THE BOOK--Playing The Percentages In Baseball

One thing I’ve never fully understood is why you apply the Odds Ratio Method to winning percentages. Thanks to your other thread, I now understand why Odds Ratio works in matchups, but I don’t understand why it’s used in this case.  Let me note two things I don’t fully understand:

- Using the odds ratio, a team of .500 batters and .300 pitchers will play .300 ball.  I understand why the Odds Ratio works the way it does, but I don’t see why this should be applied to two components of a team that don’t actually face each other.

Said differently, I can understand why a bunch of .300 pitchers will have a .300 outcome level against .500 pitchers, but not why that logic applies to replacement level splits between pitchers and nonpitchers.

- In WPA and Win Shares, it seems to me that the math doesn’t work.  A team of .300 batters and .500 pitchers played .400 ball (roughly).  I know this is true for Win Shares, using my Win Shares Percentage.

I assume you’ll say there is a difference between retroactive application of “odds” based on outcomes and a prospective “true talent” analysis.  If that’s true, does that mean that I should take my Win Shares Percentages and run the Odds Ratio on a “backward” basis to figure out what a player’s true WSP was?  If that’s even possible?

My suggestion is scrap the whole winning percentage way of talking about replacement, in favor of talking about RA and RS (or % above/below average).  W% invariably confuses people and makes the discussion difficult.  For example, the worst fielding team in baseball might be a “.460” defense.  Intuitively, that doesn’t sound nearly as bad as it actually is.  W% is also a team concept, while replacement level is really relevant at the individual player level.  (It also invariably raises the objection “what about X .260 historical team,” then Tango has to explain that wasn’t the team’s true talent level, etc.). 

For example, I believe Tango has traditionally suggested that a repl non-pitcher is -18 runs (hitting and fielding) while a repl pitcher is -12 runs (perhaps he’s modified that slightly).  I don’t find that totally persuasive, but discussing the plausibility of those numbers and competing evidence is quite straightforward.  What does converting these to W% add to the discussion?

For me, it specifically helps with Win-based stats, like WPA (your favorite subject) and Win Shares.  If you want a replacement level with these stats, I think you’ve got to use the equivalent of a winning percentage times playing time.

Well, never mind.  I think I figured it out.  I found that if you make runs scored and allowed assumptions similar to winning percentages and run them through PythagoPat, you get virtually the same answer as the Odds Ratio gives you for winning percentages.  Which is fascinating.

Like I said, never mind.

What Guy said is important, and Patriot repeats it often.  When we say a batting team is “.300 win%”, what we are really saying is “batting team is .300, if they have average fielders and average pitchers”.  Therefore, if you have “.500” pitchers, your team win%, by definition, is .500.

Maybe all that is confusing.  What is not confusing is RS and RA.  So, if we stick to that instead, and only convert to win% at the end, then we’re all at the same page.

When we say a batting team is “.300 win%”, what we are really saying is “batting team is .300, if they have average fielders and average pitchers”.  Therefore, if you have “.500” pitchers, your team win%, by definition, is .500.

It’s definitely confusing to me.  Your second sentence doesn’t seem to follow from your first.  Putting .500 pitchers with .300 batters doesn’t result in a .500 team, does it?

My bad.  I meant to type .300 at the end, not .500.

Still, I think it is confusing to a lot of people.  People interpret a “.300 offense” to mean the level of offense you’d expect on a .300 club.  But real .300 teams are weak on offense and pitching/defense, so typically would have an offense around .400 according to Tango’s definition.  So to me, “-200 runs” is a lot more clear than “.380 offense.”

I believe that had Bill James not used Offensive Winning Percentage as his rate stat, we[sabermetricians] never would have gotten into the habit of expressing the replacement level as a W%.  Now that ship has sailed.

As Tango mentioned, I like percentage of league runs or runs allowed.  Not only is it easy to understand (especially for people familiar with stats like ERA+ and OPS+, which essentially measure that), but it is easily convertable to either W% or number of runs +/- as Guy has been using on this thread.  The other two ways of expressing it are not as easy to convert, and runs +/- will not hold up if you change the underlying context (-18 runs in a 10 run enviornment is approximately -1.8 wins; -18 runs in a 8 run enviornment is around -2.1 wins).

Agreed with Patriot. 

In a 5 RPG environment, an off level of 4.0 RS and 6.2 RA will give you a win% of .300, equally split between offense and defense.  (Defense is of course pit + fld).

In a 4 RPG, you’d have 3.15 RS and 5.0 RA.

In a 3 RPG, it’s 2.3, and 3.8.

In a 6 RPG, it’s 4.85 and 7.30.

In all cases, those off repl levels hover around 80% of league average and the def repl levels are 1/.80 (or 125%) of league average.

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It is for this reason that it’s clearer to just describe a player relative to average, in terms of runs scored.  Everyone understands what average means.  The conversion to replacement level is a pretty simple step.  And the conversion to win% is also a pretty simple step.

I believe that had Bill James not used Offensive Winning Percentage as his rate stat, we[sabermetricians] never would have gotten into the habit of expressing the replacement level as a W%.

I had no interest in a player’s winning percentage until I ran across Win Shares and WPA.  Those developments have gotten me interested in a player’s winning percentage.  To me, this is an obvious extension of having a win-based system.

I know this is an old issue to some of you folks, but you might consider thinking of it in a new light.

The issue is really just one of definition.  It takes too long to explain what it means if you have a group of hitters that bat with a win% of “.300”.  Does this mean that if all the hitters performed this way, and the fielders and pitchers were equally incompetent, that the team win% would be .300?  Or does it mean that if the pitchers and fielders were .500, that the team win% would be .300?

You can define things however you want.  It just requires alot from the reader to understand what it is that you are doing.

On the other hand, telling the reader that a player created 80% of the runs an average player did.. well, that’s alot easier.  (Still not complete, because of the playing time unit being outs and/or PA.)

The issue is really just one of definition.  It takes too long to explain what it means if you have a group of hitters that bat with a win% of “.300”.

Personally, I wouldn’t say that.  But I would say that Player A had a Win Share Percentage of .400 last year, or that his Win Advancements and Loss Advancements (WPA) equaled a .400 winning percentage.

Unless I’m missing something, I wouldn’t apply the Odds Ratio method to those figures, because those figures (Win Shares and WPA) are additive to the team’s total wins and losses, not multiplicative (as in Odds Ratio or Pythagorean).

I think you are making my point.  I have no idea what “his Win Advancements and Loss Advancements (WPA) equaled a .400 winning percentage.”

Take for example Albert Pujols.  He had 18 win advancements and 9 loss advancements.  The Mills Brothers’ Player Win Average (PWA) would describe that as a .667 “win percentage”. 

What does that mean?  Does it mean that if Pujols played with 24 average players, that the team win% would be .667?  Does it mean that 9 Pujols batting would have a team win% of .667?  Does it mean that if you had 25 players of Pujols-equivalent performance, that the team would win .667?

(I know what the .667 means.  But, your typical and even hard-core reader doesn’t know what it means.)

The room to interpretation of .667 just leaves the door wide open.

Saying that Pujols created 3 times more runs than the average player, or that he added 9 more wins than an average player, would have given his playing time leaves much less room for interpretation.

(All numbers for illustration purposes only.)

Studes:
I think you’re right about additive vs. Odds Ratio. 

I don’t disagree with your .400 WS/WPA description, but I wonder how useful it is.  Won’t a lot of fans see those numbers and conclude that such a player is 80% as good as an average player?  Or worse, that a .550 player is only 22% more valuable than a .450 player? 

Or is this just an interim step for you on the way to some kind of value-above-replacement WPA meteric?

Guy, exactly.  I’m most interested in a winning percentage so I can get to a replacement level.

Tango, here is a way to turn win advancements and losses into a winning percentage.

You keep making my point!  90% of readers won’t care about what I wrote in that thread, and another 9% won’t even remember it.

Providing things as “3x league average”, or “90% of league average” gives the reader a good framework, and it allows him to translate that into anything else he wants. 

My opinion is that most reader prefer easy-to-understand data.  You can give the rest of the readers the frameworks to translate that data.

Sheesh, Tango.  I’m obviously not communicating well.

I’m interested in establishing a replacement level winning percentage, and then applying a player’s WPA and/or Win Shares to that replacement level in order to derive his wins above bench.

Actually, I do that today, with WSAB.  I don’t think it is any harder to understand than Win Shares itself.  And I already publish each player’s Win Shares Percentage today.  It’s not used a lot, but I don’t hear a lot of complaints about it being too complex.

I would like to do the same thing with WPA, and you were nice enough to provide the math to do it.  I doubt that many people who understand WPA will find WPAB confusing.