THE BOOK--Playing The Percentages In Baseball

Checking now.... in the Retrosheet Years (1957-2006, except 1999), the team that had exactly one fewer errors had a win% of .604.

If I restrict it to 2000-2006, that’s .594.

Presuming that the better quality team to begin with would make fewer errors (i.e., we are not comparing two otherwise equal teams), it’s easy to see how a control of the quality of the team would bring this down to around .575 or .580, which exactly supports our position that turning a sure out/hit the other way is worth .80 runs.

Here’s the full breakdown by Retrosheet Years.
Error_Diff Win_Percent G
1 .594 7205
2 .685 2413
3 .750 585
4 .779 104
5 .920 25
6 1.000 1
7 1.000 1

Error_Diff: difference in errors
Win_Percent: winning record of the team with the fewest errors in the game
G: number of games in the Retrosheet years where there one team made more errors than the other

As you can see, there’s about a .090 extra wins for every extra error for the opponent.

Can’t you just use linear weights?

A single is worth .46 runs, an out -.25.  The difference is .71.

(Those numbers are Pete Palmer’s from the 70s ... higher offense means today’s is 0.8, I assume.  Or maybe if you include the occasional double.)

The above was actually for 2000-2006.  Here’s the full Retro years:

1 .604 40517
2 .687 15208
3 .758 4532
4 .824 1089
5 .866 268
6 .877 57
7 .900 10
8 1.000 1

Phil, at the end of the quote I said:

“.50 runs for the hit, and about .30 runs for the out gives you the .80 runs. “

So, that is linear weights.

But, some people simply don’t buy that explanation.  Hopefully, they can buy one of the others.

Two things:

1) An “error” is worth close to .6 runs, so that is why you get such a high wp per error difference.

2) I never thought there was any controversy over the run/win value of “missed” ball.  The value of the ball, as missed, plus the value of the out, more or less.  Is there any controversy if you asked someone (who knows lwt values) the run difference between a guy at the plate making an out and the guy at the plate getting a non-hr hit?

The reached on error is worth +.02 runs more than a single, more or less.  Throwing errors on runners on base are probably worth even less.  So, I’d say all errors is probably closer to .40 runs.

As for the “controversy”, I see the confusion all the time at Primer and Baseball-Fever.

I have infield errors being .56 runs and OF errors worth .635.  I don’t know where I got those numbers, OTTOMH, but those are the numbers I am using in my UZR calcs.  Those are fielding errors only.  I would have guessed that a fielding error by an infielder is worth quite a bit more than a single, as the least of the errors allows a runner to go to first, and runners only to advance one base.  That should be worth just a little less than a single.  But then you have lots of IF errors that allow runners to go to second and third.  It’s got to be a lot more than a single.

And yes, I see that same “error” all the time (a ball not fielded cost .5 runs), but I think it is almost always an error caused by someone not thinking clearly or properly and they usually realize their mistake when it is pointed out.  I don’t think there is much “controversy” except perhaps among some people who don’t really understand baseball analytics in general.  Heck, there is “controversy” over whether Dunn is a good offensive player or Jeter is a great fielder, in some circles, but I don’t consider that “real” controvery, just as I don’t consider the debate between creationism and evolution “controversy”.  Of course, we are talking about semantics, and it doesn’t realy matter.

It is nice that you (Tango) have shown another way to do it.

Tangotiger

Talk about a coincidence...last week I was having a discussion of “how you win” baseball games with a co-worker. He refused to accept something as simple “score more than your opponent” and insisted the winner was whoever made fewer mistakes.

I was going to try to find winning percentages by difference in errors (thanks for that data), hits, BB, SO, total bases, etc. I assume it will be obvious that have less errors is nice, but having more total bases is even better. I’m not sure data will change his mind, but it would be nice to know I was right.

Is my intuition right or are errors that important?

Some people I deal with just struggle with this basic idea.  They get that the single is worth more, but the value of the extra out is confusing.  At its root, I think this is caused by the basic difference in outs between a Runs Created approach and a Linear Weights approach.  Just a different way of thinking that isn’t as flexible as what you guys have shown.

studes: I agree that it’s the out value in RC that is the root cause of the misunderstanding.  That, and people refuse to think that a great fielder can be worth +25 runs. 

***

Domer: that’s funny, I was going to do that for all events too.  I did something similar for HR here:
http://www.tangotiger.net/rc3.html
(that is, each extra HR means that you score 1.5 more runs).

Domer, each event (errors, singles, etc.) has a certain run value.  That means that on the average it adds or substracts that exact value (well, not really exact, because it depends a little on the context) to a team’s total run value for each game.  And that run value, again, on the average, can be translated to a certain win percentage.  So if one team has 10 more errors than another team in a season, and all other things are equal, they will win, on the average, right around .8 fewer games, because an error is “worth,” as Tango explains, around .8 runs (against the committing team of course), because 10 errors costs 8 runs and every 10 runs costs right around 1 win.  You can do the same thing with any event you want.  If a team has 10 more HR than another team, since each HR is worth (that is its linear weights value) 1.4 runs, 10 extra HR’s will add 14 extra runs on the average (on the average there are .4 runners on base when a HR is hit), which will add 1.4 wins on the average. SO when you ask, “Are errors that important,” I really don’t know what that means, but of course they have run and win impact, of around .8 runs or .08 wins per game, around the same as a single (a little more, as would be expected).  And of course, you can figure that out quite intuititively as an error is obviously essentially the same as a hit, mostly a single, more or less, right?  There is nothing special about an error.  It just puts a runner on base, usually first, or advances a runner a base or more which he would not have advanced had there not been an error.  A base advance, such as a throwing error after a hit, is worth less than a fielding error, on the average, I think around .2 or .3 runs, as compared to .8 runs, and of course, a throwing error is not “compounded” like a regular error (which is one reason why it is only .2 runs or so).  When I say “compounded,” I mean you are turning an out (worth .3 runs to the fielding team) into a runner (worth .5 runs to the batting team).  And when we say that an out is worth .3 runs to the fielding team (we usually refer to that as -.3 runs, since “plus” is for the batting team and minus is for the fielding team or AGAINST the batting team), we mean as compared to an average plate appearance (before we know the outcome), for an average batter on an average team, playing against an average team in an average ballpark, under average conditions, etc., which we define as exactly zero (An average PA has a run value of exaclty zero, by definition).

I should point out a little technical wrinkle, and it’s best evidenced by my Spike/Ozzie illustration.  When I say that Spike makes one more error than Ozzie, that was based on the same number of PA.  With an extra out still to go, then the frequency of each event per game (per 27 outs that is) goes up by 27/26ths.

So, when I look at the end-of-game results, and I only pick out those games where there was exactly 1 error of difference per team, that really should be 1*27/26 number of errors.  Or, I should take 25/26 of 1-errorDiff games, and 1/26 of 2-errorDiff games.  So, if the 1-error games gain you .090 wins, and 2-error games gain you .180 wins, then the true average would be .0935.

Another problem is that an “error” does not always turn a hit into an out.  Some are throwing errors that allow the runner to take an extra base.  Those errors would be simply worth .25 runs (.025 wins) or so.  They wouldn’t have necessarily led to an out.  So, if three-fourths of those erorrs are of the safe/out variety (worth .0935 each) and one-fourth are the base/not variety (worth .025 each), then the impact of an error is .076 wins.

This has nothing to do with the Spike/Ozzie illustration (which focused solely on the safe/out plays), but just a warning to be careful in how to analyze the 1-errorDiff games.

MGL, I get that each event has a run value, but I’m dealing with a neandrathal! He can’t follow the logic of run values.

I guess I am asking if historically the team with 1 less error wins 60% of the time, what percent does the team with 1 more hit win? I would guess almost exactly the same, but I don’t know.

Thanks.

winPercent n HRdiff
68% 7062 1
81% 3230 2
88% 1153 3
91% 312 4
98% 91 5
100% 31 6
100% 5 7
100% 1 8

winPercent n Hdiff
59% 2926 1
69% 2617 2
76% 2425 3
83% 2008 4
89% 1583 5
93% 1176 6
94% 889 7
97% 651 8
99% 428 9
100% 305 10
99% 182 11
100% 127 12
100% 63 13
100% 36 14
100% 24 15
100% 10 16
100% 10 17
100% 2 18
100% 3 19
100% 4 21
100% 1 23

Thanks, tangotiger!

Again, I think the reason that the wp above are a little higher than one expects from the run values of the various events is that, for example, the team with 1 more HR is probably a better hitting team for other events as well.  I don’t think that Tango is controlling for the other events.

I follow the logic of crediting the fielder with .8 runs for a play made (.5 runs for the hit saved, .3 runs for the extra PA taken away), but why is that logic not also applied to hitters? Why doesn’t a hitter who hits a single get credited with .5 runs for the single (or whatever the exact total is) plus .3 for the extra PA he’s getting his team?

He is!

Consider Spike and Ozzie (500 BIP):
Spike, 200 hits, 300 outs
Ozzie, 150 hits, 350 outs

Give +0.3 runs for an out, and -0.5 runs for a hit.  So, Spike comes out to -10 runs, and Ozzie comes out to +30 runs.  That’s a 40 run gap.

There’s a 50 play swing between the two guys.  40/50=.80.

Same applies to a hitter.

Gotcha! Thanks for taking the time to answer.

This week’s thread to bump…

Looking over this for the first time today.

Does this apply while crediting pitchers for preventing runs on hits allowed on BIP too?  Does a prevented single on a BIP = .8 runs?

Coverting a sure out into a sure hit is worth roughly that, regardless if it’s the pitcher, fielder, batter, or park.

Tom, I tried it in the Markov calculator, and went from 4.905 to 4.408 runs. All I did was take away a single and an at bat (since another batter won’t come to the plate later on because of the play saved) from the default line of 37 AB, 10 H, 2 2B, 0 3B, 1 HR, 4 BB, 7 SO.

Charlie: you converted a sure single into an AVERAGE at bat.  In order to convert a sure single into a sure out, you remove 1 H, and leave the at bat the same.

Then you have a 9.1 inning game.

The example is easier to follow if you add one hit and leave the at bat unchanged.  Now you are at 8.2 innings.  You will then need to pro-rate all your numbers up to get to 9 innings.

Follow the example at the top of this thread.

You start with the default numbers here:
http://www.tangotiger.net/markov.html

You get 4.905 runs per game.

Now, we add 1 H to 11H, and if we do that, we have only 26 outs.  We then prorate all the numbers up by multiplying each by 27/26.  So, AB goes from 37 to 38.42.  The H goes from 11 to 11.42, and so on.  Do that for everything.  2B is 2.08, HR is 1.04.  BB is 4.15, K is 7.27.  Click CALCULATE.  You get 5.776 runs per game.

The difference is .871 runs.

***

Now, you could also have done it more simply.  Refresh the Markov page so you get back your default values.  Just change H from 10 to 11.  Click CALCULATE.  You’ll get back 5.781 runs per game.  (It would have been identical had we gone to 5 or 6 decimal places instead of 2 in the above set of numbers.)

See, the Markov calculator simply prorates it automatically.  It prorates up, and prorates down.

That’s why it works.

Using the same logic as in #27, you can take out a hit and leave everything else the same, and then you have a 9.1 inning game, so you have to scale all the other numbers back to 9 innings (which the markov model already does for you-for example, try doubling all the default values; even though you double the outs, it scales them back to 9 innings and gives you the same runs per game as if you leave the default values in place).

Removing the hit removes more than just one at bat.  Say that hit you remove came with 2 outs in the 9th, so now the game is over.  If you leave the hit in, and you have 1 out left to get, on average, you will still have more than 1 PA left to get the remaining out (as in 1.xxx, not 2+ more PAs).  So, you are removing the next PA, plus the probability of that PA becoming a hit/XBH/BB, plus any PAs that come after in the instances where the next PA does produce a baserunner.