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Bill James and Estimated Runs Produced

March 17, 2010

Before I begin, let me start by saying that I’m a big Bill James fan.  I love reading his books, I love his writing style, and to say that he’s an influential man would be a vast understatement.  But as I pointed out in my Total Runs article, sometimes he misses the boat.  And here’s one of those blunders.

A number of years ago, Paul Johnson introduced Estimated Runs Produced, or ERP.  You can read the primer here, and Bill James gives him a nice little introduction.  One of the money quotes:

Last fall I received a letter from an Illinois man named Paul Johnson who claimed that he had developed a very simple method of evaluating run production that was more accurate than runs created. I receive a couple of those letters a year, and it rarely takes me five minutes to get them off my desk. Peter Palmer in The Hidden Game makes a similar claim for the linear weights method, and Pete is a good friend and an outstanding analyst of the game, but in fact linear weights do not meet any acceptable standard of accuracy in assessing an offense . . . well, I went through all that in the historical book.

I don’t have a copy of said “historical book,” but I like to think that I have a good understanding of linear weights and how they are best applied.  The method Palmer outlines in The Hidden Game of Baseball explicitly uses LWTS for individual hitters rather than on the team level.  We can switch LWTS to an absolute scale by fiddling with the out value, but it breaks down pretty easily at the extremes.  It’s ideal for individual hitters because it uses the marginal run value of an event, so the base/out state is stripped from the equation.  And it’s pretty easy to use.  All that it involves is addition, subtraction, and multiplication.  And it tells you how many runs above or below the league average a hitter is based on the ratio of runs created to outs made.  In summary: ideal for individual hitters, not so perfect for teams.  James continues:

I’m not certain that Paul’s “Estimated Runs Produced” method is more accurate than runs created—we’ll get into that at the conclusion of the piece—but I am convinced that it is an extraordinarily good method. It’s accurate, it’s simple, and it measures what we need to measure: runs. It is more accurate than runs created for certain types of players. On that basis, I felt I should ask Mr. Johnson to introduce his method to you.

Here’s the irony: James denounces linear weights two paragraphs earlier but praises ERP.  As it has been pointed out before, ERP is a linear weights estimator.  How so?  Let’s take a look.

ERP = (2 x (TB + BB + HP) + H + SB – (.605 x (AB + CS + GIDP – H))) x .16

Let’s expand the equation:

ERP = (2 x 1B + 4 x 2B + 6 x 3B + 8 x HR + 2 x BB + 2 x HBP + H + SB – .605 x Outs) x .16

Now we can begin to see the relationship between events a bit better.  Even further:

ERP = (3 x 1B + 5 x 2B + 7 x 3B + 9 x HR + 2 x BB + 2 x HBP + SB – .605 x Outs) x .16

Now we go in for the kill:

ERP = .48 x 1B + .80 x 2B + 1.12 x 3B + 1.44 x HR + .32 x BB + .32 x HBP + .16 x SB – .010 x Outs

It’s a little bit hidden, but it takes very little work to unveil the intrinsic weights.  If you look at this equation and then take a gander at a standard linear weights equation, something like this:

LWTS_RC = .47 x 1B + .78 x 2B + 1.04 x 3B + 1.40 x HR + .33 x TBB + .18 x SB – .28 x CS – .010 x Outs

You see that they’re essentially the same when all is said and done.

If that’s not ironic, then I don’t know what is.  I don’t know if anyone’s mentioned this to Bill- I’m sure someone has- but it’d be interesting to hear his thoughts on the matter.

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