THE BOOK--Playing The Percentages In Baseball

SABRMatt has come up with the most complex version of BaseRuns, and in so doing, has highlighted the impossibility of negative runs.  (This happens because of the negative weight given to the K and other components, and in some cases, this case dwarf the score rate into becoming a negative number.)

The solution is:
A * B / (B+C) * E + D

The coefficients for the B components should never be a negative number.  For those that require us to reduce the score rate, like K, CS, PK, etc, these should be included in the E component.

Whether we end up with the above equation, or something else, I don’t know.  Maybe that “E” should be C/(C+E) ?

With two unknowns the “easy way” of matching LW is not going to work. 

I wonder though if it is worth worrying about, at least before other issues. According to Matt’s data, it only happened with extremely small samples.  Now of course I am all for accuracy at all extremes, but I think that negative runs for very small PA is one of the lesser problems that BsR has.  Remember a couple years ago when you showed examples of estimating ten men left on base per inning (or worse), for extreme cases?  It would seem to me as if that is a bigger problem then the negative runs. 

My point is not that this problem is not a real one, just that it is not the biggest one.  And if the foundation is going to crack, then you put off patching the roof.

What makes most sense to me is adding it in the denominator, B/(B+C+E).  Of course, that’s just based on what looks nice, not on any theory or actual testing.  The problem is going to be the two unknowns. 

Completely off the wall here, but what if you define B in such a way that it is a proxy for advancement (i.e. it doesn’t give precise values like we use it to now).  Then put everything in C(this is sort of like the C+E thing, except now I am saying change your coefficient for AB-H too).  Homers, singles, strikeouts, everything.  And then fudge the C values.  You would lose adv/(adv + outs) construct, but that was never really a theory-based choice, just an empirical one.  I have no idea if this would work, but it would be workable through the kind of approach that I use.  If you get into multiple unknowns, you will not have a nice tidy formula anymore and will have to use a computer to solve, unless you can find a better mathematical advisor

I tend to agree about the B / (B+C+E) construction.  Of course, now we have two unknowns.

I think solving for the two unknowns should be possible.  Suppose we figured out that the scoreRate is 30%.  And let’s say that C is 700.  That means that when B=300, then E=0.

However, inside B are the negative coefficients for K, CS, PK.  If we then turn those into zero, we’ll get say, B=310, which means that E must now be forced to be 33.33.

This is just off the top of my head.  I’m not sure if by doing that I’m allowed to preserve each of the b positive coefficients, or if these now need to be rebalanced.  (My guess is that this will not work.)

Agreed about the more than 3 runners left on base per inning also being an issue.  BTW, when I run through my simple-Markov calculator, even when OBP=.999, the average cap of LOB per inning is right around 2 guys.  So, unless you have an all-BB team, that should really be the limit.

Unless this is going to kill his bandwidth, I encourage all to download Patriot’s BsR spreadsheet.  It’s a great piece of work.