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11-10-2012, 02:17 PM
#287
Czech Your Math
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Quote:
 Originally Posted by Dalton I'm not advocating using raw data to compare players across eras. I have suggested and given many examples of using percentages as a way of measuring productivity compared to peers in increasing sets of players to establish a range that a player might have achieved compared to peers in other eras.
Honestly, most of your % work was too confusing more me to follow. Some of it seemed very similar to adjusted stats though.

The problem with strictly using performance vs. peer group is that the quality of the peer group has changed substantially over time. The quality and depth of Howe's peers during his prime was likely much less than those during Gretzky's prime, etc.

Quote:
 Originally Posted by Dalton I have also suggested using reason to complement mathematical estimates.
I definitely agree with that.

Quote:
 Originally Posted by Dalton We can look at a measure of their production as a percentage of sets of peers in their eras and apply those to last year and see what shakes out. I did this with Howe and came up with some incredibly high number of goals but since we aren't actually trying to predict that shouldn't be an issue. I think the Howe result of over 300 goals is simply a reflection of just how dominating he was compared to his peers when he scored 49 goals.
Again, the quality (and distribution) of the peer group makes all the difference. The same quality of performance will appear much more dominating against a lesser quality group of peers.

Quote:
 Originally Posted by Dalton Maybe AS shouldn't be trying to set a fixed, realistic looking number to use as a measure. That just makes it look like a prediction. Comparing to peers in their own eras and then comparing those results is a better approach IMHO.
The units aren't really important, but using a "realistic looking" number gives some kind of reference point... it's as good as any.

The peer comparison tells us nothing of comparative value. As far as comparing performances from different seasons, it doesn't tell us much unless we can confidently estimate the magnitude and nature of the change in quality of the peer groups.

Quote:
 Originally Posted by Dalton Or maybe a precise definition of what AS is trying to achieve would work here. Honestly it really just looks like an attempt to predict actual GS and that clearly causes confusion. I don't see it as a measure of productivity either. What does 'value of gs' as an example actually mean. What is it trying to do?
I see two main uses for adjusted stats:

1. It gives a value estimate, based on the fixed proportion of production vs. scoring environment. 30 goals in a 6.00 gpg league should have about the same value as 40 goals in a 8.00 gpg league or 20 goals in a 4.00 gpg league. AS is perfect at this relatively simple function.

2. it is a potential starting point for comparing players' seasons, but it is complicated by many factors which affect the difficulty of attaining various levels of adjusted production in each season.

Quote:
 Originally Posted by Dalton The lack of a dominant individual should not and cannot justifiably be an argument for devaluing the productivity of those from the past.
Be careful when using terms like "devaluing", because adjusted stats are very clear and useful when it comes to the value of production in each season. Where it's not so clear is when trying to determine which player-season was of higher quality/difficulty.

Quote:
 Originally Posted by Dalton We see these outliers because of their dominant productivity. The performance of the whole era they belonged to also has higher value because of their presence. Outliers change everything. Einstein opened a whole new way of thinking that accelerated schievements in Physics that persists today just as Orr changed the way d-men play forever. Both can be seen as having built on the work of previous outliers. In a very real sense these outliers made their eras outliers. When you average eras so that their achievements are all equal, as a method of comparing them, you devalue the achievements of the eras and the outliers that led the way. Gretzky was a superb offensive machine as Newton and Liebnitz were superb mathematicians. Nothing is going on today that compares to those eras. The unintended consequence of averaging the eras to compare them is to devalue the accomplishments of the outliers themselves. Hence averaging necessarily reduces the output of the best while increasing the output of the rest. Removing the outliers does not solve this problem since they impacted the productivity of all their peers. Everybody learned something about offence from Gretzky and math from Gauss. You cannot remove their impact on their era by just removing their accomplishments. I conclude that you can only really look at an outliers productivity in the context of the era they achieved. If anything their productivity should be increased to reflect the fact that their presence increased the productivity of their peers thus closing the true gap between them and their peers. I don't think its fair to reduce the value of their peers though.
Most great accomplishment were achieved by standing on the shoulders of giants, that is true.

All I'm saying is that just because standard physics becomes inadequate when studying the very big (cosmology) or the very small (quantum physics), is no reason to discard it. Similarly, just because simple adjusted stats don't automatically tell us which player-season was of higher quality... or may have increased error when dealing with extreme outliers... does not mean they are inherently flawed and practically useless. They are perfectly good as a measure of value. I don't see any measure at this point that can tell us with nearly absolute confidence how production in different seasons varied in quality/difficulty. More study should be done in this area if that is the goal, but in the meantime I believe adjusted stats are as good as any metric in helping to assess that.