Wednesday, March 03, 2010

Runs Anything

In The Politics of Glory (later Whatever Happened to the Hall of Fame, although I still think the original title was much better), Bill James examines the history of the Hall of Fame and discusses some of the general arguments advanced on behalf of candidates.

After quoting a letter to the editor questioning Reggie Jackson's Hall of Fame worthiness due to his low batting average, James responds: "If you have to focus on one number, don't focus on batting average. Focus on runs--runs scored, runs batted in, runs created, runs produced, runs anything. Focus on what wins the ballgame."

For some reason the last phrase in his list--"runs anything"--has stuck with me since I first read the book. It seems like a great name to slap on a metric based on some tally of runs, but one the person writing about the metric doesn't actually believe in--and for that very reason I've used it here.

Let me accept the premise which is often either explicitly or implicitly put forth by non-sabermetricians, namely that estimates of runs (such as runs created) are unreliable and not based in reality. Ergo, if I want a metric expressed in runs for an individual batter, I will be limiting myself to those based on runs scored and RBI.

Let me also add an arbitrary constraint that I can only use R and RBI; I can't consider any other piece of statistical information (like home runs) in constructing the numerator of my metric. This allows us to sidestep the lively discussion about the merits or R+RBI versus R+RBI-HR.

Of course it goes without saying that I don't accept this premise, and you and I both know the myriad weaknesses of using runs scored and RBI to evaluate individual batters. I won't even insult your intelligence by listing them. Given these constraints, what is a reasonable (note that I did not say "the best", "ideal", or any of a number of possible phrases that would indicate I am taking this more seriously than I am) metric we can construct while still infusing it with some sabermetric-suggested properties?

There are three such properties that I think would be imperative in constructing such a metric. These are based on principles that are really not negotiable from my point of view; any analysis (even one constrained to using R and RBI) that does not consider them is one that is fatally flawed, IMO. Of course the points that follow are all obvious to you (although you are more than welcome to not care for how I express them):

1. You must consider runs scored AND runs batted in. Too often in mainstream analysis, runs are pushed aside while RBI are given all the attention. Of course driving in runs is just one side of the coin; someone must be on base to score them. The bias towards driving runs in seems to manifest itself most plainly in modern MVP voting, in which cleanup hitters with gaudy RBI totals are rewarded handsomely (see Juan Gonzalez, Ryan Howard, and Justin Morneau) while their teammates who get on base in front of them (Chase Utley and Joe Mauer in 2006) are ignored.

2. The proper opportunity factor for a rate of run production is outs. Certainly, we can complicate things by talking about the merits of R+/PA, RAA/PA, R+/O+, and the like, but that's beyond the scope of an exercise limiting one to only considering R and RBI, and really is a topic that has more theoretical than practical implications in any event.

It is imperative to consider the batter's role in using up his team's opportunities by making out and creating additional opportunities for his teammates by avoiding outs. Any attempt to quantify offensive performance that doesn't account for this is woefully incomplete.

3. When comparing players across eras, it is necessary to consider the win impact of a player's run contribution. Runs are not equally valuable in all contexts; the more runs are scored per game, the less win impact each run has.

I have not considered park factor here; after all, a metric of this type is designed for non-statheads, the effects are of a lesser magnitude than league scoring level, and it's way too much precision for such a clumsy metric.

So, here are the metrics I'm going to use:

R+ = (R/Out)/Lg(R/O)*100
RBI+ = (RBI/Out)/Lg(RBI/O)*100

Where outs are simply AB-H; again, we really should consider caught stealing at the least, and could consider the ancillary outs as well. I'm going to error on the side of simplicity given the inputs.

To combine R+ and RBI+ into one number, I simply average them. League RBI usually are around 95% of league runs scored in recent years, as of course RBI are not credited on every run. Averaging R+ and RBI+ counts them both equally, and I'll call this figure Runs Anything:

ANY = [(R+) + (RBI+)]/2

The result is a figure similar in scale to OPS or wRC+ and similar metrics--efficiency of run production expressed as a ratio to the league average, with the decimal point discarded.

I have also figured a runs above average figure, which I call ANYA. It is figured as the average of runs above average and RBI above average, which admittedly gives a little more weight to runs scored for an average player. I have not bothered to convert to win value; that is partially accounted for by figuring runs above average, but not completely, which is why sabermetricians are so fond of converting to wins when comparing players across divergent contexts. However, that is too much precision for me to worry about in such an inherently imprecise metric:

ANYA = average(R - Lg(R/O)*O, RBI - Lg(RBI/O)*O)

Let's look at an example that I mentioned in passing earlier through the Runs Anything framework: Ryan Howard and Chase Utley in 2009. Howard finished third in the MVP voting, while Utley languished back in eighth place. (Context-neutral) sabermetric measures are unanimous in evaluating Utley's performance as being more valuable to the Phillies than Howard, but Howard drove in 141 runs to tie for the NL lead while Utley drove in 93. I obviously can't identify exactly what the thought process was for the NL MVP voters, but it seems like a safe bet that the 48 RBI gap between the two was a key factor in their placement.

Utley scored more runs than Howard, although the gap is only seven (112-105). So by any kind of "runs produced" metric, regardless of whether you take out homers or not, Howard ranks well ahead of Utley.

However, what that analysis does not consider is that Howard made 34 more outs than Utley (444-410). The NL averages were .176 runs and .168 RBI per out, which means that Howard's R+, RBI+, ANY is 134, 189, 162 and Utley came in at 155, 135, 145.

This is a useful illustration, as we still get the "wrong" result even when using ANY. ANY does not adjust for the way batting order position affects R and RBI production, and the other pitfalls of using actual R and RBI counts are still in play. Still, the gap between 162-145 is a lot less than a cursory look at R and RBI totals for Howard and Utley would indicate. And of course the analysis ignores the difference in fielding value between the two. Even if ANY captures the true offensive value of the two players, the slick-fielding second baseman is going to come out on top when defense is taken into account.

Believe it or not, I'm going to wring another post out of this topic.


  1. BTF posted a link to this post, quoting only the Howard/Utley comparison at the end that makes it seem as if I'm actually advocating the use of Runs Anything. Great.

  2. P,

    Ironically I was just discussing a metric as simple as this one as an "easy" offensive output stat that people can use in WAR. Of course, I was using it just to illustrate that any sort of offense number can be used in WAR so long as it's in runs.

    I like the outs idea, I myself used PA, but I know that that isn't as good as using outs as the denominator/opportunities part.

  3. Interesting. I wonder if converting runs or RBI to wins first wouldn't be a better way to introduce WAR to a casual fan than the standard way, which is to first introduce your runs created metric and later convert it to wins.

  4. And of course the analysis ignores the difference in fielding value between the two. Even if ANY captures the true offensive value of the two players, the slick-fielding second baseman is going to come out on top when defense is taken into account.

    Some moron on BTF read this and is accusing me of ignorning positional scarcity. A) that's part of "defense being taken into account" and B) what kind of idiot do you think I am? And you obviously didn't RTFA, because comparing Howard and Utley is not the purpose, it's an example. "Think" Factory indeed.


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