THE BOOK--Playing The Percentages In Baseball

We talked about this long ago, but I’ve been out of touch, and perhaps there have been advances....

Is WPA using a consistent range of values for all contexts, or is it being adjusted for circumstance.  In other words, are the WPA values for circumstances with Pedro 2008 on the mound the same as were used for his games in 1999 ?

WPA changes based on run environment.

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Also posted at Primer:

WPA has two components: one is performance by game state, and the other is Leveraged Impact. 

A bases loaded tie game ninth inning would count a PA say at 10 times more than a random PA, while a PA in a blowout game would count a PA at close to zero.  That’s Leverage Index.  On its own, people like it as a descriptive measure of situation.

That same situation would say that a walk is as good as a HR and leads to the same amount of impact (walkoff win). 

You can take the win impact of that situation (+.054 wins for a safe event, regardless of walk or HR, and -.027 wins for an out event) and multiply it by the LI to give you WPA.

Now, we know that the walk has, on average, +.030 win impact.  In some situations (1B open, 2 outs) it is worth alot less, and in some situations (bases loaded) it is worth more, and in even more situations it attains its maximum value (see above, worth same as HR).

So, WPA/LI ensures that the win value of the walk is centered around +.030 wins, and will max out at +.054 wins (or so).

It is only when you take WPA/LI and multiply it by LI that you start getting into crazy WPA talk (all of a sudden, a walk add +.540 wins, and people go crazy that one event can have that much impact).

Therefore, any misgivings one has with WPA is completely undone by WPA/LI.

And WPA/LI can be exactly described as wOBA by Game State, as each PA is guaranteed to be worth 1.00 weight.

If you still have misigivings on WPA/LI, basically, I’ve done a bad job of explaining it.  In no way shape or form should misgivings of WPA carry over to WPA/LI.  If you can at least accept that, then we can move on.

MGL’s last two comments have been moved to its own thread here:
http://www.insidethebook.com/ee/index.php/site/comments/true_talent_v_sample_performance/

And WPA/LI can be exactly described as wOBA by Game State, as each PA is guaranteed to be worth 1.00 weight.

So, WPA/LI ensures that the win value of the walk is centered around +.030 wins, and will max out at +.054 wins (or so).

Sorry Tango, I am still confused.  When you say that each PA has the same weight, then what factor determines the variation in the win value of a walk?  Does its value vary entirely due to the particular base out situation, or is there any remaining variation due to inning and score?  If it is just due to base out situation, why would WPA/LI be a better measure of anything than linear weights by base out states (BRAA, Tom Ruane’s value added, or delta runs)?  Just because WPA/LI contains an estimate of how many runs is equal to a win?

The variation is due to the game state (inning, score, base, out).

If you think of the bases loaded, tie game, bottom of 9th situation (HR = walk), then the win value of every safe event will be identical.

But, if this was top of the 1st under otherwise same conditions, HR does not equal to walk, and so the win value of each safe event will differ.

Tango - So an entirely average batter would have a WPA/LI equal to his number of PAs?  And a batter whose WPA/LI is greater than his number of PAs could be because his linear weights are greater than average or because he is better at doing the appropriate thing at the right time?

WPA/LI, by definition, will equal to exactly 0 for an average player.

I think I’m not describing something properly, so let me try it another way.

wOBA sets the value of the average walk to 0.72 and the average HR to 1.95.  All the values in the numerator are safe events.  And the weighted average of the safe events in the numerator is equal to 1.000.

And so, that’s why wOBA = OBP for the average hitter.  OBP makes the values of each safe event equal to 1.00, be it a walk or HR.

Now, with the bases loaded, tie game, 9th inning situation, wOBA will set the value of the walk and the HR to 1.00.

With a 1b open, 2 out situation, down by 3 situation, let’s say wOBA makes the value of the walk 0.3 and the value of the HR 3.0.  (Just making this up.)

So, wOBA by game state has a value of the walk centered around 0.72, and it will float between say 0.3 and 1.00.  The value of the HR will float between 1.00 and say 3.00 (don’t know the top-end value of the HR).

Ok, so wOBA properly values each event based on the game state.  The numerator is balanced properly.  The denominator is always the number of PA.

WPA/LI *is* wOBA by Game State.

That make more sense?

Peter, let me know if you are on board or not.  As an “early adopter”, it helps me to know if I’ve reached you or not.  There are plenty of people who come to this blog, think about this stuff as much as I do, and don’t appreciate WPA/LI as much as I do. 

So, whatever concerns you (or anyone else for that matter) has on WPA/LI is appreciated by me, as it gives me something else to consider in trying to make my case more cogent.

One thing I would ask is whether players really change their approach by game state as much as WPA/LI implies. Maybe in a few situations they do (man on 3rd, less than 2 out, close game), but by giving them credit for ALL of base/out aspect of their performance, how much noise are you tolerating to get at the amount of true signal?

David/9: That is a perfectly valid position to take.  To the extent that people talk and believe about the batter/pitcher approach (man on 3B, less than 2 outs, or 1B open, 2 outs, man on 2B and moving him over on a GB out, etc), then WPA/LI speaks to them.  It satisfies their requirement.

For example, look at this chart in post 4:
http://www.insidethebook.com/ee/index.php/site/comments/linear_weights_by_men_on_base/#4
which is only by base/out, but you can easily construct it by game state (inning, score, base, out).

The more the numbers differ by 1.0, the more you should expect that the batter/pitcher will change their approach.

So, it’s a legitimate question: do players change their approach when the situation dictates it?  When the impact of a HR is very low, does the batter chop down on his swing?  When the value of the K is super high and the value of the walk is super low, do pitchers throw on the edges alot more?  As I said there:

For the walk/K relationship, that dynamic completely changes with one state in particular: man on 2b and 3b with 1 out.  In this case, a walk costs very little and a K is extremely valuable.  So, a Nuke Laloosh would be fantastic here.

So, it’s be great if the PITCHf/x-ers can show us how the Armando Benitez’s of the world do in this kind of situation, where they can just let ‘er rip, especially against non-contact hitters.

Tango - Sorry that I have not responded sooner.  I was reviewing your three part article on LI at the HardBall Times and your definition of wOBA in The Book.  I am trying to understand in what way WPA/LI is better than linear weights by BaseOut state.  I don’t see WPA/LI having any closer relationship to wOBA than it has to linear weights.  To me wOBA has always represented an imperfect but close enough translation of linear weights above zero per PA to the OBA scale.  I had been using a modified OPS of (1.83 * OBP)+ SLG prior to your invention of wOBA and it performed the same function for me as wOBA does for you so I never switched. 

I have never really cared for WPA except for the possible exception as a measure of career performance.  The very large swings in value due to inning and run differential seemed to over value luck in any sample less than a long career rather than represent a real ability of a player to perform better in high leverage situations.  WPA/LI obviously removes a lot of the large fluctuations of WPA alone.  But I am feeling a little dense because even with your explanation I am not entirely sure what is causing the remaining fluctuations in WPA/LI and whether they are something that represents a rela ability beyond what I am measuring with linear weights by base out state (BRAA).

Thanks for your response.  I think what I need to do is write a full and complete article (likely a multi-parter) to lay out the entire structure of it.  It’s long overdue anyway.  Hopefully, I can take the great care and precision I need to make my point.

WPA/LI is not as good for a pitcher, since a pitcher is his own team, and each PA should not necessarily be treated as if they are as impactful as any other PA.

Isn’t part of a pitcher’s WPA dependent on the defense behind him?  I’m not sure how that can be factored in unless you do something like what tRA does, and assign run and out values to the different batted ball types and the stats that are not impacted by defense (HR, BB, HBP, K) instead of assigning WPA based on results.

There is an enormous difference between WPA/LI and WPA.

The impact of the defense on WPA is the same as it is in WPA/LI and in ERA and in component ERA.  So, I’m not sure I follow the objections here.

Nonetheless, don’t be thrown off by the WPA part in WPA/LI.  WPA/LI really has very little to do with WPA. 

The basis for my statement of saying that WPA/LI is not good for pitchers is that it treats each PA as being worth “1” meaning that each PA has the same amount of overall impact.  But in fact, a pitcher that gives up lots of baserunners will have a higher LI than one who never gives up any baserunners.  And so, it is not fair to make each PA have an LI=1, which is what WPA/LI does.

However, comparing similar kinds of quality pitchers will have the same bias, and therefore, WPA/LI is fine for pitchers.  You just can’t compare Roy Halladay to Dontrelle Willis using WPA/LI in an unbiased manner (the bias is systematic).