' raw number of shot attempts as the game progressed. As you can see, the Sharks started this game outshooting the Blackhawks by a sizable margin until the goal that put them up 2-0. At that point, the Blackhawks' shot rate increased at a much higher rate than the Sharks' until they finally overtook San Jose in the shot department when they potted their second goal to tie the game. The teams were engaged in a tight battle until the Sharks retook the lead at which point they were content to cede territory to Chicago until the Hawks once again tied the game. San Jose scored soon after to take a 4-3 lead and Chicago predictably outshot the Sharks for the remainder. This type of in-game trajectory isn't uncommon and is why most analysts prefer to focus on a team's Corsi ratio with the score either tied or "close" (defined as tied at any time or within a goal in the first or second period), thereby refraining from rewarding teams who spend a disproportionate amount of time trailing and thereby having a better opportunity to inflate their shot totals. JLikens of the terrific Objective NHL showed that a team's score-tied Corsi ratio in any sample of their schedule is a superior predictor of their winning percentage over the remainder of their schedule than either their winning percentage or goal ratio in the initial sample (click to embiggen):

Predictivevalidityofwinning_bmp_medium

It's worth noting that score-adjusted Fenwick, a metric developed by Eric T. of Broad Street Hockey, has been shown to have even greater predictive value than Corsi Tied but we'll get to that later in this series. To summarize, a team's Corsi ratio is the best indicator we have of how much time the puck is spending in their offensive zone. Given what we know about the transience of PDO (5v5 shooting percentage plus save percentage), it isn't surprising to learn that a team's Corsi ratio after accounting for score effects is a better predictor of their future winning percentage than either their current winning percentage or current goal ratio.

What does it tell us at the player level?

Although Fenwick has mostly taken precedence over Corsi in team-based analysis, Corsi is still the preferred method of gauging individual players' contributions to puck possession and outshooting. The reason is sample size: even the most heavily-used defensemen in the league only spend about 1500 5v5 minutes on the ice over a full season while teams as a whole play about 4000 minutes of 5v5 hockey on average. The additional events added by including blocked shots are beneficial at the player level.

The main reason Corsi is an important factor to consider in player evaluation is that the objective in hockey is to get more, which isn't always the same thing as getting lots. If a player contributes to 30 goals being scored by his team but also contributes to 35 being scored at the other end, all things being equal, he's less valuable than a player who contributes to 20 goals for but just 15 against. Granted, things are very rarely equal which is why it's absolutely essential to account for the zone in which a player starts his shifts, the quality of opponents he faces and the talent level of both his most frequent linemates and his team as a whole. Additionally, the direct representation of a player's impact on goal difference--plus/minus--is problematic for a host of reasons, the most important of which was discussed in this space last week: that the majority of players don't tend to sustain a PDO substantially higher or lower than 1000 in the long run. Therefore, in most cases, a player's Corsi number can tell us his true talent at impacting goal differential rather quickly while it takes several seasons to gain confidence that a player's plus/minus rating is an accurate portrayal of his skill.

The aforementioned Eric T. took a look at this issue from another angle, using scoring chance data compiled by yours truly and several other bloggers that focused solely on tracking shot attempts from a dangerous scoring area and produced a metric for individual players showing what percentage of scoring chances they were on the ice for at evens were earned by their team. Eric looked at the correlation between that stat and Fenwick% which, again, is Corsi minus the blocked shots:

Scoring_20chances_20vs_20fenwick_png_medium

The correlation is extremely strong (between 0.8 and 0.85 depending on the games played cutoff) and even more revealing was that players who outperformed or underperformed their Fenwick% with their scoring chance percentage one season were not able to repeat that feat the following year. Granted, data from only 18 teams were available so it's best to not make sweeping generalizations based on this study alone but, at least for this sample, there don't appear to be players capable of generating shot attempts from far more dangerous locations than average without giving up a commensurate amount of dangerous shots at the other end of the ice. This still doesn't mean that everyone's plus/minus should neatly line up to their Corsi in the long run--some players are legitimately above-average finishers (Alex Tanguay, Ilya Kovalchuk and Steven Stamkos among them) and some players play in front of legitimately above-average goalies. Still, for the vast majority of the NHL population, the territorial advantage their team is able to gain with them on the ice 5v5, after making proper contextual adjustments, can tell you in a small sample of games what it takes years for plus/minus to accurately show.

Here's a list of Sharks players who appeared in at least 30 games last season sorted by their on-ice 5v5 Corsi number per 60 minutes of ice time. Again, quality of competition, teammates and zonestarts are all crucial components of the equation, all of which we'll discuss at a later time in this series. The page also includes a column for sorting the players by their "Corsi Relative" which takes a player's on-ice Corsi number and subtracts from it his team's overall Corsi number when he's not on the ice, thereby attempting to gauge the extent to which a player improves his team by entering the game. The point of that stat is to ensure players aren't overly punished for being on a bad team or having their numbers overly inflated by playing on the Penguins or Red Wings, although it isn't without its critics.

To summarize, a player's Corsi number is essentially an expanded and all-encompassing version of his plus/minus as it includes all shots on goal, missed shots and blocked shots when he's on the ice. It tends to be a very good indication of the extent to which a team is winning the scoring chance battle with a player on the ice but undoubtedly needs to be adjusted for the quality of competition a player faces, the quality of teammates he plays with, where he starts his shifts and other team effects (all of which will be discussed later in this series) in order to be truly useful. Corsi certainly isn't the be-all, end-all of player evaluation as some players do consistently finish their chances at an above- or below-average rate or allow for their linemates to do the same, in its raw form it assigns individual credit for things accomplished by everyone on the ice as a whole, and value on special teams needs to be taken into account as well. Still, it's a really valuable tool for evaluating players on a holistic level when used in the proper context.

Why should Sharks fans care?

Loads of reasons. Even though the counting stats may have looked somewhat underwhelming, Corsi gave us a glimpse of how effective a player Logan Couture was going to be before his great rookie season. In the 2010 Stanley Cup Playoffs, Couture (playing predominantly with Manny Malhotra and Torrey Mitchell) finished +17.6 per 60 in Corsi meaning, on average, the Sharks directed nearly 18 more shots at the opposing team's net than they had directed at their own for every 60 5v5 minutes Logan was on the ice in that postseason. That ranked 17th among all players to appear in at least 10 games during those playoffs, ahead of guys like Marian Hossa and Jonathan Toews on the Cup-winning Hawks. More recently, Corsi provided a good measure of how much Douglas Murray struggled last season; something that was probably obvious to anyone who watched him closely but wasn't really reflected in traditional measures like plus/minus. At the team level, Corsi was also one of the reasons the Sharks went on that terrific run at the end of the 07-08 season after trading for Brian Campbell. A lot of that was PDO regression seeing as the Sharks were already a 54% Corsi Tied team before adding Campbell but they improved to a ridiculous 58.3% Corsi Tied percentage during the post-Campbell part of their schedule. That may have been the best Sharks team ever regardless of what seemed like a mediocre defense corps on paper.

Where can I find this stat?

Behind the Net has a database that's updated daily during the regular season with the on-ice Corsi number and Corsi Relative of every player in the league. You can use the drop-down menus to navigate between seasons, teams, player positions or set a minimum games played threshold. David Johnson's site has a list of every player in the NHL; click on any of them and use the gray box at the top of their page to see their "With Or Without You" numbers--their Corsi when on the ice with and on the ice without each of their most frequent teammates--in any single season or any combination of seasons. If you're interested in finding teams' Corsi ratios, you'll need to use the scripts at timeonice.com for which there's a terrific how-to guide here.

Where can I read more about it?

Why Shooting Stats are Better Than Goals by JaredL at Driving Play; Even Strength Outshooting and Team Quality by JLikens at Objective NHL; The Relationship Between Outshooting and Outscoring Over Time by JLikens at Objective NHL; Outshooting leads to winning. News at eleven. by Derek Zona at The Copper & Blue; Introduction to Hockey Analytics Part 4.1: Possession Metrics (Corsi/Fenwick) by garik16 at Lighthouse Hockey; What is a Corsi Number? by Gabe Desjardins at Arctic Ice Hockey; Intro to Advanced Hockey Statistics - Corsi by Steve Burtch at Pension Plan Puppets

Finally, in case you needed more evidence that Corsi can be a valuable tool, here's Don Cherry ripping it on Hockey Night in Canada:


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