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Monday, November 14, 2011

Replacement-level: playing time

By Tangotiger, 03:32 PM

A reader asked about using plate appearances (PA) instead of innings played (IP) as the playing time component in replacement level. 

Notably, leadoff hitters earn more value than a 9th place hitter, even if both are equal as hitters.  Since replacement level is roughly .003 wins per plate appearance, and the gap between the number of PA for a 1st and 9th place hitter is 8/9 x 162 = 144 PA, that’s roughly 0.45 wins extra the leadoff hitter gets.

I agree, and PA is being used only because of lack of IP data being available.  And general laziness.  I think Rally accounts for this rWAR.(*)

(*) By the way, who started calling it bWAR?  It’s rWAR.

The only issue is what to do with PH and DH.  What you can do for them (and for all of them) is to look at fractions of PA for the lineup slot they are in.  So, if they have 4 PA for the day, and their lineup slot came to the plate 5 times, then you give them 80% of a game.

Of course, we should do the same for innings played, so if they played 8 innings out of 9, that’s 89% of a game.

Generally speaking, a non-pitcher’s value is generally about 62.5% offense and 37.5% fielding.  So in the above case, I’d credit the player with 83% of a game.

So, if you care about every 0.1 or 0.2 wins to give out, use this method instead.


#1          (see all posts) 2011/11/14 (Mon) @ 16:02

Seems like the 0.4 wins/yr would matter taken over the course of a career. Though usually we’re talking about better players, so they will have a smaller gap.


#2    Tangotiger      (see all posts) 2011/11/14 (Mon) @ 16:08

Right.  When we’re talking about more similar high-level players, we’re talking about a leadoff hitter and a fifth place hitter.  It’s more like a 0.2 win gap per year.  So, after 15 years, it’s 3 wins.

Given that no one is going to proclaim any superiority between a 68 WAR and a 65 WAR guy, it’s not that big a deal.

But, if you want to dot i’s and cross t’s, then you should be aware of this.


#3    David      (see all posts) 2011/11/14 (Mon) @ 17:21

Hey Tango.

I’m not a math whiz.  I love your site, and I like the analysis.  I like watching other people do math, and I get it most of the time, but I don’t have the chops to do a lot of the legwork myself.  I say all that so that, if I’m ridiculously off-base in this analysis, you can let me know how and why.

You said that the average position players value is (roughly) 5/8 offense, 3/8 defense.  If this is correct, and the sum of all offensive players is equivalent to half of all production, then don’t position players, in total, account for 80% of baseball?  Pitching being 20%, with fielding being 30%?  This is not at all what I’m used to seeing, and my gut says this is wrong, but that’s because my guy is heavily influenced by the Bill James numbers from Win Shares (O/P/D = 48%/35%/17%, though admittedly, I always thought that was odd, too, with offense coming in at less than 50%).  Anyway, let me know if I’m misunderstanding something.


#4          (see all posts) 2011/11/14 (Mon) @ 17:46

If the defensive side of the equation is 5/3 pitching/fielding (I always use 40% of balls in play for fielding myself nowadays), then baseball would be 5/16th pitching, or 31.25%. It seems a tad low to me, but not ludicrously so.

Oh, James stopped using the 48/52 split with his latest revisions of Win Shares.


#5    Tangotiger      (see all posts) 2011/11/14 (Mon) @ 18:01

I was afraid that we’d get into this!

It’s been a year or two, so I guess we have to talk about the difference between standard deviation and variance (which is the square of standard deviation).

SD is denominated in units, while variance is in units-squared.

The variance adds up, but the SD does not.

What we care about, ultimately, is SD, not variance.

So, we have these values:
5 units: hitting
4 units: pitching
3 units: fielding

It doesn’t matter what the units represent, but it runs per a certain number of games or whatnot.  It’s just important that you note this relationship.

So, we have
off = def
sqrt(5^2) = sqrt(4^2 + 3^2) = 5

So, it works at that level.

That means that nonpitchers get this:
sqrt(5^2+3^2) = 5.83

And pitchers are obviously 4.00

So, the relationship between nonpitchers and pitchers is 5.83 to 4, or roughly 59% for nonpitchers, and 41% for pitchers.

Among nonpitchers themselves, it’s 5 units for hitting and 3 for fielding, so 62.5% for hitting and 37.5% for fielding.

***

Try to understand these numbers.  You can feel free to manipulate these numbers, and get a wrong conclusion if you like.  I recommend you not do that, but everyone wants to try to do it anyway.

(Yes, yes, that sounded arrogant.  If this bothers you, avoid this thread.  It’s going to get worse.)


#6    David      (see all posts) 2011/11/14 (Mon) @ 18:06

Oh!!!  Okay.  I actually get this.  It was just confusing to see the 5/8-3/8 thing without seeing what was behind it.  It actually makes perfect sense.  Without knowing where the numbers come from, it’s hard to see what exactly they mean.  But I appreciate your explaining it.  Like I said, I can FOLLOW mathematical reasoning; I just don’t have the chops to do it myself.  Sorry, by the way.  I wasn’t trying to sidetrack anything, just to understand.  Thanks.


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