THE BOOK--Playing The Percentages In Baseball

Tuesday, March 30, 2010

Secondary Average

Bill James created a great stat 25 years ago called Secondary Average and it was everything that Batting Average was not.  Where Batting Average gave “1” for a single and home run, Secondary Average counted 0 for a single and 3 for a home run.  Basically, the “missing” bases.  It didn’t stop there, as it also included SB and walks and hit batters.  And, as luck would have it, the number of “missing” bases was equal to the number of hits.  And that meant if you divided all these missing bases (these secondary bases), by at bats, you get a league Secondary Average that matched the league Batting Average.  The range was far wider with Secondary Average.

Now, can you just add them?

Using the two metrics in conjunction--either as a linear combination (something I’ve been using pretty frequently as of late and I’ve dubbed “APS"* (Average plus Secondary Average)) or as two separate metrics--gives us a pretty good idea of a player’s overall offensive value. At least a lot better than the metrics that were currently employed.

*It’s my contention that this metric, APS, should have been popularized rather than OPS. Now that we have things like wOBA and EqA, there’s not too much use in crusading for the widespread use of APS. I still prefer to use it, rather than OPS, if I’m trying to get a quick and dirty look at a player’s overall offensive value.

Seeing that we have the same denominator, we should be able to figure this out rather easily.  wOBA already tells us that the weight of a HR relative to a 1B, when the denominator is PA is about 2.2.  And since Batting Average gives a “1” to 1B and HR.  And since Secondary Average gives a HR a “3”, then we simply need to get Secondary Average to count the HR as “1.2”.  And 1.2/3 is 0.4.  And so, using just singles and HR, we’d scale it as:

Batting Average plus 0.4*Secondary Average

However, the walk is 0.8 the value of a single (when the denominator is PA).  Here we have a bit of a problem, since our two metrics have AB, not PA in the denominator.  In any case, we’re going to see that the weight to Secondary Average is going to be close to 0.8 if we’re going to base it on the walk.

If you use the double (should be 1.4 times the single), then we’d have the same formula as the HR version.  And if we use the triple (should be between 1.7 to 1.8 times the single), then we still have the same formula.

On the other hand, the stolen base should be 0.3 times the single.  So, we’d want something like:
Batting Average plus 0.3*Secondary Average

Anyway, you just have to run it through a plus1 method to see what the best-fit weight should be (best-fitting against Linear Weights).  I’m going to guess you’ll get something close to:
Batting Average plus 0.5*Secondary Average

(I’ll do this in the morning, unless someone wants to do it ahead of me.)

And, that pretty much will lead you to the genesis of Equivalent Average.