I think the pythagorean GF/GA data is important in to some degree supporting the effect on win % and interesting in detailing the effect and its reasons. The matter of exponent is likely a small complication in this, if one is calculating expected win% from such data.
In a way, I think factual won-loss stats are what should be used. A win is a win, no matter if it's by 2-1 or 7-2.
In another way, I like the nuances one gets by using GF and GA to calculate pythagoran win %.
So I combined the two, making them equally important, rather than doing two separate studies. (I had already done some "boring" research of more mathematical nature, sort of like I tried to suggest in your stickied thread, so I felt confident I knew what I was doing.)
One can think more, deeply think more, about the above two things. On a team level, focus is basically only on it's about factual win %. On a player level, most stats focus on GF and GA related things. For example, +/- is GF and GA related, while points scored is GF related.
So our apprach to stats may be seen as partly contradictory. Player stats focus a lot on team GD (GF-GA). The better team goal difference, the more beneficial for the players' +/-, and vice versa. While on the other hand, on a team level, goal difference is (especially in the NHL) made relatively unimportant.
The "best" for a player (skater), statistically, is when his team gets as good goal difference as possible, because that will be benificial to his +/-, and the more GF his team scores, the more beneficial to his scoring stats. But a team doesn't necessarily care for those things, because they just want to win, or get into a penalty shootout, and to gain as many points as possible. If a team leads by several goals, they may bench(?) certain players.
Okay, the above two things often may go hand in hand. But basically we often treat player stats (like +/-) as if the main goal of the NHL teams is to gain as good goal difference as possible, when it's actually not.
Regarding the exponent, I think the key is to know what one is doing and what effects different exponents have. This too includes "boring" mathematical studies. For example, it matters how far from "average" the results ends up. I can't really express this properly in English, but let's have two series where one has a wider spread from average than the other. Then the highest results from that series will be higher than the highest from the other series, and the lowest results will be lower. (Oh, if this is not understandable, please ignore it, as I can't express myself propoerly.)
IIRC, some your work was more within games themselves, and used per-minute type data to some degree. If this is correct, I'm not sure how comparable this would be to metrics using whole games, but could be interesting nonetheless.
No, I used whole games.
But now that you mention it, I'm open to experiment with including icetime as well. But it's not a priority, I'm not sure about it's real meaningfulness, and I won't do that within any near coming future
This isa good point, that individual seasons should also be examined. In Sakic's case, the effect from '98-00 is still less than others, and is neutralized by his '97 and '03 data.
With examining individual seasons, I not only meant looking at the results for those seasons. I rather meant taking the time to also manually look up what the roster looked like for each game. Like a table with player names on one axis, and game numbers on the other, so that one can easily see which players were out simultanously, when players got traded, etc. I can get that info within 2-3 seconds, just having to enter season and team and push a button, and I hope a site like hockeyreference will soon show that kind of info too.
(There are so many things that could be done, and I've thought about starting a stats website, providing things that aren't very easily conducted/found, but decided it would probably not be worth the effort and cost. A boring Stanley Cup playoffs, followed by an exciting Football European Cup/Championship even further convinced me.)
I agree with you mostly. I think adjusted plus-minus is the better metric, given it's wider availability and much larger sample of data. I understand that players are utilized differently, but the metric captures something very important: how much better the team was with or without the player on the ice at even strength. There are complicating factors, as in most metrics. In such cases, it is important to look at other data and look at similar players to see if what the metric suggests is reinforced or contradicted by other data and/or the same metric for other similar players.
I've actually become more and more skeptical towards +/-, including traditional attempts at adjusting it. Anyway, I think that if one wants to adjust +/-, one should start by trying to get rid of the effect of goaltending.
If one should manage to "adjust away" the influence of goaltending, then team stats would look differently. The team GF might perhaps be affected by a goal or so, but the team GA would be affected tremendously!
Colorado, taking away the effect of Roy, would perhaps suddenly look pretty average, rather than like the constant elite team they were. That despite having guys like Sakic, Forsberg, and a bunch of great defencemen (Blake, Bourque, Foote...). Forsberg's and Hejduk's great league leading +/- from 2002-03 would not be as impressive.
The above is another case that I think needs "boring" mathematical research. One needs to methodously(?) first learn to isolate the goalie effect, something that would likely take lots of time and effort and not resulting in very publicly appealing results.
Of course, it might be a very difficult study too. For example, to what extend was a certain team's goaltending stats affected by its playing system and skater performance, and vice versa?
IF one would manage to "adjust away" goalie influence, I said that team stats would look differently. And here one might also want to think more deeply about that. For example, we again can focus on the thing at the beginning of this reply, namely factual win % vs pythagoran win % (based on GF and GA), and also the "conflict" between what teams want and what players "want" regarding their stats. We likely would need to face arbitrariness, as well as the fact that we would be looking at "goalie riddened" stats from a World that was included goalies as an important part of the game.
Example: "See, Colorado without Roy actually were quite average. That is, their skaters as a whole performed average. And Forsberg (bad example, but anyway) actually looks only slightly better than the average player, rather than like a candidate for the best/MVP player." But, things were as they were, and we actually don't know how things would have turned if they had an average goalie instead of Roy.
I have .63 with and .56 without, but the difference could be in how we count SO/OT W/L. I counted all W/L the same, none as ties, since it would take much more time to differentiate between the two (no info about SO/OT in player game logs on HR).
I think I used decimals. 2 for 60min win, 0 for 60min loss. Maybe 1.333 for overtime win , 0.667 for overtime loss. Maybe 1 for OT draw, thus ignoring the shootout result (although I did include it when examining the goalies).
This is true, and one reason per-game data and per-minute data must often be taken with a grain of salt. It's one thing for a player to miss a few games or 1/4 season on occasion and perform at a similar level in the past/future. It's another when a player suddenly performs at a higher level for a half season or less (see Kariya, Bure, Crosby, etc.). Forsberg too, had by far his best season after a full season off, which must be considered IMO. In the end, we can most fairly evaluate what players did, and much less so how they would have done, although external circumstances and differing environments should also be considered.
Yes, I think we basically have to judge players based on their (f?)actual performance. Not try to adjust for "healthyness" or "degree of injury".
By the way, Forsberg himself recently stated something like... First he had his techical skills, and his strong desire to fight and win. Then he had a time when he could add an increased understanding of the game, and this coincided with his Hart win and his biggest playoffs scoring success. Then his body got worse, and he had to rely on his understanding of the game. (I'm not sure I agree, as I think he "always" understood the game greatly, but anyway, sort of.)
