THE BOOK--Playing The Percentages In Baseball

Very nicely laid out.

This reminds me a lot of the old “How Runs are Really Created” article.

Studes: right, nothing much new here for the regulars.

That’s a very nice summary you’ve written.  But a small nit to pick with the last sentence: considering the run environment is necessary accounting, but it says nothing one way or the other about whether linear weights work.

Linearity working (or not working) is due to the accuracy (or inaccuracy) of using average run values for the base/out situations.  If using average run values leads to accurate estimates, then linear weights is working.  If using average run values leads to inaccurate estimates --- imagine a game with modified rules where having Matt Holliday and Albert Pujols together creates much more value than the sum of their individual contributions --- then linear weights is not working.  Even if the accounting is tight.

Ben, I don’t disagree with you.  I guess if I point people to The Book to read Chapter 1, then we can see how the delta in the run expectancy of the 24 base/out states works, and therefore leads to Linear Weights.  This was really more for people who didn’t read The Book.

I should also clarify that by Linear Weights, I mean the framework that establishes the zero-level idea.

I don’t mean LWTS in terms of the static nature of the values.  The run values can change as noted by this Markov calculator:

http://www.tangotiger.net/markov.html

There is something about this I am not getting.

I understand this is an argument against using some sort of statistical combination of outs and total bases.  Where I’m lost is how someone got the idea in the first place that this was a worthwhile thing to try to do.

The out hurts the offense, and helps the defense, by advancing the inning one third towards is conclusion.  That is one third towards the defense becoming the offense again.  For the team with a lead, an out is valuable by advancing the game one fifty-fourth towards being over.  Teams that are behind have more reason to try to avoid committing outs.

A baserunner can only be stranded, in a nine inning game, by nine of the twenty-seven outs his team commits.  And you can score in many situations from Second, even in a few situations from First.  Why even look at where the baserunners are when someone makes an out?

Sorry, I hadn’t read the following post before posting the above comment.

Still, it seems the value of an out in terms of getting the inning over greatly outweighs any consideration of which baserunners are stranded.  That third out eliminates any chance of one team to score runs and gives the other team a chance to score runs, which they didn’t have before.

If baseball ran according to a clock, or each team took a certain number at bats each inning regardless of the number of outs, then the main value of an out would likely be to stop the baserunner from advancing.  It would be a very different game.  Even then, the out would take time off the clock or use up an at-bat.

Ed: I have no idea what your point is.  Do you have a question that I can answer?

Ben: “If using average run values leads to inaccurate estimates --- imagine a game with modified rules where having Matt Holliday and Albert Pujols together creates much more value than the sum of their individual contributions --- then linear weights is not working.  Even if the accounting is tight.”

I do not understand where you are going with a game with modified rules. You could use a simulator or theoretical team baseruns to come up with custom linear weight values for Holliday and Pujols. Obviously, the simulator would be better.

My question is why would anyone bother to incorporate who is on base when the out is made into the calculation of the value of the out.  Isn’t this an example of overthinking things?

Ed: you are probably not appreciating where I was going with this.

I was describing why the out has the negative value it does: it’s based on the “resetting” the bases at the end of the inning, as well as shortening the inning.

The actual value of the out would be given out based on something like RE24.

There is a theoretical comparison possible between two different baseball-like games.

Both are played the same way as in baseball, except in one game, outs shorten the inning but do not remove the baserunners.  The inning ends after three outs, but any baserunners left stranded return to the bases they occupied at the end of the last inning, when their team again returns to the offensive, until the ninth inning.

In the other game, innings are ended by some other measure, like at bats or minutes.  Otherwise outs perform the same function as in baseball.

In which of the alternative games would the value of the out weaken more, compared to normal baseball?

Ed, in your first game, it is essentially a one-inning 27-out game.  So, you send 36 batters, 12 reach base, 2 are left on, 7 score, 3 are doubled-up, and 24 make a batting out. 

In your other game, you send 4 batters per inning.  The number of outs is irrelevant.  There’s no inning-killer cost or base-advancement cost.  The runs scored per game will be much lower as well. 

It’s obvious then that the value of the out is far lower in the second game than the first.

What is your point?

Terpsfan: as an extreme case, imagine letting Holliday and Pujols do all the batting (with ghostrunners ... like pickup games as kids).  Yes, you could create a new set of linear weights for this situation, the “Pujols-Holliday” linear weights (which would be slightly different for Pujols than for Holliday).  And then the “A-Rod-Cano” linear weights, etc.  And then the poor team with the “Brendan Ryan-Skip Schumaker” linear weights.

Or, more conceptually more simple (in my view), you could say that the global linear weights is unable to account for correlations.  Which is most of the time fine, but when you have this extreme situation, the correlations matter.

You could, with this conceptually simpler view, create a run estimator theory of correlations that isn’t particular to Holliday-Pujols, or Cano-A-Rod, or whatever.  Having a universally applicable set of linear weights, and a universally applicable method of building in correlations gets more to the heart of what’s going on.

But as we all know, this mostly isn’t needed in real baseball, and linear weights capture most of what you want to know.