Stats, history, fun with numbers and the HHOF

Editor's Note: 1967ers looks at how normalized scoring has been determined. I actually have that book Total Hockey and I might go looking for it to see if I can find anything interesting about the Leafs.

It was with great interest and a deep sense of dread that I read the statistical argument for Wendel Clark going to the Hall of Fame.  Interest because, well, Wendel is still my fave and dread because I saw where it was going with respect to comparative stats.  This evokes dread because it draws forth two competing interests within me - the worship of all things Wendel versus the history buff in me and the fact that my entire professional life is about data and what you can and can't do with it.

And to make a long story short - while I love Wendel and want him in the hall, you can't do this with his numbers.

Now - I fully suspect that Wendel's Moustache also knows you can't do this with the numbers, which is why he only goes so far as to suggest that they don't make Wendel's inclusion unreasonable - not automatic.

The problem with the numbers as presented is that they are out of context.  None of the players in the list is from Wendel's era.  Wendel racked up most of his scoring totals in a very high-scoring era.  Of the listed players, the closest in terms of era is Clark (nice name) Gillies, who actually outpointed Wendel, which is something I didn't realize.

Most of the others played the bulk of their careers in the pre-expansion era, and many of those were spent in the late 1940s and early 1950s, which is the most defensive era of all time, save for the late 1920s prior to the introduction of the forward pass.  25 goals scored in 1949 is a very different thing than 25 goals scored in 1987.  In 1949, that total put you in the top ten forwards in the game.  In 1987, that made you a marginal top-six forward on a good team.

So how do you compare them?

In the late 1980's, Klein and Reif put together some of the best statiscal analysis on hockey I have ever seen.  Among other creations like the goalie Perserverence Index, they introduced the notion of normalized scoring.  This would allow them to compare a 25-goal season from 1949 to a 40-goal season from 1987 and see which player had had the better year.  The principle behind it is that each season would be compared to what was going on in hockey at the time and then mapped to a hypothetical baseline year.  You could then hope to eliminate the problems caused by defensive/offensive eras and changes in roster size that affected the ice time a player could expect to get.

The basic math looks like this:
Player A scored 22 goals in a league in which the goals were scored 80% as frequently as in in the baseline.  He played 58 games of a 60-game season on a 15-man roster.  His ice-time was therefore about 33% more than could be expected in an 18-man roster.

Normalized against a standard 80-game season, his numbers would look something like this:
22/58*((58/60)*80)*1.25/1.33

Where
22/58 is the GPG
(58/60)*80 gets us the amount he'd have scored in an 80 game season,
1.25 is the multiplier when goals are 20% less frequent
1.33 is the correction for ice time.

Those 22 goals are worth 27.6 normalized goals.

Our 40-goal scorer played 77 of 80 games on an 18 man roster, so there are no corrections there, but goals were scored 33% more than on our baseline.

The math would be :
40/77*((77/80)*80)*.75/1

So those 40 goals are worth 30 normalized goals.  Our 40-goal scorer outproduced our 22-goal scorer, but not by as much as it would appear.

There was a book called Total Hockey that came out a few years ago where they took everyone's stats and baselined them against 1969-70, which was the most statistically average year they could find.  Darryl Shilling also did great work online, but much of it is lost now.  The difference between them was that Total Hockey assigned everyone an equal percentage of ice time, while Shilling gave stars a lion's share which might have been unsupportable in reality.

The problem with all formulas like this is that, other than the fact that they are all based on assumptions, they break down in extreme cases.  In the first years of the NHL, assists were incredibly hard to come by.  Where many players might only have 5 of them, a guy with 10 finds himself with something like 165 normalized assists.  For numbers more or less in the middle, though, it's passable.

The point of all this is that the players used for comparison really can't be used that way since the numbers they had were produced in a completely different era.

What is an interesting comparison, though, is that a lot of those players were added through the veteran's category.  This seems to be where the two-way players get in, or the defensive defensemen - players who contributed an awful lot more than their raw stats suggest and players who, in hindsight, deserve recognition they didn't get at the time of their retirement. 

Wendel Clark, anyone?