## Monday, March 09, 2009

### Power Factor v. Isolated Power

This is just a quick hit post, but it’s something that pops up from time to time and I wanted to record my thoughts here for posterity’s sake.

Sometimes you will see total bases per hit proposed as a measure of power. Eric Walker of High Boskage calls it Power Factor. Another common measure of power used is isolated power, in use since the days of Branch Rickey and Allan Roth and possibly longer, figured as (TB - H)/AB, or extra bases per at bat, or slugging average less batting average.

Which is better? Well, better is a nebulous term--as with so many issues in sabermetrics, the answer depends on what you are trying to measure. So let’s take a step back and think about what each of these formulas actually does measure.

Power Factor, TB/H, or SLG/BA, is quite obviously the average number of total bases per hit. As such, it can be thought of as a measure of bang for your buck--given that the batter gets a base hit, how many bases does he get?

Isolated Power is a measure of extra bases per at bat. Each base gained on a hit, beyond first base, goes in the numerator. Rather than dividing by hits, this sum is divided by at bats. It can be thought of as a measure of propensity to collect extra bases given that the ball is put in play.

If you have two players with an identical number of at bats, and identical numbers of each type of extra base hits, then they will have the same ISO. If one has less singles than the other, he will have a higher PF.

Consider the career statistics of Rob Deer and Mike Schmidt, presented below. Schmidt has a higher ISO, but Deer has a higher PF. Schmidt collected more extra bases, even per at bat, and by a substantial margin (.260 to .223 in ISO). But Deer collected substantially fewer singles (.119 per AB versus .146), and so when it comes to PF, his extra base contributions are less “diluted”. Thus, he has a slightly higher PF than Schmidt, despite the fact that Schmidt hit for extra bases at a higher rate:

So what are you trying to measure? Are you trying to measure some concept of “raw power” in which a player like Deer, who when he does hit safely often hits the ball a long way, is celebrated? Or do you want to recognize the frequency and number of extra bases a batter achieves, regardless of whether he also is proficient at getting humdrum singles?

Of course, there are other things that can be taken into account as well. Perhaps you want to draw a distinction between home run power and “doubles power”. Perhaps you only want to know what happens when the batter actually puts the ball in play, and want to ignore both at bats in which the ball is not put in play (which are included in ISO’s denominator). This school of thought would hold that strikeout rates not relevant to the question of power. So you could look at extra bases or total bases per balls in play, as Jim Furtado did some time ago. You could also try to draw a distinction between power (doubles and triples) and speed (triples) as Robert Dudek did. Perhaps you want a measure of hitting style or a measure of the value of power relative to a player’s other skills (in other words, the shape of his performance). In that case, Power Factor might be a better tool than Isolated Power.

There is any number of possible definitions, and none is inherently superior to any other. For me, though, the most interesting of these questions is “How much did the player contribute to his team through power hitting”, and for that, ISO is clearly superior to PF. That Schmidt hit more singles doesn’t make his power contributions less valuable. That Deer struck out a lot should not be ignored if you want to measure the impact of his extra base hits on his team.

One could also point out that both PF and ISO are somewhat crude. Each adheres to the standard total base weights (or the total base weights less one, which gives you extra bases). You could use the average base values (including all bases gained by the team--batter plus baserunners) or, similarly, the linear weight run values of the hit types (either total or beyond that of a single), to give a more precise measure of value contributed. This is the approach that Rob Shandler took with his “Linear Weighted Power” metric.

Since either of these power measures is not itself a statement of total value, but rather gives insight into how that total value was created, I don’t mean to suggest that there is necessarily anything wrong with using TB or EB weights. I just want to point out that you could go even further in refining the question than does ISO, and that ISO is not necessarily a fundamental baseball measure.

In conclusion, I’m not trying to suggest that Power Factor is useless, just that it doesn’t measure or approximate the value of extra bases. It is a measure of shape, and it does approximate at least one definition of what we mean when we talk about power. But I get the suspicion that most people are more interested in the type of question that Isolated Power speaks to.

In case you were curious about how to convert between ISO and PF, all you need is BA and you can derive these relationships:

PF = ISO/BA + 1
ISO = BA*(PF - 1)

#### 5 comments:

1. I'm way way late on this Phil, but I was wondering if you could look at PF versus contact ISO (cISO, which is basically ISO minus the strikeouts in the denominator). It seems that those two will probably show similar results, but I'm not so sure about that.

2. The main difference between cISO and PF will be that cISO still takes outs on balls in play into consideration. Between cISO and PF, I don't have a strong preference--the biggest issue for me is identifying the question of "raw power" v. "power contribution". Given the former choice, one could make a case for either cISO or PF.

Incidentally, I am not Phil--I don't mind but I don't want to get confused with Phil Birnbaum or some other smart cookie.

3. Sorry about that Patriot, it was a bit late when I wrote that.

4. Great read, thank you. Can you provide further readings into this subject?

I love looking at PF in combination with AVG simply because that paints the more complete picture. Your example of Rob Deer is great, and when you factor in his AVG you can see why Schmidt is a better hitter (e.g. Deer only hits HRs, but he doesn't hit many..)

5. I'm not aware of a lot of other material on this particular subject. It's possible there is a thread on the Book blog, and there may have been a thread at the old FanHome, but none jumps to mind. Bill James wrote a little about this in one or two of his early Abstracts (1982-1984 I think).

To put my view another way, if we accept for the sake of argument that PF measures the "tool" of raw power, ISO measures how effectively that tool is translated into on-field production.

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