Friday, August 10, 2007

Assessing Goalies: Goals Saved

It is a tough problem in sabermetrics and hockey to properly assess goaltenders statistically. This is because goaltending statistics are heavily influenced by the team in front of the goalie.

Nevertheless, the hockey outsider (Peter Albert) has tried to come up with a single number with which to rank a goalie's contribution to his team. He calls this method goals saved. The idea is to come up with a team independent measure of how many goals a particular goalie saved (when compared to an "average" goalie).

The idea is to find the extra number of saves a goalie makes when compared to "average" and multiply it by his workload on an "average" team (for the number of minutes he played in the NHL with his actual team).

In order to determine how many shots a goalie saves (when compared to an average goalie) we look to his saves percentage. Ideally, we would want to adjust for shot quality but since I have never seen this data tabulated before the 2002/03 season it eliminates most of the history of the NHL from this analysis. Nevertheless, clearly differing shot quality can lead to incorrect results with this method. The use of saves percentage limits this analysis to the 1951/52 season and more recent as this data does not exist further back in history than this (to the best of my knowledge).

In order to compare a goalie's saves percentage to the "average" level in a league, average must be calculated. For the purpose of this analysis we take average saves percentage to mean the saves percentage of the league (once the saves and shots faced by the goalie in question are subtracted out - this is significant because in the original six days one single goalie on a poor defensive team could face more than 20% of the leagues shots in a season). There is a potential problem with this definition of average, namely that it changes every year. For example, in an expansion year, it will suffer due to quality of opposition issues. If the league adds a couple of expansion teams that play bad goaltenders on bad teams with bad defences, these goalies will reduce the league averages. Due to the fact they are bad goalies, they will have lower saves percentages than the rest of the league. Due to the fact they are on bad teams with bad defences, they will face more shots against than the average team (thus having larger than average effect on the average saves percentage calculation) and the shots will be of higher quality (thus making their contribution look even worse since shot quality is not taken into account).

Once we have the difference in saves percentage between our goalie and the "average" we need to look at a goalies workload. We know how many minutes a goalie played and we can calculate the average shots per minute in the NHL (thus we are not penalizing goalies for playing on teams that face very few shots or over-rewarding those who face lots of shots).

Now we merely multiply these two numbers to give us a team independent goals saved value for a particular goalie (relative to "average" as we defined it and assuming neutral shot quality).

This is a simplified analysis which gives us one number to compare goalies. Comparisons that stay within one year are likely far more valid then those stretching several years - because of the floating definition of average. The fact that shot quality is not taken into account is a problem (although this data only exists for a handful of years and is of questionable quality so that cannot be avoided). This also removes many second order effects that goalies can have that can make a big impact on a game. For example, goalies with better puck playing ability can reduce goals against by fielding dump-in attempts which are not shots on goal or goalies who allow many rebounds will face higher shot totals than those who tend to hold onto the initial shot. These effects could significantly impact rankings, but cannot be taken into account. Given the quality of goalie statistics kept in the NHL, an analysis like this is the best that can be done, however it is not any final ranking of goaltenders. I will write about the leaders in goals saved in some future posts.

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