Friday, June 17, 2005

Daryl Shilling Adjusted Scoring Stats

On Monday, I wrote about Total Hockey's Adjusted Goals/Assists/Points calculation. Their method is in no way unique. Another similar method is used by Daryl Shilling in his hockey project.

He adjusts for the same three factors. They are rate of scoring in the season, length of schedule and approximate playing time. These are not necessarily the only factors one might attempt to correct for. One might attempt to correct for quality of opposition (for example applying this method to a pee wee league would probably produce that false result that some kid in that league is equivalent to Wayne Gretzky) or amount of power play/ shorthanded time (since scoring chances increase on the power play and decrease shorthanded) or any other number of effects that one might imagine are important.

In order to correct for the amount of offence in the league, Daryl does roughly the same thing Total Hockey does. He calculates the goals per game in the season in question after subtracting those goals scored by the player in question. Then he multiplies the players actual goals scored by the "average" goals per game in NHL history divided by the normalized goals per game (goals per game subtracting the player in question) for that season. The only difference is that daryl defines the average goals per game to be 6.13, which is close to the NHL's average.

In order to correct for the number of games in the schedule he does exactly the same thing as Total Hockey. He takes the corrected value so far and he multiplies by 82 games played divided by the number of games played in ther league in the season in question and then multiplies by the percentage of the schedule the player in question played.

The major difference between the two methods is the way he adjusts for playing time. Daryl assumes that the player in question is the star of his team and will have his playing time maximimized. Total Hockey merely multiplies by the ratio of roster sizes, which is closest to correct for the "average" player but likely there has been little change in playing time for superstar players despite the roster increases of the last 50 years or so from 15 to 18 skaters. Daryl uses an empirical formula of his own design. He assumes that the average ice time is about 30 minutes per game and divides this by (5/# of skaters dressed per game * 100). This is his approximate value for the amount of ice time a player. It gives almost 28 minutes per game in today's 18 skater NHL. Thus ice time assumption will fail if we attempt this calculation with any player who does not actually get superstar ice time. Ideally, we would want to use the actual ice time that the player actually played per game - but for most of the NHL history, this number has been lost.

If we establish as good a formula as possible to adjust scoring stats, we can attempt to do sabermetrics calculations with hockey. We must notice that this adjusted scoring calculation is NOT exact. It is at best an approximation and it leaves out many possibly significant effects. Any study done using these types of formuals is, at best, only as good as the formula used. As a result, all calculations attempted from this starting point will be approximate and may leave out some important effects.

I didn't know that data needs to tune in to get the best of it. but it makes results more interesting.
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