Sunday, July 27, 2008

The Chicago +/- Anomaly

In this summer's sabermetrics and hockey posts, I have been writing about +/- ratings. I have shown two ways to adjust +/- ratings between teams: one as a rate stat using on and off ice performance and one as a counting stat. I have compared the top 20 players under both methods here and here. One of the larger discrepancies in this exercise comes with Chicago Blackhawk players. On the counting stat list, Duncan Keith rates fifth and Patrick Sharp rates 14th. However, the rate stat list does not identify either as nearly as exceptional. Keith is ranked 57th and Sharp 81st. Why is this? Why does one list not select their performances?

The problem is the rate stat compares +/- ratings when a player is on the ice to their team's performance when they are on the ice. On most teams, most players play a relatively well defined role where they play with roughly the same calibre of linemates against roughly the same calibre of opposition throughout the whole season. This well defined role helps in the identification of exceptional players (either good or bad) since it will have them more clearly contrasted with other teammates who played in other well-defined roles. In Chicago, teams did not keep their well-defined roles over the whole season.

At the beginning of last season, Chicago played Martin Havlat and Jason Williams as their top two forwards who garnered the most ice time. On defence, Duncan Keith, Brent Seabrook and Brent Sopel were the most heavily played defencemen fro a group of defencemen with few standouts. By the end of the year, Patrick Kane and Jonathan Toews were played most frequently as the top forwards. Patrick Sharp emerged as one of the top forwards and the number one guy in defensive situations, when early in the year he was just another forward in their depth charts. Keith and Seabrook had established themselves as the top defencemen on the team and were pulling in more minutes and tougher assignments than those they had early in the season. It was a season of upheaval for the Blackhawks. Nobody maintained a well-defined role throughout the season. Essentially, everybody played with everybody in all situations. What this does it makes everyone's off ice +/- approximately equal. When compared to players on teams with more well-defined roles, it makes it harder to identify exceptional performances on the team. Duncan Keith and Patrick Sharp had better off ice +/- ratings than players like Sidney Crosby, Jarome Iginla and Joe Thornton who played on significantly better teams.

The on/off ice adjustment fails to find the strong performances of Keith and Sharp. This is a failing of that system. It is more team-dependent to find exceptional performances. They can be lost because of anomalous situations occurring while a player is off the ice. Although one could argue a similar situation of anomalous performances where a player is off the ice could also create what appears to be an exceptional performance, when it didn't occur, this is a much harder proposition. It is far easier for a team to be average when a given player is off the ice than it is for them to be truly spectacular or awful when a player is off the ice without this situation being a meaningful measure of the player in question. Where there is an effect, is when we rank players failure to identify an exceptional performance or two will push other players up (or down) those one or two points in the ranking chart that would have been held by the unidentified player.

In an on/off ice +/- adjustment it is more possible to miss out on an exceptional performance because of anomalous circumstances making a player's off ice performance appear more average than it normally should have been than for it to create what appears to be an exceptional performance because of an anomalously good or bad off ice performance. As a result, some exceptional players can be lost in the on/off ice +/- adjustment. This happened in Chicago in 2007/08 where Duncan Keith and Patrick Sharp had very good performances, but were lost due to the upheaval in the Chicago Blackhawks roster which changed the roles of essentially everybody throughout the season and averaged out off ice performance numbers. Keith and Sharp had very good years, which were found by the counting stat method and missed (for the most part) by the rate stat.

This might be a bit of a nit-pick, but shouldn't it be the other way around? The on ice/off ice stats should be most useful when ice time and player match-ups are completely random (or better yet, perfectly evenly distributed). Then the impact of an individual player is easier to identify because any given player plays equal time with every other player. A good player will always be on the ice with at least one good player (himself) and similarly for a poor player.

It's just relative to other teams that have well-defined roles, where good players tend to play with good players and that throws off the stats, that those stats look out of whack. (Which is of course where quality of teammates and competition come into play, but those have their own problems not really relevant here.)
If all roles, linemates and opposition were totally random, the statistics would be the most valuable and need the least interpretation. Of course, we know they are not. We know that almost every team has relatively well-defined roles throughout a season. The rare team that doesn't may have numbers that better show the value of their players with respect to one another on that team - but the problem comes in the comparison to other teams. In this case, the rate stat adjusted +/- does not find Duncan Keith and Patrick sharp as having done as well as they did. That is an artifact of comparing teams with well-defined roles to Chicago where that didn't exist.
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