This is good work, I have done similar work on my site. It includes ratings for players for discrete categories and then blends them into an overall rating. It passes your Crosby/Bozak test.

http://xtrahockeystats.com/ratings.php

Nick

]]>You could argue that Jake Gardiner plays with forwards with weak shooting percentage and that’s why his assist rate and GF/60 rate isn’t so good. But his TMGF/60 rate is a lot higher than his GF/60. Jake Gardiner is a good puck-moving defenseman but he’s not the playmaking prodigy that analytics fans think he is. And for an “offensive defenseman”, he sure stinks on the power play. Jake Gardiner doesn’t have the hockey IQ to work a power play. He doesn’t have the hockey IQ to actually make good plays consistently. Even though the scoring chance metrics say he does. He scored at a 0.4 PPG clip in his rookie season and received a lot of hype for this. And despite increases in his PP time, he has yet to match, let alone surpass his rookie PPG rate after playing 3 full pro seasons in the NHL and one short season. I think Jake Gardiner’s concussion with the Marlies in late 2012 might have affected him. If I were to include Jake Gardiner’s rookie season and look at 4 year data, his numbers improve. But if you can’t get back to where you were 3 years ago, a rookie season, something smells.

]]>Yes Malkin and Sutter both have an impact on Crosby’s numbers, as will the fourth line centre. However, the fourth line centre will only have a significant effect on Crosby’s numbers if the rest of the fourth line sees decent ice time with Crosby. Which doesn’t happen.

I don’t think it is a coincidence that Toews has great RelTM stats with a coach who likes to juggle lines. I don’t think it is a coincidence that Crosby has surprisingly low RelTM stats when he is consistently partnered with the same wingers (who will realistically see the second most ice time with Malkin).

These conclusions arise almost immediately from examining the formulas used. The RelTM stats need some sort of accompanied perturbation analysis to be taken seriously.

]]>It isn’t perfect (we will never have the perfect stat) and there may need to be more normalization across teams (this is an extremely difficult thing to do, if even possible) but I think the stat is telling us something useful. More useful than the alternatives.

]]>The point being that this stat can’t be looked at in isolation. RelTM stats are dependent on how players on the same team who never see ice time together relatively perform.

I would bet a fair bit that this is why Crosby’s numbers are dragged down in some of these stats.

]]>Just a bit of a background here. Traditional ‘Rel’ statistics perform a similar relative comparison but instead of at the player level as I do it is done at the team level. So the Rel statistic is On Ice Stats – Off Ice Stats. The problem I had from these Rel statistics arose many years ago when comparing Red Wing and Islander players. The Red Wings were one of the best teams in the league and the Islanders one of the worst. In these Rel statistics Kris Draper looked terrible (worst in the league) and yet he was selected for the Olympic team. The reason is he was playing with Maltby while he never got to play on the Red Wings top two lines which were stacked with Yzerman, Datsyuk, Zetterberg, Shanahan, Holmstrom, etc. Even good players would look terrible against those guys. Meanwhile a lesser 3rd line player on the weak Islander team would look far better because he didn’t have to compare with a stacked top two lines. For that matter weak teams often shuffle their line up a lot and that 3rd line player probably got ice time in the top six. Draper never did. I wanted to come up with a better system where a players on-ice statistics are not being compared to the teams performance when they aren’t on the ice and using players he rarely gets to play with.

There is where I came up with the idea of looking at whether the players he does play with perform better or worse with him than apart from him. As you point out this is not a perfect system either but I think it is better and I know some others have used it in models and found it provides better results. There is still a bit of a problem with players on strong teams getting penalized because they can’t make a superstar look better while if they were on a weak team they may be able to make a mediocre player look better but I think it is less of a problem using RelTM than traditional Rel statistics. Furthermore defensemen are inserted into the equation and defensemen play with everyone on the team, from first liners to fourth liners. The defensemen on the team will come closer to representing team average statistics so they act as a bit of a neutralizing effect to minimize some of the problems you bring up. So, in reality your specialized scenario never really exists to full effect. Also, increasing to longer time periods provides for more mixing and matching of players, including movement between teams, which will again normalize things.

How to best isolate an individual players talent and how to normalize that across the league so we can best compare players is a really tough question that we probably can’t solve perfectly with the data we have. We have to do the best we an and I believe (though I may be biased) RelTM is currently the best method to do so.

To finish up, yes, players on extremely good teams or playing primarily with extremely good players may be getting penalized a bit for doing so. Similarly players playing on an extremely poor team playing primarily with extremely poor players probably are getting over valued. There is a lot of parity in the league right now though so this minimizes the necessary corrections some what.

]]>To begin, some notation: TOI(A,B) is the time on ice player A spends with player B, and TOI(A,#B) is the time on ice player A spends without B. With this convention, TOI(A,A) is player A’s time on ice. Similarly, GF(A,B) is the goals for stat for player A when player B is not on the ice. Finally, SUM(1,n)[f(k)]=f(1)+…+f(k).

We will be looking at the stats of player 0, whose team is made of players 1,2,…,n.

Let’s examine the GFRelTM. I’m not bothering about the ‘per 60′ aspect, as that is just a coefficient that factors out.

We have that the GFRelTM of player x is:

[GF(x,x)/TOI(x,x)] – SUM(1,n)[W(k)*GF(k,#x)/TOI(k,#x)]

Where W(k) is the weighting factor of player k with respect to player x. Now, I suspect that:

W(k) = TOI(k,x)/TOI(x,x)

Let’s contrast two scenarios. Each scenario will consist of Crosby, a second line centre, and four identical plugs. In these examples, hockey is a 3v3 game.

Crosby and the other player never play with each other (so they always play with two plugs). Every player is on the ice for 10 minutes. Crosby always scores 1 goal per minute. The plugs never score.

First example: The second line centre is Malkin, who scores at a rate of .8 goals/minute. In this case the GFRelTM of Crosby and Malkin respectively are -0.6 and -1.2.

Second example: The second line centre is Bozak who scores at a rate of .2 goals per minute. In this case the GFRelTM of Crosby and Bozak are 0.6 and -1.8.

To contrast, Scott and Glass never play together, have 4 identical plugs who never score, and both of those guys score at a rate of 0.01 goals/minute. Their GFRelTM are both -0.01.

Either I’m misunderstanding these RelTM stats, or they are very inherently flawed.

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