## Monday, May 03, 2010

### Why I Like Secondary Average

Over the summer, there was a thread on Baseball Think Factory about Baseball-Reference and other statistical sites. A poster said that one category missing from the seemingly endless array offered by B-R was secondary average, which led to this reply by Colin Wyers:

Baseball Reference has secondary average.

That said - does anyone need secondary average? Really?

I assume that if you are reading this blog, you are familiar with Colin's work--if not, you should be. I'm certainly not trying to pick on Colin here. Besides, he's right--no one *needs* secondary average. There are two big reasons why not, aside from the actual weighting of events in the metric itself:

1) it's not an overall measure of offensive production--in fact, it is sort of nebulously defined as "stuff that batting average doesn't account for".

2) it's not expressed in a fundamental baseball unit like runs or wins--it's total bases beyond first, plus walks, plus steals per at bat--hardly a unit that cuts to the essence of the game. In the past I've argued that slugging average doesn't have a fundamental baseball foundation, but at least what it (crudely) measures is clear--rate of bases gained by the batter on hits per at bat, and it can be used directly as an input in a crude dynamic model of run scoring (basic Runs Created) . Secondary average's logical basis doesn't even approach that level.

All that being said, I personally like secondary average, and I use it occasionally on this blog. Admittedly it doesn't really have any analytical value, and in a world in which everyone agreed with the central tenets of sabermetrics, there wouldn't really be any need for it.

However, that's not the case, at least not yet. There are still many people who start their evaluation of an offensive player with his batting average. It might be better if they'd start with OBA, or start with OPS, or start with any number of other metrics, but as long as BA is widely-used, secondary average has some utility as a way of considering everything that doesn't go into BA.

Bill James introduced secondary average (I'm going to start using the abbreviation SEC interchangeably) in his Yankees team essay in the 1986 Baseball Abstract. James defined SEC = (TB - H + W + SB)/AB, although some later versions have removed CS and sometimes SB are excluded altogether. James' discussion ran for several pages, and I have lifted some quotes and paraphrased some of his points, as many of his reasons for liking secondary average are the same as mine.

What was the purpose of the new stat? "[It] focuses on the major areas of offensive productivity which are not reflected in the player's batting average...It does not constitute new knowledge; rather, it is a new way of expressing a set of values which have already been accepted."

James explains that he had been endeavoring for several years to express a player's non-BA offensive contributions in a straightforward, easily understandable manner. (Keep in mind that this was even more of a challenge in the mid-80s than it is now, when the importance of OBA and SLG and other sabermetric principles about offense are in the mainstream). He recounts a number of his previous efforts:

1) He tried calling players with significant non-BA contributions "percentage players", but it focused too much on the numbers rather than the player and was already in use to mean something else.

2) He referred to a player having good or bad "peripherals", but thought that the word had some negative connotations. (However, it is now widely used in sabermetrics in regard to pitching statistics.)

3) He tried calling players "Ted Williams" or "Joe Morgan" types, with players of the Joe Morgan class having less power but more speed. James decided that this language invoked specific comparisons, usually inappropriate, to two players and could be misinterpreted as referring to attributes other than offensive shape (including body shape).

4) He referred to players as AA or CC (or BC, etc.) type players, where AA players hit for power and drew walks, CC players did neither, and so forth. This was hard to explain to people not already familiar with his system and James says that even he had trouble keeping straight whether the letters represented (power, walks) or (walks, power).

James then stumbled upon secondary average, and obviously decided to introduce it in the Abstract, making several points about its nature:

1) Average SEC is similar to average BA, on the macro level. For example, in 2009 the AL had a .280 SEC (figured with SB; without, it was .260) and a .267 BA. Before the offensive explosion, the inclusion of steals served to bring the figures closer, generally, on the league level.

2) It makes use of only important, easily available statistical categories--no sacrifices and the like. This was a much bigger deal from the perspective of the mid-80s than it is today, I suppose.

3) "Secondary average is more important (a better indicator of hitting ability) than is batting average" because of the larger spread in individual figures. "One point of secondary average is clearly not as valuable as one point of batting average."

4) SEC is a "collection category" like Total Average--it adds together like things but doesn't attempt to quantify the value differences between them.

In summation, I agree with Mr. James that secondary average is useful to give a quick glance at the size of a player's offensive contribution that does not come from batting average. In 2009, Willy Taveras hit .240, Yunieksy Betancourt .245, Adam Everett .238, Dan Uggla .243, David Oritz .238, and Jack Cust .240. As you well know, though, the latter three were much more productive offensive players. Secondary average quickly and simply captures their contributions that did not go into BA. Their SECs were .379, .360, and .359 respectively. The first three players came in at .089, .151, and .151. Their batting averages are indistinguishable, but secondary average shows that there was a huge productivity gap between the two groups.

So the usefulness of SEC as a gauge is largely tied to the degree to which batting average is used as the starting point for player comparisons. If you are a sabermetrician, or even a user of OPS, then you don't need secondary average; in all likelihood you hardly even look at batting average, which along with the meaningless units of SEC makes an opinion on the statistic like the one I quoted from Colin perfectly understandable. However, if you want a relatively easy tool you might be able to explain to an uninitiated fan, or you like me have a personal bias for players who draw walks and hit for power, then secondary average is a fun, junk-ish stat to have at your disposal.