THE BOOK--Playing The Percentages In Baseball

That situation has a WE of .1032, with an LI of 1.98.

Getting the batter on this base… gets this WE… for a change of this:

1B, .1993, .0961
2B, .2157, .1125
3B, .2430, .1398
HR, .2187, .1155 (*)
out, .0510, -.0522

(*)You will note the absurdity here.  This is one of those quirks I talked about two years ago when The Book came out.  (Check out the archives, and it’ll be one of the very first threads.) What happens here is that by using a standard base/out state-to-state transition matrix, certain things are expected to happen (basically a fielding team will give up extra bases to get an out).  For your typical inning, that’s fine.  But, in the 9th inning, this is not how a fielding team treats each base.  So, what they would allow with having a runner on 2B with 0 outs down by 2 in the 3rd inning, they would not in the 9th inning.  What you really need is a state-to-state transition matrix that not only includes base/out (of which we have an abundance of empirical data), but also inning/score (which is problematic).  So, you really need to set aside the spreadsheet, and start thinking like a real baseball fan, and start to make some reasonable assumptions by looking at the empirical data and coming up with a logical model.

Anyway, if you focus on the single and the HR, and presume the double and triple will be in-between, and make everythign relative to the out, we see that the gain from a single is 1.84 times the loss from the out.  The HR is 2.21 relative to the out.

Our standard win-LWTS values, across all base/out and inning/score states, would give (using Table 11 of The Book):
walk: +.028 wins
single: +.042 wins
HR: +.123 wins
out: -.026 wins

Relative to the out:
bb: 1.08
1b: 1.61
HR: 4.73

As you can see, and is MGL’s point, a dramatic shift in terms of what benefit you really get out of the HR in this case as well as the walk.  A HR is, basically, very close to a walk, as all the events collapse themselves very close to being around double the value of the out. (*)

(*) Which makes sense of course to balance things out.  If the OBP is .333, then you have twice as many outs as getting on base.  And to balance it out, each time on base is worth twice the out.

***

Let me take this opportunity to talk about WPA/LI.  Remember I said the LI was 1.98?

Well, take this chart:
1B, .1993, .0961
2B, .2157, .1125
3B, .2430, .1398
HR, .2187, .1155 (*)
out, .0510, -.0522

And divide the last column (change in WE, aka WPA) by 1.98.  Here’s what this chart now looks like:
event, WE, WPA, WPA/LI
1B, .1993, 0.0961 0.049
2B, .2157, 0.1125 0.057
3B, .2430, 0.1398 0.071
HR, .2187, 0.1155 0.058
out, .0510, -0.0522 -0.026

Notice something interesting about the out?  That’s right, -.026 wins, EXACTLY like our standard win-LWTS, irrespective of game state.  This is what WPA/LI does: it gives you game-state Linear Weights.

The walk and single is now +.049 wins, above our standard values, and the HR is +.058, far below the typical value of +.123 wins.

***

To the extent that MGL and others believe that a hitter approached a PA differently based on game state, you CANNOT decide to give the hitter +.123 wins for his HR, if the effect of the HR is virtually the same as the walk.

This is why WPA/LI (which I am trying to call Situational Wins) is so powerful.  It does two things:
1. removed the impact of the leverage, since we don’t want to give the hitter extra value for being lucky enough to being in an LI=2.0 situation, so we divide all WPA values by two

2. treat each situation for what it is, and give value based on that; in this case, a walk and HR are very close to each other in value, certainly a far cry from their standard differences; we respect that, and give out wins accordingly

Now, whether pitchers/batters REALLY change their approach such that a power hitter will drastically reduce his SLG and increase his OBP is up for research.  To the extent that they do, then WPA/LI (Situational Wins) is what you want.

***

I LOVE the POZterisks.

1. removed the impact of the leverage, since we don’t want to give the hitter extra value for being lucky enough to being in an LI=2.0 situation, so we divide all WPA values by two.

Why don’t we want to give a hitter credit for the leverage index, which is essentially giving him credit for being “clutch” or “non-clutch?” We are not trying to measure “true talent” here.  If we were, we wouldn’t be using WPA in the first place.  Why are we giving credit for the hitter when he happens to hit a HR with the bases loaded (which results in a high WPA and WPA/LI)?  If we give him credit for the game situation (which WPA does, right?), why not give him credit for the leverage as well?  WPA or WPA/LI is an “mvp” type stat anyway, right?  We have no idea whether it is “repeatable”.  In fact, we don’t think it is, right?

I don’t see why WPA/LI is better than WPA.

WPA/LI (situational wins) is the *only* stat around that explains that the win value of the walk and HR in your situation is very close.

So, to the extent that the batter/pitcher approach your situation as something that is real, and that they can manipulate, then WPA/LI is exactly what you want.

WPA/LI is different from WPA in that every single PA counts as “1”.  WPA, in effect, would count an LI=2.0 PA as double.  And a LI=10 would count that PA as worth 10.  This is ridiculous from a “true talent” perspective, since there is no reason to count the sample 10 times more than average.  So, WPA must be discarded when discussing “true talent”.

WPA/LI ensures that every single PA counts as “1”, and it ensures to rebalance the BB,H,HR appropriately based on its impact to the game.

Again, to the extent that you believe that a pitcher/batter can change their approach, then you definitely want WPA/LI.

On the other hand, if you think the pitcher is trying to avoid a HR in this situation, and the batter is trying to get a HR in this situation, and therefore a HR should count as 4 times as much as a walk, then we have no use for WPA/LI, and we should stick with just Linear Weights.

Choose your poison.

Well, lwts adjusted for the game situation is what I want.  In my 9th inning example, that number is going to be the same for the walk and BB (as it always is with no runners on base), the HR, 2B, and triple will be almost exactly the same (slightly less because of the possibility of a pickoff or line drive DP), and the single and BB will be slightly less valuable, because of the DP and force.

We KNOW that WPA is not a good true talent indicator over and above regular lwts. But we also know that WPA/LI is also not a good true talent indicator either.

So why do we use either one of them for batters and pitchers (as opposed to trying to figure out the values of various events)?  I assume it is for “mvp” (non-predictive value or repeatable) type of value.  If that is the case, why not give a player credit for not only is approach, but his contribution to the change in win expectancy as well?  That is even more important than just his approach, isn’t it?

I guess I don’t see why you would use WPA/LI for a batter or pitcher but not want to use WPA even more?  You can’t use either one for “true talent,” so that can’t be the reason.  I don’t think you have answered that question yet, unless I am overlooking or not understanding the answer.

WPA/LI rewards a GS home run more than a solo HR run, right?  We can’t seriously think that a player has much, if any control over when he hits his HR, can we?  I have no problwm, though giving him “credit” (a pat on the back, an “attaboy,” or even an award) for that. WPA alone rewards it even more when the game is on the line, right, and the HR changes the wp a lot?  Hey, let’s give the batter or pitcher even more credit for that!  He deserves it!

I don’t think you are understanding WPA/LI.

You say this:
“Well, lwts adjusted for the game situation is what I want. “

That is EXACTLY WPA/LI!

In your specific example, I said that the win value (WPA/LI) of the walk and single was +.049 and the win value of the HR was +.058 and the win value of the out was -.026.

These are the values you want, right?  The “scale” is correct, in that the absolute values of those numbers, weighted by the frequency of the event will come out to .0346 wins (which is the average for the average PA).  And the relativeness is correct in that the walk and HR are very close to each other.

So, I’m giving you linear weights adjusted for the game situation.  It’s right there.  And it’s called WPA/LI.

***

“WPA/LI rewards a GS home run more than a solo HR run, right?  “

No, it does not!

Think of everything as relative to the out.  Now, go here:
http://www.tangotiger.net/lwtsrobo.html

Check out the run value of the HR with bases empty and 0 outs.  It’s 1.00, natch.  And the out is -.27 runs.  So, we see that the HR is almost 4 times the impact as the out (1.00/.27=3.7).

Now, check out bases loaded 0 outs.  The HR is +2.17 and the nonK out is -.52.  Guess what, the HR is just a bit more than 4 times the nonK out.  Relative to the K out, it’s 3 times.

If you presume that 25% of outs are strikeouts, then take 25% of -.71 and 75% of -.52 and the average out in the Bases loaded situation is -.57 runs.  The HR, at +2.17, is 3.8 times as impactful as the out.

As you can see, it’s virtually the same!

So, your premise is wrong, and WPA/LI doesn’t reward the BL, 0 outs HR more than it would with bases empty.

And in fact with TWO outs, it’s the OPPOSITE!  The HR is given much more value with WPA/LI with bases empty than bases loaded.  Why is that?  Because a single with bases loaded and 2 outs is worth half a HR, while a single with bases empty and 2 outs is almost worthless.

Since the batter and pitcher know this, the pitcher is trying to avoid a HR at all costs with bases empty and 0 outs.  At 2 outs, he’s trying to avoid any kind of hit, since he knows at least 2 runs will result from it.

WPA/LI gives you exactly what you want.

If you are still not convinced let me know.

I wrote too fast.

This:
“Since the batter and pitcher know this, the pitcher is trying to avoid a HR at all costs with bases empty and 0 outs.  At 2 outs, he’s trying to avoid any kind of hit, since he knows at least 2 runs will result from it.”

Should read as:
Since the batter and pitcher know this, the pitcher is trying to avoid a HR at all costs with bases empty and 2 outs.  At bases loaded and 2 outs, he’s trying to avoid any kind of hit, since he knows at least 2 runs will result from it.

If you were trying to create a wOBA equation for your specific example, you would start with what WPA/LI is giving you:

“the win value (WPA/LI) of the walk and single was +.049 and the win value of the HR was +.058 and the win value of the out was -.026.”

You add +.026 to all that, which means that the walk and single is .075, the HR is .084.  And you would divide all that by around .080.  That gives you .075/.080 = .94 for the walk, single, and 1.05 for the HR, and around 1.00 for the double, triple.

So,
wOBA = (.94*BB + .94*1B + 1.00*2B + 1.01*3B + 1.05*HR) / PA

Isn’t this what you want?

In a post on my blog in August last year, (http://gorangers.wordpress.com/2007/08/27/who-was-that-wearing-the-padilla-mask), I gave a rough guide to CJ Wilson’s pitching propensities.  I need to update it, and make it a little more rigorous, but what you’re describing is typical CJ:  if it’s a close game, he’s lights-out, if it’s easy, he’s prone to losing control.

I honestly think if he came in with a one run lead, with bases loaded and no outs, he would strike out the side with 95mph heat, but if he came in with a five run lead he’d throw slop and give up four runs and finish with the bases loaded.  He’s a heart-attack to watch sometimes, he just needs the super-intensity to get it all working properly.

OK, I see that WPA/LI gives me the lwts values given the situation, which allows me to see how a batter and pitcher adapt their hitting to the situation.

I have to think about how that is useful and how that compares to just WPA.

WPA/LI is NOT useful for any kind of true talent estimate unless we think or know that there IS true talent in batters and pitchers adapting their hitting and pitching to the situation. Is there?  How much?  Just saying that there IS talent, like there IS a clutch ability, doesn’t mean much unless we know HOW MUCH ability, right?

Okay, so if there is little or no ability in WPA/LI (and I don’t know that that is true), what is it’s value?

I assume that the value is a “retrospective” MVP-type thing. If that is the case, why not use just WPA.  Doesn’t THAT tell us exactly how much a player changed the WE of his team?  Isn’t that the ultimate MVP-type credit we want, whether the player has any control over it or not?  (We don’t really care about “control” for MVP-type credit, do we?  We get to reward players for being in the right place at the right time, don’t we?)

So, again, I don’t get why we want to give players credit for WPA/LI and not WPA.  I think I get the distinction, but I don’t know why one is better than the other in terms of looking at what a player did (not in terms of the type of analysis I was doing, which was simply determining the “custom” lwts values).

If CJ Wilson is doing things like that on a regular basis (walking batters with a multiple run lead with no one on base, etc.), then he is simply a “dumb” pitcher who is not getting nearly as much value from his physical talent as he should.  And I would blame the management for not straightening him out.  If he literally does not understand that when the batter is less than the tying run, that he needs to throw MORE strikes and more of whatever his best control pitch is, then his pitching coach should take him into the back room and beat it into him.  I used to teach my kids that in Little League.

The first thing a pitcher needs to do when a batter steps to the plate is determine whether he minds walking him or not. The entire approach to the PA should be dictated by that.  Everything else is secondary.

Ok, so the first thing I wanted to establish is that WPA/LI is Linear Weights by the Game State.  This is the thing we want to know.  So as not to confuse WPA/LI with plain old WPA, I’ve been trying to call it Situational Wins.

WPA/LI basically has the win value of the out as -.026 wins, more or less, all the time.  The average positive event is roughly +.052 wins, all the time.  (The weighted average is naturally exactly zero, all the time.)

The game situation dictates how far the walk and the HR hover around that +.052 (and the single, double, triple are in-between there to some degree).

Ok, so what is the value of WPA/LI?
1. We already established that it is Linear Weights by the Game State.  As a result, its most important value is in the batter/pitcher matchup.  Much as you need to know the count, so as to know whether to swing or not, where in the strike zone to throw, you need to know the game situation so you know how costly a walk, K, and HR are, or are not. 

In some situations, a walk = HR.  Therefore, the batter/pitcher must change their approach drastically.  Do they?  That leads to…

2. To the extent that they do change their approach, then this tells us that something real is going on.  But, how much is that extent?  That’s mgl’s question.  Does a 50HR guy become a 20HR guy and does a 30 walk guy become a 60 walk guy in situations where a HR=walk?  I don’t know.  That needs to be studied.

If they totally do that, then the sum of WPA/LI is exactly what we want in terms of establishing a player’s true talent level.

If they don’t do that at all, then the sum of Linear Weights (i.e., walk is always worth +.028 wins or +.32 runs) is what want.

The true answer will of course be somewhere in the middle.  How much needs to be determined.

***

The above satisfies everything that MGL would want out of WPA/LI.  What follows next MGL has no interest in, based on his past posts.

***

3. The third third thing to establish is “MVP”, retrospective.  There you have your choice of WPA/LI and WPA.  When an LI = 10, that means that the PA itself counts as 10.  Clearly from “true talent” perspective, there is no reason that one PA should count as 10, another as 0.1, another as 1.5, etc.

However, what about in terms of retrospective?  The argument in favor of WPA/LI (keeping each PA equally weighted) is the argument for #2 above, and that is, we give the player total credit for changing their batter/pitcher approach, and therefore if they are in a situation where a walk = HR, we give them that value.

We don’t want to give them credit for happening to stand next to Warren Buffet as he doles out inside information about Coke.

The argument for WPA (each PA weighted based on its leverage) is that standing next to Warren Buffet listening to him talk about Coke made you a millionaire.

So, what is it that we want to credit the player with?  That’s the argument for #3.