Hockey-Reference.com Revised - Part 1: Adjusted Statistics

This is the first part of an intended series of threads revisiting Hockey-Reference.com's three in-house attempts to contextualize player contributions: adjusted statistics, goals created, and point shares.

Adjusted Statistics, According to Hockey-Reference.com

Hockey-Reference.com said:

In order to account for different schedule lengths, roster sizes, and scoring environments, some statistics have been adjusted. All statistics have been adjusted to an 82-game schedule with a maximum roster size of 18 skaters and league averages of 6 goals per game and 1.67 assists per goal.

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As described above, the individual adjustments seem to make sense. Adjusting for schedule length is self-evident. A roster size adjustment seems to be logical since the roster size affects player deployment and ice time. Adjusting for goals per game and assists per goal makes sense because it takes into account the difficulty of scoring. How does Hockey-Reference.com go about doing its adjustments?

Hockey-Reference.com said:

Adjusted Goals​

We will use Gordie Howe's 1952-53 season as an example, a season in which Howe scored a career-high 49 goals.

The first step in this process is to calculate a schedule adjustment for each player. In order to do this, divide 82 by the number of scheduled games per team. In 1952-53 the NHL played a 70-game schedule, so the schedule adjustment is 82 / 70 = 1.17.

The roster size adjustment is computed by dividing the maximum roster size for the season in question by 18. Teams were allowed to carry a maximum of 16 skaters at home and 15 skaters on the road during the 1952-53 season, so the roster size adjustment is 15.5 / 18 = 0.86.

Next calculate the era adjustment, which we will do by dividing 6 by the league average goals per game without the player in question. In 1952-53 a total of 1006 goals were scored in 210 games. Without Howe this works out to (1006 - 49) / 210 = 4.56 goals per game, so our era adjustment is 6 / 4.56 = 1.32.

Finally, we put everything together. Take the player's actual goals and multiply by the adjustments we computed above. For Howe in 1952-53 this is 49 * 1.17 * 0.86 * 1.32 = 65 adjusted goals.

Adjusted Assists​

Once again we will use Howe's 1952-53 season, when Howe had 46 assists, as an example.

First compute the schedule and roster size adjustments as above. The era adjustment is found by dividing 10 (which is the product of 6 goals per game and 1.67 assists per goal) by the league average assists per game without the player in question. In 1952-53 a total of 1513 assists were awarded in 210 games. Without Howe this works out to (1513 - 46) / 210 = 6.99 assists per game, so our era adjustment is 10 / 6.99 = 1.43.

Adjusted assists are then computed by multiplying the player's actual assists by the three adjustments. For Howe we get 46 * 1.17 * 0.86 * 1.43 = 66 adjusted assists.

Adjusted Points ​

Adjusted points are simply the sum of adjusted goals and adjusted assists.

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Now, looking at all player seasons that are equivalent or better than 110 adjusted points (with 110 adjusted points being a decent estimate of an Art Ross "contender"), we can get a decent estimate of the era distribution of top player seasons according to Hockey-Reference.com's adjustments.



That's definitely an odd distribution. It's pretty evident that the Original Six era is underrepresented here. On the other hand, the 1920's and 1930's appear to be over-represented. Perhaps if we narrow it down to the top 30 or so seasons, we'll be able to pick out some anomalies.

So, what are the top 30 seasons according the Hockey-Reference.com's adjusted points?


That's certainly... a list. Of names. With numbers beside them. A few immediate red flags pop up:

1) The most dominant Art Ross win in the entire Original Six era (a period that spans 25 years), Gordie Howe's 1952-53 season, is only tied for 30th on this list.

2) There's certainly a lot of names from the early post-consolidation era when roster sizes were set to 10-12 skaters. Most of those seasons, forward passing in the offensive zone was not allowed.

3) Dick Irvin's 1926-27 season (36 real points) definitely looks good on here, with 145 adjusted points. It's especially impressive since Bill Cook, who tallied an extra real point (37 real points) for the league lead, doesn't make this list. It should be noted, however, that Irvin had significantly more real assists than Cook (18 versus 4).

The above points to two potential problems with Hockey-Reference.com's implicit assumptions about roster sizes and calculation of assists.

The Roster Size Adjustment and Ice Time: Who Loses When the Roster Gains

When Howie Morenz first skated in the NHL in the 1923-24 season, the roster size was limited to 9 skaters. It's not entirely a surprise that one could expect Morenz to be given roughly double the ice time of a modern NHL skater. Is "roughly double" accurate enough to be used in a calculation?

When Gordie Howe in his prime was playing in the 1950's, the roster size grew from 15 to 16 skaters. Can we definitively say that ice time was spread divvied up evenly from all the other skaters? How would that even work depending on if the extra skater was a forward or a defenseman?

Let's look at the median scoring points of each line and pair since post-consolidation and calculate the fraction of scoring by each to estimate deployment. (The assumption here is that the relative talent of a median 1st-line forward or 1st-pair defenseman is reasonably constant, so what we're supposedly measuring is relative deployment.)

Forwards:


Defensemen:


For the median first line forward, their fraction of forward scoring points is actually relatively stable starting from 1949-50.

For the median first pair defenseman, their fraction of defenseman scoring points stablizes around 1982-83, which is when the roster size was finally set to 18 skaters.

As such, it makes more sense to use a deployment adjustment rather than a roster size adjustment. Between 1982-83 through 2020-21, the median 1st liner accounts for 42.1% of forward scoring while the median 1st pair defenseman accounts for 52.1% of defenseman scoring.


Outlier, or Fair Game?

Going on a brief tangent, another odd aspect to Hockey-Reference.com's adjustment method is the removal of player contribution to league totals. While this appears to be a sound method to remove potential outliers, this actually causes problems in the early eras with few teams and few players. Let us consider 1918-19, when the NHL had 3 teams. Here are all 32 (yes, thirty-two) skaterswho played in the NHL that season:


Looking at scoring points, the interquartile range (IQR) is 12.25, and the third quartile (3Q) is 15. Using the outlier detection method, we find that 3Q + IQR*1.5 is 33.375. No one is an outlier in this small sample. As such, it is a better idea to use league averages just as they are.

What is the Point of a Scoring Point?

Going back to Dick Irvin and Bill Cook in 1926-27, here are their actual scoring and adjusted statistics:


It's true that Irvin contributed significantly more through his passing than Cook in this season. However, one must ask what a scoring point is measuring. Cook contributed to one more real goal scored by his team than Irvin. It seems ahistorical for the actual scoring leader to trail the runner up by 62 adjusted points. Given that the game was vastly different prior to forward passing and offsides, it is likely a better idea to directly adjust for points and find assists by subtracting adjusted goals from adjusted points (with assists being defined as non-goal-scoring contributions).

For Hockey-Reference.com's target environment of 6 goals per game and 1.67 assists per goal, this amounts to 16 points per game.

Putting It All Together

For 1926-27, here are relevant figures necessary for adjustment:


The schedule adjustment is 82/44 = 1.864.

The deployment adjustment for Cook and Irvin (both forwards) is 0.421/0.710 = 0.593.

The goals adjustment is 6.00/4.00 = 1.500.

The points adjustment is 16.00/5.92 = 2.703.

For Bill Cook:

33 goals x 1.864 x 0.593 x 1.500 = 55 adjusted goals
37 points x 1.864 x 0.593 x 2.703 = 111 adjusted points

For Dick Irvin:

18 goals x 1.864 x 0.593 x 1.500 = 30 adjusted goals
36 points x 1.864 x 0.593 x 2.703 = 108 adjusted points


Ironed but Still Wrinkled

What are the player seasons with 110 or more adjusted points using this revised adjustment method?


Looking at the era distribution of the revised method, it's clear that it is better than before, but due to the inability to gauge overall league strength by using only league averages, it is possible that the pre-consolidation era and WHA era is over-represented while the O6 era remains underrepresented:


Looking at all the players with at least two 110+ adjusted point seasons (up to and including 2020-21), comparing between Hockey-Reference.com and the revised method:


So as the section title says, by using a deployment adjustment rather than a roster size adjustment, by ignoring "player contribution" to league totals, and by directly adjusting for points, this irons out the glaring problems with Hockey-Reference.com's adjusted points... but wrinkles remain.

Season by season results will be posted later.