THE BOOK--Playing The Percentages In Baseball

When you adjust a player’s plus-minus, what do you use for the baseline? Total team EV plus-minus, or the team’s EV plus-minus when the player is off the ice?

I use the off-ice method, as I think it more accurately captures the impact of a player like Bobby Orr that gives his team completely different results when he is on the ice. It looks like Tom Awad is using the total team performance as a baseline, but I can’t see the advantage of that.

overpass: you understand my system the closest so far!

Tango, that’s like saying shootouts aren’t even hockey anymore.  Kind of true, but… they’re still really exciting, especially to casual fans.

I took my girlfriend to a Bruins game last week, and there ended up being a 5-on-3 for about 1:30.  I specifically remember telling her that those were my favorite part of hockey as a kid (well, in addition to overtime).  I was a defenseman, and I loved the excitement of being down two, and the chance to really bum out the other team by keeping them off the board during it.

In fact, my favorite hockey memory in the last 10 years or so is probably the college national championship the year it ended with a team down 0-1, having a 6-on-3 for the last minute and a half.  How exciting is that!  In the history of hockey, has that ever happened before in such a big game?!

Mike, it sounds like we agree on what it is:

It’s kind of like shootout hockey actually: ... but there is alot of tension, especially when a team can kill off that penalty. 

The only question is whether you want 5-3 as part of hockey or not.  There’s a reason that there’s no 5-2 hockey right?  At that point, penalties are served consecutively, not concurrently.

When you adjust a player’s plus-minus, what do you use for the baseline? Total team EV plus-minus, or the team’s EV plus-minus when the player is off the ice?

I use the off-ice method, as I think it more accurately captures the impact of a player like Bobby Orr that gives his team completely different results when he is on the ice. It looks like Tom Awad is using the total team performance as a baseline, but I can’t see the advantage of that.

I see at least two problems with this.  First of all, Awad seems to be assuming that player contribution to goals for/against is equal.  His system would, I think, probably give too much credit to defencemen.  Even amongst forwards, I’m not sure that it works - someone like Joe Thornton probably drives the +/- more than someone like Jonathan Cheechoo but if they play together the vast majority of the time, their +/- will be sort of tied together.  I’m sure there are ways around this but still.

Second, I have some trouble with the WOWY thing here.  Taking the Oilers as an example, guys like Horcoff/Hemsky are kind of joined at the hip.  I don’t know how much you can separate their performances.

Third point - the goaltending probably has to be done on an individual basis, rather than on a team basis.  Within a team, there can be a big spread in on-ice save percentages, one that I’m not sure has a ton to do with how the player plays.

That said, this is, I think the right idea, it’s just a matter of sorting out how you do it.

Tyler: yes, agreed.  It’s all about trying to figure out where the non-randomness or biases exist, and adjust or account for it.  I’m having a HAG_list discussion on this issue with Tom Awad, and I will reprint everything I have said this morning on this topic:

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> on their teams. Normalizing Mario Lemieux’s 1989 season
> from +37 to +77 doesn’t make any sense. Neither
> does boosting Jarome Iginla’s 2002 from +37 to +75.
> Also, I don’t know why you end up with players at -1000.
>
> The reason why we normalize plus/minus is to take into
> account the other players who are on the ice with you,
> not the players who aren’t! Comparing on-ice to off-ice
> plus minus, while interesting, is not an adjusted plus/minus.
> It’s just comparing a player to another group. By definition,
> if you’re Mario Lemieux, you’re being compared to third
> and fourth liners. If you’re an enforcer, you’re being
> compared to Lemieux. Not fair.

I disagree about the “doesn’t make any sense”.  If you look at the total pluses and minuses as you are doing it, it includes the big pluses the others got because of Mario.

There are further adjustments you can make (and there is a big bias if you have a Triple Crown type line), but the core of this system (With Or Without You, WOWY) is the way I also do it.

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> The first method is valid, the second is not. I assumed,
> based on the results, that the second method is what
> was used.
>

I don’t see how you conclude that the first method is valid.  You agree that it includes all the big pluses for the 4 guys who played with Mario.

The second method does NOT compare Mario to 4th liners (let’s not make the argument so extreme as to make it absurd… there are 17 other skaters and if Mario always played with the same 4, that’s still another 13 skaters left).

If Mario was used equally with all other players (which he was not obviously), then the second method is valid.  How much Mario was used with other players tells us how good the second method (WOWY) is.

The idea is to figure out how good are the 4 guys Mario played with.  The question is if the performance of the players when Mario was not on the ice (the 17 skaters) is representative of the 4 guys he did play with.

A pure random system would say: “yes”.  A pure combo (the Russian 5) would say no.  The level of non-pairing determines the level of representation.  On a career level (guy with long career), the WOWY system works, because at that point in a player’s career, he will have played with so many other players as to make the comparison group representative.

For those new to WOWY, I’ll point you to this article:
http://tangotiger.net/catchers.html

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I should also point out that I have done it both ways:
1. using the gross pluses and minuses, and removing the player’s individual pluses and minuses

2. using the team pluses and minuses, and removing the player’s individual pluses and minuses (i.e., WOWY)

I would not conclude on the validity or invalidity of either method.  I’ve done, and continue to use, both methods.  The smaller the number of games, the more the pairings exist, the more I use the first method as a way to “stunt” the extremisms of things like Howe/McCrimmon, or Dionne/Taylor/Simmer.  The more the number of games, the less the pairings exist, the more I use WOWY.

Again, it’s all based on trying to determine the bias in the metric, and trying to find the best way to get representative data out of sample data that is not random.

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> Obviously that doesn’t happen, so the question is
> how extreme the pairings are. I’m always suspicious
> of metrics that give me extreme results, so I’ll keep
> digging, but I’ll concede that, mathematically, under
> the assumption of random linemates, the second
> method is the more correct one.

Right, the most extreme results you will find are likely the Howe/McCrimmon year of +85/+83: poor Doug Crossman, who was a -5 as he certainly never played with either of the other two guys.  So, his defense partners were the dregs on that team.  He would look terrible here.  In addition, Howe and McCrimmon would BOTH look lights out.  On top of that, if you add up their two adjusted plus/minus figures, using WOWY, you’d end up with +170 or something.

Similarly, you can look at poor Butch Goring in 1980 who was -21 as he (likely) rarely played with Taylor/Simmer, and so, he’s going to look horrible, while the Triple Crown will add up their individual scores to come out with a +100 or something.

The key question being asked is: “How much of that +85 breaks down between Howe, McCrimmon, Propp, Kerr, Poulin, Ekulnd, etc, etc, etc”.  You get to use Crossman’s -5 because he ALSO got to play with Propp, Kerr, Poulin, etc, etc.  But, not at the same frequency.

This problem is exactly and no different than the “strength of schedule” that confronts everyone.  To solve this problem, you need to know how often each player (or team) plays with (and against) other players and teams.  Indeed, implicit (in our past discussions) is that Mario and Howe et al have had an “average” opponent.  This again is another source of bias.

As long as we agree that we can make no conclusions nor discard any process, then I really have no issue with anyone’s opinion as to the best way to proceed.

"Second, I have some trouble with the WOWY thing here.  Taking the Oilers as an example, guys like Horcoff/Hemsky are kind of joined at the hip.  I don’t know how much you can separate their performances.

Third point - the goaltending probably has to be done on an individual basis, rather than on a team basis.  Within a team, there can be a big spread in on-ice save percentages, one that I’m not sure has a ton to do with how the player plays.”

Tyler - I don’t know if you can separate Horcoff/Hemsky. Basically the WOWY plus-minus number for Horcoff is (Horcoff + Hemsky + linemate). I don’t think it’s possible to separate that - certainly not for historical data. Even for more recent years where there is far more data on who played with whom when, the sample size of (Horcoff without Hemsky) and (Hemsky without Horcoff) is probably too small and too skewed to specific situations to conclude anything with confidence. I don’t think there’s a way around that.

Goaltending - yes, ideally the numbers would adjust for on-ice SV% and shooting %. That’s not available historically, and we just have to hope that it evens out over time. Adjusting for team SV% would probably be an advantage. I haven’t done that, but if I did it would be a partial adjustment, as the skaters should bear partial responsibility for the SV% also.

...as the skaters should bear partial responsibility for the SV% also.

I would not go there, unless you back that up.  For example, if you look at Hasek’s league-leading save % year after year, do you really want to assign any of that to any of his players?  I know I don’t.

You can do: Hasek’s goals above average, divided by minutes played, times number of minutes Pat Lafontaine played.  And make that the adjustment.

It gets more complicated with EV/PP/SH, but that’s the basic idea.

In no way would I only give Hasek partial credit.  This is the same issue I have with Dewan’s adjustment in The Fielding Bible II.

Tango - I would give Hasek full credit for his SV%. I would give most NHL goalies of the past 20 years full credit for their SV%, as there have been few really dominant or terrible teams.

I wouldn’t give Ken Dryden full credit for his SV% - I think he would face easier shots playing in front of a historically great defence. I wouldn’t give Ron Low full blame for his SV% in Washington - he had a historically bad team in front of him.

I’m not sure how to map that onto individual skaters. I’m not aware of a consistent way to predict shot difficulty for a team based on team factors, so it may not be possible to assign partial responsibility for SV% to individuals. In some cases I would prefer to. It seems likely that if the data was available, Larry Robinson would have a better personal SV% compared to his team than, say, Reijo Ruotsaleinen.

Actually, divide that by 5 (or 4.8 or something) as the adjustment.

overpass: I don’t disagree with your basic premise. Trying to figure out shot quality (without event data) would certainly be quite the feat.

Tango - I would give Hasek full credit for his SV%. I would give most NHL goalies of the past 20 years full credit for their SV%, as there have been few really dominant or terrible teams.

I wouldn’t give Ken Dryden full credit for his SV% - I think he would face easier shots playing in front of a historically great defence. I wouldn’t give Ron Low full blame for his SV% in Washington - he had a historically bad team in front of him.

Yeah, I agree with this.  My sense is that, within a broad level, there isn’t a huge difference in shot quality over the course of a year.  I actually wrote a post on this earlier (click on my name) this year and I found that the skaters at the extremes through the first half of the year tended to be at the league average for the next half of the year.

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Gabriel, who has one of the best hockey stats site around also chimes in:

http://www.puckprospectus.com/article.php?articleid=70

He also does the “with or without you”, but he doesn’t do the “80%” part.

I like his presentation, since it’s all based on “per 60 minutes”, akin to “RC per 27 outs”.