THE BOOK--Playing The Percentages In Baseball

I should also note that this is a 1yr prior to 5yr post curve.  If you know more about the player, like his win shares at ages 23 through 25, you would of course rather have than, than just basing it on his win shares at only age 25.

If you look at the nonpitchers and pitchers aged 30 and older, you will see that they retain around 55% or so of their value in the subsequent 5 years.

If you remember how I do my aging for WAR, I simply remove 0.5 wins per year.  So, a guy with 3.0 WAR would have the following over the next 5 years:
2.5, 2.0, 1.5, 1.0, 0.5, for an average of 1.5.  That is, they retain 50%. 

Win Shares and WAR are not of the same scale (Bill James gives out 81 wins per team, and I give out 34 wins per team, so that’s pretty clear).

I’m new to the site so I was wondering if it wouldn’t be too difficult for you explain the method you use to calculate WAR.  Is it similar to Baseball Prospectus?

Thanks in advance.

It is not the same as BP.  If you can find one person outside of BP that appreciates their replacement level, please send them to me.

Replacement level is calculated as the following:
1. For nonpitchers, it’s 2.25 wins per 162 GP, below average.

Because of the difference in quality in AL and NL, I set it to 2.5 for AL, and 2.0 for NL.  The quality of players is that different.

2. For pitchers, it’s .380 win% for starters and .470 for relievers.

Again, the league differences sets it to .370, .390 and .460, .480, respectively.

So, as an example.  Say that you have a player that is 1 win above the average NL player, per 162 GP, and you expect that player to play 140 games.

His WAA per 162 G = 1.0
His WAR per 162 G = 1.0 + 2.0 = 3.0
His WAR per 140 G = 140/162 * 3.0 = 2.6

That’s his WAR.

For a pitcher, let’s say you have a starter in the AL, and his win% is .540.  (And by win% I mean his component win%, meaning the expected win% based on how many runs you expect him to allow.) Let’s expect this guy to pitch 198 IP.

WAR = (.540 - .370) * 198/9 = 3.7

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For relievers, there’s an extra adjustment.  You need to figure out his Leverage Index (assume 2.0 for a closer and 1.3 for a setup guy).  You give him bonus WAR for his wins above .570 (.560 for AL, .580 for NL), multiplied by his LI minus 1.

Let’s say you have Mariano Rivera, with a .660 win%, and 72 IP.

His straight WAR is:
(.660-.460) * 72/9 = 1.6

Figure his LI is 2.0.  So, his bonus WAR is:
(.660-.560) * 72/9 * (2.0 - 1) = 0.8

So, Rivera gets 2.4 WAR in this case.

Thanks a lot.  I don’t even know how BP calculates their WARP.  I’m sure the formula is available, but they don’t make it readily available, which makes me very skeptical. 

Is there an easy way to calculate the LI of a reliever or do you use the one that’s published on Fan Graphs? 

By the way, this is by far the best site on baseball that I’ve found.  I just wanted to let you know that and I hope you keep the good work up by enlightening us idiots who don’t understand as much as you do, but keep trying.

BP uses a very low level for replacement level.  For example, while I have the average nonpitcher at 2.25 WAR, they would have him close to 4.0.

And while I have the average replacement at a .410 win% (.380 for starter, .470 for reliever), they have him at around .300.  That is, my average pitcher is +.090 wins per 9IP above replacement, while theirs is double that.

This goes with the standard assumptions, as I use .300 as the team replacement level (average team is +.200 wins above replacement), BP uses a team replacment level of .150 (average team is +.350 wins above replacement).

I’ve beat this drum alot around here, but I’ll keep doing it, since no one at BP is ready to challenge me on it: there is not a single analyst out there that would argue for a replacement level that low.

BP should be ashamed at doing what it’s doing, plain and simple (especially considering what Woolner himself has done goes contrary to WARP… talk about talking out of both sides of your mouth).  I’m pretty sure I’m persona non grata with some of them now, but I really don’t care.  When it comes to choosing sides, I’ll stand on the side of the truth.

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As for LI, since David at Fangraphs implements all the versions of LI exactly as I’ve described them, I use those.  They are, in effect, Tangotiger-sanctioned Leverage numbers.

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Thanks for the kinds words on our blog!

Just to be clear, I don’t have any personal beef with BP; I have a professional disagreement with them.

Are we sure that method doesn’t get distorted for relievers? For example, if I use a league average of 4.8 R/9 and assume Rivera gives up 3.0 R/9 in 72 IP, that’s a pythagenpat win% of .700. Using your method, that is 1.9 WAR + 1.1 LI adjustment = 3.0 WAR.

Since relievers typically pitch one inning per game, if I figure runs allowed for Rivera as (4.8*8/9 + 3.0*1/9) = 4.54 R/9 for a pythag of .520. I’m iffy of what to do from there. If a replacement AL reliever is -.04 wins per game, I guess that means -.0044 wins per inning, so a replacement win% would be .496? (.520-.496)*72 = 1.7 WAR. For the LI adjustment, a replacement AL closer is +.06 wins/game or +.0067 wins/inning. So win% of .507. (.520-.507)*72 = 0.9. 1.7 WAR + 0.9 LI adjustment = 2.7 WAR (rounding error). The first method is 13% higher than the second (3.03/2.68).

Not a huge difference, I guess, assuming I did all that correctly, although it’s roughly equal to the league adjustment. The second method seems to mimic reality better, I think.

Yes, we’ve had this discussion a little while ago.  The “win%” should really be based more on a reality situation, as you are describing it.

If Rivera is pitching 72 IP in 60 G (1.2 IP per G), then you are applying his Runs allowed per 9 IP to those 1.2 IP, and the league average to the other 7.8, and then comparing with a replacement getting 1.2 IP.

Let’s say the runs allowed is 4.8 per 9 IP, and Rivera gives up 3.3 per 9 IP.  If he were a 9 inning pitcher, his win% would be .666, according to pythagenpat.

But, at 1.2 IP, he gives up 0.44 runs, and the other 7.8 by a league average pitcher is 4.16, for a total of 4.60 runs.  That’s a .520 win % for a team in which Rivera pitches 1.2 IP.

Doing the same with a replacement (5.10 runs allowed per 9IP) gives us a team win% of .496.

So, Rivera is +.024 wins per game pitched, times 60 games = +1.44 wins.

Otherwise, he’d be .666 - .470 times 72/9 = +1.57 wins.

Recasting the +1.44 wins back into a “linear win%” number:

+1.44/72*9 + .470 = .650

That is, his 9-inning .666 win% that’s you’d calculate using a straight PythagenPat is equivalent to a .650 win%, if you go through all the machinations of post 9.

Tango, can you explain why you don’t just double a closer’s WAR (or his IP - same thing) given a leverage of 2.0?

Aren’t we comparing a closer to a replacement reliever (.470) who also would pitch in high leverage situations?  A player’s value is always as compared to a “free” (min salary) player pulled from some place other than your own team (to avoid the effects of chaining) put into that same role.

If Rivera does not pitch 72 IP with a LI of 2.0, won’t a replacement reliever, who is a .470 pitchers, have to pitch those same 72 IP with a LI of 2.0 also?  Doesn’t that just double Rivera’s WAR, if we calculate his WAR without considering leverage?

Also, while I agree with you about the BP WAR thing, the one thing they do (I think) which is good, is to use different baselines of replacement for each position.  Hasn’t it been shown that each position has a very different replacement level (lwts below average for that position)?  How does that jive with your (our) method of using the same replacement (below average) for all positions?

Don’t forget I give all SS +0.5 wins and all 1B -1.0 wins.  So, the positional adjustment plus the replacement level does come out different.

What’s wrong with their replacement level is presuming that the average at each position = same.

The “different replacement levels” that you are referring to is KEith Woolner, and that is not WARP (Clay Davenport).  Confused?  Join the club.

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The reason is that SOMEONE will pitch those high leverage innings.  If it wasn’t MAriano’s 3.0’s RA, it would be Latroy HAwkins’ 3.7 RA, or some other reliever.  The leverage WILL be there.

What we are doing is figuring out the “replacement level closer” (win% = .570), and only giving Mariano “extra credit” for achieving a performance above that level.

Since he had nothing to do with that context, but his talent does allow him to exploit that context, it seems to be the ideal way to model this.

Credit GuyM.

You can also think of “chaining”.  That is, if you take MAriano out, then everyone in the bullpen goes up a rung.  The setup guy’s .600 win% will be used in 2.0 LI, not 1.3 LI.  The #3 reliever’s .510 win% will be used in 1.3 LI not 1.0 LI, and so on and so forth.

If you work out the difference in wins between the Mariano-led bullpen and the Mariano-less bullpen, you will end up with a win impact similar to what the GuyM model proposes.

And, it’s also easier to code Guy’s model.

If you are looking for a general Win Shares aging function, here’s what I get at an r=.98

For nonPitchers:

23
+ 0.64 * WinShares at Age
- 0.78 * Age

So, a guy with 25 Win Shares at Age 22 is estimated to average 22 win shares over the next 5 years.

For Pitchers:

8
+ 0.50 * WinShares at Age
- 0.25 * Age

So, a pitcher with 25 Win Shares at Age 22 is estimated to average 15 win shares over the next 5 years.

The correlation was run with players with at least 5 win shares, in those bin classes I posted, each equally weighted.