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04-30-2012, 12:53 AM
Czech Your Math
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Originally Posted by plusandminus View Post
I didn't study it as thorough as you seem to have done. I didn't really feel/think it was as interesting as other things. But now that you posted this thread, and I got involved in a conversation with you, I have thought more about it. And I think what you're doing is interesting and a good approach. As you have pointed out in the thread, your method automatically accounts for several things, like partly strength of era. If I have the time, energy and focus, I intend to try to repeat your study and experiment with it a bit. I have things like age and nationality in my database. Nationality may be of interest if we for example want to study Canadian players in comparison to say European.
I'd certainly be interested in what results you generate with a similar approach. Have you given any consideration to using regression? It seems to me that this could study several different variables without needing separate studies, and should have a relatively high degree of accuracy and low error. It would also eliminate some variables as irrelevant and so reduce the error when the calculations are redone without such variables.

Originally Posted by plusandminus View Post
Agree. But, maybe there are ways we can get around that, as at least partly suggested by your method.

As I tried to say yesterday... Traditional adjustment just makes each season equal, no matter what quality level. Each season gets the same number of goals per team to distribute throughout the league. First, we distribute the goals on a team level. Then we distribute them within each team.
The higher gap between the best and worst teams, the more "favoured" (rightfully or not) the players on those team's will be compared to seasons where the gap was smaller.
The higher gap between the best and "worst" players, scoring wise, within a team, the more favoured the best scorers will be.
"Traditional" adjustment of scoring is basically based on comparing teams and players to averages. But the average team of one era/season might be considerably better than the average team of another era. Same with players.
I just wonder how much the distribution of scoring within a team, for instance, really tells us. Gretzky's teams were or were among the top scoring teams in the league. He outdistanced his teammates by incredible margins. Does that somehow make his production (relative to the league averages) better or worse? If so, by how much and why?

I definitely agree that the general strength of the league and distribution of talent within the league (among different teams) is an important factor though.

Originally Posted by plusandminus View Post
Regarding +/-, I'm currently leaning towards separating defencemen and forwards (which isn't black and white either). If we take forwards, they show a consistency in scoring, in that their scoring (except when playing with Mario, Gretzky, etc.) is fairly constistent from season to season. Their GA (goals against) may however change dramatically from season to season, and we also know that goaltending is hugely affecting +/-. So maybe the best thing for forwards would be to treat their "+" as they are, and then goalie adjust their GA and then perhaps even half them.

Because... It is often being said (at least it used to be said) that the "goalie is half the team". So why then "discredit" forwards so much for the goals againsts they are on the ice for? Maybe points scored is a better measure of forward performance than +/- is? I have experimented with formulas giving a point e.g. 1.25 and being on the ice on a goals for without getting a point say 0.7. Or maybe even 1.4 and 0.55. Then we get their offensive value. (Now I should have learnt more about Alan Ryder's methods.)
Raw plus-minus is obviously a severely flawed statistic, influenced greatly by the quality of each player's team and to the assumption that each skater is equally responsible for each GF or GA while he is on the ice.

You make some good suggestions about dividing the responsibility less equally. It seems much easier to appropriately divide GF than it is to divide GA among those on the ice. Whatever the assumptions made, I would guess the end result is still going to be a very rough estimation and subject to a large error (as I believe points shares and even strength win% are).

Originally Posted by plusandminus View Post
Yes. I took it further and integrated PP and SH. I was going to post it here, and even started writing about the methodology, etc., but didn't follow it through.

First, I was going to give each team a number of points. (To make it simple one could just look at the standings and take their factual points there. I, however, used another method.) Then one distribute those points among the players on the team.

I like the method. It rewards players for playing and for contributing. +/- doesn't work like that and may actually "punish" a player for playing, compared to a teammate who is benched. The win method also produce results that can be meaningfully divided by games played.
I briefly reviewed the "Even Strength Win%" formulas which I created and have mixed feelings about them. As you say, it rewards players for playing and contributing, but my hunch is that it tends to give too much credit for simply "being there" on great teams and too little credit for being outstanding on hapless teams.

That's likely no accident, since it was created after Overpass expressed concern that his "adjusted plus-minus" system didn't give enough credit to lesser players on great teams.

I think with substantial further improvement, such a system might eventually be a viable alternative or complementary statistic to HR's "point share" system. However, there seem to be enough arbitrary assumptions inherent in either of these systems to leave me preferring "adjusted plus-minus" at the end of the day.

Originally Posted by plusandminus View Post
Yes. I have tried to handle that wisely.
It's impossible to get significant results for any player who didn't miss many games. No matter how wisely you handle the data, there's just not enough "without player X" data to make any sort of reliable conclusion.

Originally Posted by plusandminus View Post
I haven't yet digged deep into your analysis of the three "eras" you mention, but now is the time for others to give their thoughts on your findings. (If I remember right, what you write seem similar to the impressions others here have.)

Thanks again for positive words.
There seem to be inherent limits in comparing across eras, but especially from the O6 to more modern hockey. I think it's fairer to basically separate it into pre-expansion and post-expansion periods, with the '70s basically being the buffer zone. So Howe, Hull, etc. would be in the former group, while Esposito, Orr, etc. would be in the latter group.

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