Monday, June 13, 2005

Adjusted Goals/Assists/Points

In late May, I posted about sabermetrics and hockey. In it, I said I would further discuss the various hall of fame metrics (scores people have developed to determine if a given player is worthy of hall of fame induction). That is a big story. I figure I will break it into a few sabermetrics posts. The first one (today) will discuss the method that the book Total Hockey editted by James Duplacey and Dan Diamond developed to adjust goals, assists and points.

The motivation is that goals/assists/points are not the same from one season to the next. How does one go about comparing point totals from different eras? For example, is a 50 goal season in the sixties the same as a 70 goal season in the eighties? Dan Diamond has developed one method to attempt to compare this. In my 2nd edition of Total Hockey, he has calculated adjusted goal/assist and point totals for all the players who ever played in the NHL. I think that many people attempting to do sabermetrics with hockey use these numbers without trying to reproduce them. As much as i have tried, I cannot exactly reproduce them. I get close values but not exactly thec same value.

Diamond identifies three factors to adjust for. They are the rate of scoring in a given era, the number of games in a season and the amount of ice time players recieve. He attempts to adjust for the scoring rate by multiplying by the ratio of the average of the various season averages (which in 2000 when the book came out was 6.11213 goals per game) to the number of goals scored per game in that season. As an example, in 1952/53 Gordie Howe scored 49 goals. There were 4.7905 goals per game that year. So that gives 49*6.11213/4.7905=62.518 goals so far. (In fact, Total Hockey subtracts out the goals scored by the player in question when doing this calculation it is a minor adjustment that will make no difference to the example I am giving. It only matters in the very early years of the NHL - where for example Joe Malone scored 13% of all the goals in thew league that year). The next adjustment is for the number of games played in a season. This is done by expressing the number of games played by the player as a percentage of the season and multiplying by 82 (the current length of an NHL season). Gordie Howe playe all 70 games that season. So the next adjustment is 62.518*82/70=73.236 adjusted goals so far. The next adjustment is to factor in roster size. Today, 18 skaters play per team per game (plus goalies). In Gordie's day 16 skaters played per team. So that would give Gordie extrat ice time (in theory), Likely, the stars of that time played roughly as much as the stars of today. This adjustment is much nore important for the earliest days of hockey when roster sizes were much smaller. This adjustment is 73.236*16/18=65.099 adjusted goals by my calculation. Total Hockey quotes him as having 67 adjusted goals (they round off all calculations to the nearest integer). My calculations are always close to their value, but rarely are exactly the value in the book. I am not exactly sure of the problem.

I suspect that the problem MIGHT be due to the average number of goals per game, I suspect that when the first edition camer out they used the average goals per game that existed at that time. Scoring has since dropped in the NHL. I think when they did the calculations they used that value (which by reverse engineering would be roughly 6.24 or so goals per game). I think that when they re-wrote the adjusted scoring page in Total Hockey, they changed the average goals per game number to reflect thew years since the first edition, but they did not change any of the calculations to reflect this. I am not sure if I am correct.

The problem with the way this is presented in the Total Hockey book is that they do not give any numerical examples. They have a one page write-up explaning in words what they did and roughly their motivations. I had to try to do this numerical example. I cannot get it (or others I have tried) to work out exactly. They all come close to the correct value. If anybody has any insight into the discrepancies please leave me a message,

Of course this is not the only way to adjust scoring. In my next post on this tgopic, I will explain the method Daryl Shilling uses. It has the advantage that I can make the math work and he uses a numerical example. These methods can then be compared and contrasted and the general use of these types of methodws can be discussed.

NOTE: On Friday, I realized this calculation is slightly incorrect. In the 1952/53 season teams could dress 16 skaters for home games and 15 for road games. So I should use 15.5 as the number of skaters dressed per game. This would reduce Gordie's adjusted goals to 63 and increase the discrepancy with Total Hockey's calculation.

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