# Value of Corsi possession measured in goals

The average on-ice shooting and save percentages a player experiences tends to be influenced by their average time on ice per game. This relationship likely occurs due to a combination of factors: shooting talents of linemates and opponent, defensive talents of linemates and opponent, system and psychological effects, and an effect I like to call “streak effects”.
(See bottom for discussion on these effects)

Regardless of the reasons why, these effects indicate that not all Corsi percentages are created equal in impact. This has been discussed previously on Hockey-Graphs both here and here. So, can we measure this difference in impact?

Building off of work by former blogger Tyler Dellow, I sorted all player seasons from 2007-2012 by average 5v5 TOI per game and then split into buckets of equal games played. From this you can determine what the typical results are for players on different lines.

Figure 1: 2007-12 NHL forwards in equal buckets of combined games played + fourth bucket split in half

Figure 2: 2007-12 NHL defenders in equal buckets of combined games played + third bucket split in half

The next step was sorting each bucket (ie: line/pair) into groups of equal players by Corsi% and then looking at relationship with goal differentials. All these steps in detail can found here.

From this you can create simple formula looking at expected goal differentials of a player with a particular Corsi% and 5v5 TOI/60.

Figure 2: Expected goals algorithms from Corsi%

Note: R^2 values are not for how well Corsi% predicts a single players goal differential, but rather the relationship each group of players and their goal differentials used in the steps linked above. Each data point on the graph for each bucket represented 5% of each bucket’s sample (about 20-30 players). This process diminishes the extent that luck, goaltending talent, and other sources of outliers affect goal differentials which is why we see a much stronger relationship than we would in reality.

Now you can describe the value of Corsi in terms of goal differentials over a season.  First look at what a player’s 5v5 TOI/60 was to determine which bucket they belong to. Then plug in a player’s Corsi% as a decimal (ex: 50.0% equals 0.500), multiply by slope, and add the intercept.

For example, Matt Halischuk and Eric Tangradi are two players who averaged 4th line minutes on the Winnipeg Jets. Tangradi finished the season with a 53.9% Corsi, while Halischuk was at 44.0%. Over the span of a season, forwards with those Corsi% would be expected to have on average of -1.04 and a -4.77 goal differential respectively. Therefore, on average, a 53.9% Corsi fourth line forward is worth 3.73 goals more than a 44.0% Corsi forward. Another option is comparing these players to the 46.8% Corsi% of an average fourth line player. The goal differentials can then be used to estimate win values using Pythagorean relationships.

There is a caveat with using raw Corsi% to estimate goal differentials; all effects -such as zone starts- still apply. The estimated goal differentials would be no more predictive than Corsi is; however, you can now easily and more accurately measure Corsi impact in terms of goals and wins.

Those of you who frequent this site have likely seen this before: Corsi used in player evaluations can never be separated from the conditions and environments that surround said player.

These conditions are not limited to the contextual nuances in how a player is deployed -like zone deployment, linemates, and line-matching-. Other conditions include ice time, coaching system, the player’s “role” and what game state a player tends to be deployed in (leading, lagging, tied, etc.).

The founding statistical analysts in hockey used a cocktail of numbers. They employed gut feelings on whether a player performed admirably while looking at comparably deployed players and taking in account which conditions have a larger influence over results. A mixing of science with art.

Recently though, Stephen Burtch (and others) have attempted to diminish the extent of subjective grey areas with regression methods, such as dCorsi. If these regression methods one day become effective enough to accurately predict a players Corsi% given neutral deployment, we can then use Corsi% to create a far better source of WAR than Goals Versus Threshold.

#### Extra: As promised, a short discussion on shooting percentage effects with TOI

As I noted above, there is a relationship with a player’s TOI and the observed on-ice percentages. However, do not be quick to view all of it as shooting talent, as there are multiple variables at play. Shooting talent exists but it’s not the only factor.

There of course is the 5 opponents on the ice. While defenders do not have substantial control over shot quality, there is likely some there.

There is also the system and psychological aspect to the game. Scorers are expected to score and will take risks to score. They may take chances that lead to superior scoring chances that lesser player might not. Coaches also deploy scorers relatively more in situations when scoring is needed, like when trailing or tied. Non-scoring bottom forwards may try to play it safer. They may be more worried than a scorer of the personal consequences with making a costly mistake. A coach may also instruct a 4th line to get the opposing goalie to cover the puck for an offensive zone draw for the top line.

There is also the “streak effect”, first shown to me by Eric Tulsky. Players on hot streaks tend to be given more ice time by coaches, while players on cold streaks tend to receive opposite treatment. This may cause an artificial inflation of a players TOI post hoc. A player who has benefited due to bounces may garner more ice time the next few games. Unless the player then receives an equal amount of poor luck with bounces, both TOI and scoring rates become inflated.