September 22, 2011

Between The Numbers

Addition by Addition

by Colin Wyers

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I’m going to introduce a few new stats for our sortable reports and cards in just a moment, but first I’d like to talk about what kinds of things we’re looking to add and what our decision process looks like.

Our readers really like baseball stats, but they like looking at ones that matter. It’s our job to make sure that our statistics matter, that they communicate something meaningful, and that they do it in a useful way.

For us to add a stat, it doesn’t have to be world-shaking. It can merely be interesting (and some people may not even agree on that). But it does have to meet a few criteria:

• It needs to be different enough from our existing metrics to provide added value. Perhaps not substantively—it can say the same thing, so long as the presentation is different enough that there’s some value in having both presentations.
• When a new metric disagrees with an existing metric, it’s important to make sure that we can clearly communicate why the two differ, and what the value is to having both answers. If we think one metric is provably better than the other, we use that one instead.

We plan to continue adding things to our sortable reports over the offseason, but when we do so it’ll be guided by those two considerations. Now, on to the fun stuff.

We’ve introduced two new metrics that should seem rather familiar to most of you, even if we’ve never presented them ourselves. They’re “plus” metrics, similar to OPS+ and ERA+ from Baseball Reference.

Let’s start with RPA+ (RPA_PLUS in the sortables), which is our new offensive rate stat along the lines of OPS+. What it isn’t is a departure from how we evaluate hitters currently; TAv and RPA+ will return the exact same rank order of batters. At the core of both of them is the exact same adjusted runs per plate appearance, figured using linear weights values derived from run expectancy tables. In this case, there is no right or wrong way to handle the scaling of adjusted R/PA for presentation—some people find it more intuitive to look at R/PA scaled to batting average, others to 100. (There are also technical reasons to prefer either, based upon what you’re doing with each.) Essentially, they’re two ways of looking at the same information—complementary, rather than redundant or competing.

So why might you prefer RPA+ to OPS+? There are a few reasons:

• RPA+ includes a league quality adjustment. Batters in the AL face tougher pitchers, and so the same batting line in the AL means a better hitter. TAv and RPA+ capture this, while OPS+ ignores it.
• RPA+ is a better estimate of a batter’s production than OPS+, which undervalues high OBP, low SLG players and overvalues high SLG, low OBP players.

The complement to RPA+ is Fair RA+, again similar to ERA+. Unlike with RPA+, Fair RA+ will return a different order than Fair RA, because it includes park and league adjustments. Why favor Fair RA+ over ERA?

• Fair RA separates what a pitcher has done from our estimate of his defensive support.
• Fair RA uses all runs, not just earned runs—ERA+ will overrate a groundball pitcher relative to a flyball pitcher with equivalent production.
• Fair RA uses a different construction to produce the scaling factor. ERA+ is actually the league average ERA divided by the player’s own ERA, in order to make larger values better (rather than allowing smaller values to be better). We take Fair RA, divide by the league average, and subtract the result from two. This gives the same “bigger is better” property ERA+ has but keeps the units meaningful and makes it easier to work with mathematically. Patriot explains the reasons for this, but in summary, taking a weighted average of ERA+ across seasons is more unnecessarily complicated, and it makes the units of ERA+ essentially meaningless. A Fair RA+ of 110, for instance, means a pitcher's Fair RA is 10% better (that is to say, lower) than the league average. ERA+ doesn't behave linearly at all. Comparing the two methods, setting 4.5 as the league average:
  
  

What I've called "two-minus" is the method we are using; "inverse" is the method behind ERA+. What you find is that an additional 10 points of ERA+ means different things based upon where on the curve that additional 10 points occurs, while 10 points of Fair RA+ consistently means the same thing for any point of the scale.

Since I’ve taken the time to point out yet again how OPS falls short of linear weights-based measures of offense, I’d also like to announce that we’ve included TAv and RPA+ on the batter and pitcher opponent quality reports. We’ve retained the slash lines and OPS as well, but this is one place where we can put our money where our mouth is as far as putting our preferred offensive metrics out there for consumption. We’ve also added TAv against for pitchers, for those who want to see a pitcher’s performance in those terms. (Yes, TAv against attributes all fielding performance to the pitcher. Under consideration is a derivation of TAv against that is more DIPSy.)

We’re also introducing a new breakdown for batting WARP, which you can find in this custom sortable report. We’ve broken WARP apart so you have a better idea of what goes into each players’s numbers. Included are:

• Batting Runs Above Average, or BRAA
• REP_LEVEL, which is the amount added to a player’s BRAA to give us runs above replacement.
• POS_ADJ, which tells you how many runs a player is credited based on his fielding position,
• And TOT_DEF, which is POS_ADJ plus a player’s FRAA—in other words, everything in WARP that measures a player’s defensive abilities.

This is only the start—we’ve got some other things cooking, and we’re really excited to continue to improve these sorts of offerings. (Of particular interest is defense for catchers, including Mike Fast's work on catcher framing.)

And as a reminder, while the default sortables are available to everyone, custom sortables are reserved to subscribers only. Right now, you can save six bucks on a yearly subscription with our Big September coupon code.

Colin Wyers is an author of Baseball Prospectus. Follow @cwyers
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