Discussion in 'The History of Hockey' started by Weztex, Jan 17, 2007.

1. ### WeztexRegistered User

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I'm searching for each year scoring champion in adjusted points since I'm not so good a mathematician. I think this have been floating around at some times but cannot retrieve it. I hope someone (pnep maybe) possess those informations.

2. ### God Bless CanadaRegistered User

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pnep, HO and Czech Your Match are the guys you want to talk to.

3. ### Hockey OutsiderRegistered User

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A few points:

1) I'm playing around with some of the estimates needed to calculate the adjusted scoring numbers. These results are very sensitive to changes in ice time estimates. What I posted represents my "best guess" for now, but might change them in the future.

2) This takes into account regular season offense only. It doesn't consider defense, physical play, leadership, playoff performance, etc. Also, it doesn't try to analyze the offensive numbers further and account for linemates, total ice time, PP vs ES vs PK ice time, etc.

3) Interestingly, the 2006 numbers required virtually no adjustment. It's as close to an "average" year as we've ever had in terms of the variables included in the formula. This was a fluke; this formula was made prior to the lockout.

4) You might notice that, except for the first few years, the average points scored by a top five scorer has increased over time. It's actually a very steady trend from around 1930 to the present. There are two possible causes. One, there might be inherent problems in this formula that cause me to underrate older players and/or overrate modern players. Two, the NHL has more players each year. If the adjusted level of scoring is held constant, as the number of players increase, by probability alone you'd expect a few players to have a really high-scoring season. (Or, in stats terms, generate some random variables. Take the five highest observations with 60 samples; then take the five highest observations with 1,000 samples. Even though the underlying distribution is the same, the average of the highest samples will be higher in the second case almost 100% of the time).

Last edited: Jan 17, 2007
4. ### reckoningRegistered User

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Do any of the math experts here have an idea how to fix the adjusted assist totals from the 1920s so they're not so unrealisticly high?

5. ### allin4466Registered User

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How do you arrive at those numbers? Do you pick a base year, and deflate everything back to that base year?

6. ### Hockey OutsiderRegistered User

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I agree the assists from the 1920's are unrealistic. To put it into perspective, on my list, there have been 25 seasons with 90 adjusted assists. Eight of those are Gretzky. Thirteen occured between 1925 and 1932. (The rest are Orr in '71, Lemieux in '89, Jagr in '99 and Thornton last year). That's definitely unrealistic.

Why does the problem occur? I think it's because the assists are put through so many adjustments. First, they're doubled (or more) because the schedule was 30-44 games during the 20's. Second, the assists are multiplied by 1.3 because the 20's were generally low scoring. Third, you multiply the assists by 3 or 4 to get them close to the all time goal-to-assist ratio. With all those adjustments, errors creep in. If you take a piece of data and multiply it 7 to 10 times, it can get distorted. Three flukey assists over the course of the season can quickly turn into 20-30 adjusted assists, and that's unrealistic.

I tried fixing the assists by averaging with them with the year before and after (in an attempt to limit the huge variability in assists from year to year). However, that causes more problems than it solves. Instead of having one 100 assist year, you'll have something like three 80 assist years in a row, which is even more unrealistic.

Another potential solution is to give up on trying to make the assists match the all-time average of 1.6 assists per goal. The benefit is that this will eliminate the flukey 100-assist seasons. However, the downside is that players who legitimately and consistently get huge assist totals (like Frank Boucher, with 692 assists in 731 games in his prime) would be penalized too much.

7. ### Nalyd PsychoRegistered User

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For all intents and purposes, it is impossible to compair pre 1930 assists to post 1930 assists.

8. ### RedLightDistrictRegistered User

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It'd certainly be interesting to see how Ovechkin and Crosby's Adjusted scoring for their careers are compared to gretzky and lemieux's first NHL seasons after the conclusion of the regular season.

9. ### Czech Your MathRegistered User

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HO, fantastic list!

You mention adjustments for ice time, but then say you don't adjust for total ice time. I'm assuming you made adjustments for individual player ice time, but didn't adjust the league goals/game data for team ice time (from seasons with overtime)? I don't see it as crucial to adjust league goals/game for overtime seasons, since any increase in goals as a result of overtime will be reflected in the goals/game data. I have seen differing league goals/game data for some seasons and am guessing that some are adjusted for total (team) ice time and some aren't.

If you adjust for individual player ice time, how do you do so? I can see why a league-wide adjustment might be made to adjust for differences in ice time between eras, but if it's done on an individual player level, that would seem more problematic.

You bring up a good point about a larger number of players possibly leading to a more extreme point totals. The upward trend of the average of the highest 5 scorers is something that needs to be studied further. I think the average of a larger number of players (12-30?) might be better, since the presence of dominant scorers (Gretzky, Lemieux, etc.) would have less influence on such a number. I'm not sure whether it would be more accurate to use a constant number of players (assuming a relatively fixed number of elite scorers at a given time), or a number proportional to the number of teams in the league (since there's a limited amount of power play time, proportional to the number of teams). I'm guessing neither would be a perfect solution, but either may help smooth the results. The work done by others with standard deviations also may be of some use in solving such a problem.

I don't see an easy solution to the high assist totals from the '20s. Probably the fairest way to compare would be to only compare those players on the basis of at least 2 or 3 consecutive seasons.