Tuesday, June 28, 2005

Hall of Fame Monitor: Calibration Between Different Positions

Over the past few days I have posted Pnep's Hall of Fame Monitor for forwards, defenders and goaltenders. The major problems that comes next is calibrating these different positions so that there is no advantage or disadvantage in a hall of fame monitor statistics for playing a given position. You want the top players to be a healthy mix of all positions. You want dominant players in all positions to have equal chance to rise to the top. You want lesser players in all positions to also get to their appropriate ranking.

In Pnep's system this problem has already been solved. He has tailored the monitor fomulas so that they roughly work out to have an appropriate mix od players in all positions. Of course, he created some inconsistencies in this process. For example, goalies get 250 points for winning a Hart trophy, defenders get 175 points and forwards get 150 points. How is that fair? The same achievement has different value depending upon position. Another example. Defenders get points for games played. Neither forwards nor goalies do. These inconsistencies will have to be fixed to improve this system.

As a rough guess, the top 20 players should include 12 forwards, 6 defenders and 2 goalies since that is the number of each position usually dressed in a hockey game. This is only a rough first guess, but lets compare it with the results of the Hall of Fame monitor formula. The top 20 players by the formulas are:

1. Wayne Gretzky 8827.02 Forward
2. Gordie Howe 6171.61 Forward
3. Ray Bourque 4664.82 Defender
4. Mario Lemieux 4586.35 Forward
5. Jean Beliveau 4253.44 Forward
6. Phil Esposito 4096.48 Forward
7. Bobby Orr 4037.97 Defender
8. Maurice Richard 3829.98 Forward
9. Bobby Hull 3671.88 Forward
10. Stan Mikita 3583.61 Forward
11. Doug Harvey 3467.36 Defender
12. Jaromir Jagr 3237.64 Forward
13. Patrick Roy 3235.65 Goalie
14. Dominik Hasek 3221.51 Goalie
15. Glenn Hall 3155.64 Goalie
16. Guy Lafleur 3060.04 Forward
17. Jacques Plante 3036.02 Goalie
18. Mark Messier 3030.49 Forward
19. Paul Coffey 2958.37 Defender
20. Red Kelly 2925.27 Defender

This gives us 11 forwards, 5 defenders and 4 goalies. Thats pretty close to the initial guess, so it could be somewhat accurate. I think the excess of goalies is explanable. Goalies can dominate a game more than any other position.

The ultimate calibration for a formula like this is to compare the totals for all players on a team in the season to the standings that year. The totals for the best team should be the highest and as we drop in the standings, the totals should get progressively lower. To the best of my knowledge, no such comparison has ever been attempted but I doubt it would turn out well. For example if a Hart trophy winner (or other major award) came from any team that was not first in the standings, those points would likely cause that team to be overrated significantly in the standings. Also, high scoring teams would do better than low scoring defensive teams with equivalent positions in the standings.

Pnep's hall of fame monitor is a good first try. It highlights roughly the best players of all time. It can get their order wrong (Bobby Orr is definitely too low). It has some arbitrary values for the same stats between different positions in order to try to calibrate between different positions. It requires the input of voters (who may be wrong) as it includes the winners of trophies in the point schemes. Its a good start and interesting to look at, but I don't think it is in anyway definitive and players may be siginificantly misvalued due to some biases in the formulas (short careers, defensive players get underrated).

...For example, goalies get 250 points for winning a Hart trophy, defenders get 175 points and forwards get 150 points. How is that fair?....

Total players who have "Hart" or "Hart Runner Up" - 164
Goalie who have "Hart" or "Hart Runner Up" - only 23

Total players who have "Conn Smythe" - 73
Goalie who have "Conn Smythe" - only 19
Equivalently you could argue. Number of players who won the Hart Trophy who have last names that begin with "A" 2 - Sid Abel 1949, Tom Anderson 1942. Number who have names that begin with "B" 6 - Jean Beliveau 1956 & 1964, Andy Bathgate 1959, Max Bentley 1946, Toe Blake 1939 and Billy Burch 1925. So winning the trophy when your last name begins with "A" should be worth more points.

Or we can do the rational thing and realize they did they exact same thing in winning the Hart Trophy and should get the same number of points.

Another question. The Conn Smythe trophy has been given out once a year since 1965. It has had 40 winners (why do you claim 73?)
I understand. You are claiming "would-be" Conn Smythe winners according to the Hockey News count the same as actual Connn Smythe winners. I'm not sure I'd be so willing to accept that.

Its one thing to use other people's opinions in these formulas (I would advise against it). Its another to use opinions made many years after the fact by people who in many cases are not even old enough to have seen the games. They picked these would be winners in 2001. How many can clearly remember the 1918 Stanley Cup playoffs in the year 2001?
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