June 17, 2003

Rockies' #634

Park Factors and OBP

by Boyd Nation

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Sometimes a big epiphany just leads you back to a better understanding of a mundane truth. Let me walk you through one of mine.

A few months back, I finally hit upon a useful algorithm for determining reasonably accurate park factors for all 287 NCAA Division I baseball programs. Given that, in any given year, a given team will only play 25-30 of the other teams, and that over half of those matchups will not be home-and-home contracts but will involve a smaller program playing only at a larger one (which is of no benefit in determining park factors), I was quite pleased with this discovery.

Current major league park factors, relatively speaking, are a little dull. Sure, you have Coors Field, which routinely comes in around 160. The rest of them, though, hover within about 20% of each other from top to bottom. It matters if you're picking at the fine details of performance analysis, but for a lot of fans it causes the issue to just resolve down to "the Rockies and everyone else." College park factors, on the other hand, have a good bit more range in them, from the lows down in the 60s up to New Mexico, at an astounding 211. In other words, a theoretical game played at New Mexico will produce more than twice as many runs as the same game played at a neutral park like Fresno State.

I then set about finding practical applications for these park factors. The most common use for park factors is to take performance metrics, both team and individual, and place them in a neutral context. So I began thinking of ways to park-adjust statistics and look for players and teams who were actually better or worse than they appeared at face value. Suddenly, it occurred to me that the park factor for runs scored was not the same as the park factor for OBP, and that the relationship between the two was not linear; it was exponential. In other words, if the park factor for OBP increased from 130 to 140, that would result in a greater increase in runs scored than 100 to 110.

Now, the notion that a given park has different factors for different statistics is hardly a new one. Although the most common use of park factors involves just using a single number (usually the factor for runs), more sophisticated investigators such as my hosts here at BP have recognized for years that a given park may increase homers and decrease doubles, for example. I had never seen a discussion of the relationship between increasing OBP and runs, though, although it's implied in the various component models such as Runs Created (RC) or Extrapolated Runs (XR).

To get a feel for the non-linear nature of the increase, consider a pathological case with one game for a team that produces only singles or walks and outs:

OBP    OB    PA   Runs
.250   9     36    2
.300   12    39    4
.400   18    45    8

OB is the number of baserunners, while Runs is the expected number of runs given the usual random distribution of runners per inning. Now, this is kind of an extreme case because of the lack of extra-base hits, but it illustrates the mundane truth I've come full circle to underline: Don't make outs.

Because of this nonlinear relationship, though, the question of how you translate a given player's OBP, for example, to a neutral performance in an atmosphere like New Mexico's (or the Rockies) gets interesting. Home-road data is not available on anything other than runs scored for the college ranks, for the most part, so that's not an option. It turns out, after playing with the various forms of RC and XR, that the best approximation for the relationship between the two is

PFR = PFOBP1.25

In other words, the park factor for runs is approximately the park factor for OBP to the 1.25 power. The biggest reason for the exponential relationship is that, when you don't make an out, you get another plate appearance as a reward, and sometimes you don't make an out then, either; since you can't make more than 27 outs in a regulation game, you get a feedback mechanism that pushes the number of runs up somewhat faster. There are enough complicating factors (a team that gets more of its slugging from home runs than from doubles will benefit differently from the added plate appearances, for example) that trying to fine tune it more than that probably isn't worthwhile, but that's a useful piece of information.

It also turns out that the question, "How do I find a factor for translating OBP given that I have a factor for runs?" is the exact converse of another interesting question, "How much does a given percentage increase in OBP increase a team's run scoring?" Nothing in the analysis above requires that the increase in either runs or scoring be due to park factors; a pure increase in ability will suffice just as well.

For most teams, that's just a reminder that OBP is Everything. For the Rockies, though, and for the small percentage of college teams with park factors over, say, 150, the nonlinear nature of things could imply that, for them, OBP is More than Everything. If your park factor is neutral, increasing your team OBP by 10% increases your runs by 13%. If your OBP park factor is 145, though, then that by itself increases your opponent's runs by about 60%, about what happens at Coors Field. If you then increase your team OBP on a neutral basis by 10%, though, then your runs are increased by about 80% relative to a neutral field. Similar benefits are available on the other side of the ball, since the math works the same in both directions.

I realize that this is the 634th published Plan to Save the Rockies from Themselves, but there's a certain appeal to the notion that getting back to the absolute basics of the game--get on base more often, keeping the other guys from getting on--might just be even more beneficial for them than for anyone else. The Rockies have tried speedy defense, they've tried big sluggers, they've tried guys who never strike out. They've tried a deep staff and they've tried overpowering strikeout pitchers. It's time for guys to load up with guys who know where the strike zone is.

Boyd Nation is the sole author and Webmaster of Boyd's World, a Web site devoted to college baseball rankings, analysis, and opinions. In real life, he's an information security analyst with an energy company. He's writing a series of articles for BP on the college game and the College World Series. He can be reached at boyd.nation@mindspring.com