Another look at replacement level

With the increased use and acceptance of Wins Above Replacement (WAR) statistics, more of our analysis than ever depends on our definition of “replacement.” Replacement level is one of the most important concepts in our analytical toolkit, but it’s also a bit nebulous.

To get us all on the same page, let’s spend a moment talking about what “replacement level” means—or at least is intended to mean.

“Replacement level” refers to the amount of production you’d expect from a freely-available replacement—the type of guy you could call up from Triple-A, or grab on waivers, or convince another GM to give you in exchange for a player to be named later. We’re not talking about prospects; we mean minor leaguers (or maybe major league 24th and 25th men) who are interchangeable enough that their organization doesn’t value them much.

If we’re thinking about the team level, “replacement” is 25 of those guys, all making the major league minimum. Depending on how you define replacement, that team is going to win something in the neighborhood of 40 or 50 games.

Calculating WAR

For today, I’m interested in replacement level for position players. There are three elements of WAR that are relevant to what I want to discuss: offensive value, defensive value, and the positional adjustment.

In setting replacement level, most analysts determine a level of offensive production. This makes sense, partly because it’s much easier than trying to measure every aspect of the player’s contribution, and partly because it is equally applicable to players at every position.

So, a big part of a player’s value is how he performs offensively relative to replacement level. Rightfully so. This is independent of his position.

Defense is treated differently. Instead of comparing a player’s defense to some notion of replacement-level defense, we usually compare it to average. This is because a replacement-level player is not replacement-level in all things. While there are some clunky fielders that fit the profile of a replacement-level player, a more useful image might be someone like Colin Curtis or Will Rhymes—a middling offensive player who has at least some defensive skills.

So our hypothetical replacement-level player provides offense at a defined, minimal level and is an average defender. (We can extend the reasoning for defense to other things, like baserunning.)

But, of course, a player who is +40 runs at the plate and +3 runs in the field is a lot more valuable at some positions than others. That’s why WAR has a positional adjustment. Such a player is worth more at catcher or shortstop than he is in left field.

The positional adjustment

This is where things get a little tricky. Positional adjustments are important to any WAR calculation and the precise numbers are reasonably well established. But they are better at comparing players among positions than they are at contributing to our understanding of replacement level.

The reasoning behind commonly used positional adjustments (e.g. +7.5 runs for a shortstop, +2.5 runs for a center fielder, etc.) is that some positions are easier to play than others. That’s certainly true, and we can quantify the difference by looking at players who move between positions. If the average guy who plays both center field and left field is 10 runs better (per 150 games) in left than in center, it tells us that left field is 10 runs easier to play than center.

If we want to compare the value of Colby Rasmus to the value of Matt Holliday, this is fantastic tool. But positional adjustments, as we use them, ends up oversimplifying replacement level.

Prospects around the diamond

Positional adjustments themselves aren’t the problem—the issue is that we can’t let that be our only way of managing the differences in positions. The adjustments do a good job of representing the difficulty of playing each position, but it doesn’t consider the challenges of filling each position.

Consider the options of a GM who has a sudden need for a player but doesn’t want to spend much to fill it. First, he’ll consider his own double-A and triple-A squads. If there’s a reasonably good option there, he’ll take it. If not, he’ll scour the minor leagues look for a “freely” available replacement.

That’s the case regardless of position. Let’s focus on a couple of different scenarios. If a GM needs a shortstop, he probably only has two or three legitimate contenders within the organization: the starter at triple-A, and maybe the triple-A backup or the double-A starter. If none of those are good options, he looks outside the organization, and gets a player someone is willing to part with.

If a GM needs a left fielder, he might logically start his search with his triple-A leftfielder, but he has far more choices. He might choose a center fielder or right fielder from the minors. He might even choose an infielder—just about every infielder, except for some first basemen and a few weak-armed second basemen, can play left field. He is also more likely to be able to draw on the backups already on the roster. Then he can fill the backup’s spot with any minor leaguer he chooses.

The point is this. If a GM needs a player at a difficult position, he’s stuck with a very few choices within his organization, and probably no good ones outside his own franchise. If he needs a player at an easy position, he can choose nearly any position player in his own organization, and he can choose his favorite freely available player from the rest of baseball.

Back to positional adjustments

What positional adjustments don’t advertise is that they don’t always work in both directions. It’s a safe bet that most shortstops can play second, or third, or center field, and on average, their defensive numbers increase accordingly. But many outfielders can’t play second, third, or shortstop. Few non-catchers can play catcher.

I’m not claiming a breakthrough with this explanation—we all know that there are more potential left fielders than there are catchers, more first basemen than shortstops. Positional adjustments are based on players who were chosen to play multiple positions, so even if we were willing to stick Mark Teixeira at shortstop, he probably would be worse than the adjustment would predict. And he’s a righty—the situation is clearly worse for lefthanders.

The adjustments might not hold up if we started indiscriminately sending shortstops to left field and center fielders to first base, too. But it seems like a safe bet that the tough-position guys would do better switching to easy positions (relative to positional adjustments) than vice versa.

What, then, is replacement level?

My point is simple: Replacement level differs by position, and positional adjustments don’t explain the whole difference.

Our conceptual notion of a replacement player is probably about right for shortstops and catchers. If you need one and you don’t care to promote your guy at triple-A, you’re probably stuck finding someone like Eric Bruntlett or Chad Moeller.

But if you need a left fielder, you’re more likely to find your answer in your own system. You’re also more likely to be choosing a prospect who you wouldn’t make freely available to another club—that is, someone who is better than the conceptual definition of replacement.

That’s why so many prospects end up starting their major league careers out of position. Miguel Cabrera spent years in the outfield before returning to third base; Melky Cabrera and Jacoby Ellsbury both played more left than center upon their initial callups, and Chris Coghlan won last year’s Rookie of the Year Award as a second baseman playing left field. Hell, Jackie Robinson spent 1947 as a first baseman.

In real life, we’ve always known that replacement level is contextual. What’s I’m suggesting is that, as we get farther to the easy side of the defensive spectrum, it gets more and more contextual.

But regardless of the numerical replacement levels that result, it is clear to me that in most cases, a team’s replacement level is lower than we think at difficult positions and higher than we think at easy ones.

It follows, then, that we may be overvaluing players at the easy positions and undervaluing those at the hard ones. That may be part of the reason that “strength up the middle” appears to translate into more wins. The linked study was based on Win Shares, so it may not apply to other WAR-type stats. But I suspect the underlying problem is what I’ve described, and it affects other versions of WAR as well.

In my mind, the notion of replacement level just got a whole lot more complicated.

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Comments

  1. MikeS said...

    Very good article.  Two things really stand out to me.

    I now understand why defensive WAR numbers are never as impressive as offensive numbers.  It’s not because the spread of talent is assumed to be different, it’s the definition of replacement level talent for each of those skills.  If a replacement player is average defensively and bad offensively it is going to be much easier to rack up superior numbers when compared to a bad player than an average one.  Defensive “Wins Above Replacement” is really “Wins above Average.”

    Second, I think it’s great that people actually look at the methods used to derive the stats and wonder if they are accurate, test them and either confirm or refine them.  I see so many people say “John is a better fielder than Steve because he has a better UZR and UZR is the best defensive stat we have.”  They miss the point that the best stat may still not be any good.  AVE, RBI, fielding percentage and ERA used to be the best stats we had, didn’t mean they were any better then than they are now.

  2. Peter Jensen said...

    If the average guy who plays both center field and left field is 10 runs better (per 150 games) in left than in center, it tells us that left field is 10 runs easier to play than center.

    Although this is the most commonly held interpretation of positional adjustment it is technically incorrect.  The average center fielder IS a better outfielder than the average left fielder.  But the fact that a center fielder switching to left field is 10 runs better per 150 games only tells us that he is being compared to a different pool of players as a left fielder than as a center fielder.  That left field pool is, on average, 10 runs less talented than the center field pool.  But the 10 run difference doesn’t reflect the degree of difficulty in playing center field versus playing left field.

    Center field gets more fielding opportunities than does left field or right field because there are 15 to 20% more balls are hit there.  Of course, it makes sense to play your best outfielder in center field because he will save the team more runs there PER SEASON than he would in left or right.  But the defensive metrics compare center fielders to only to other center fielders and on a PER CHANCE basis.  The positional adjustment is an estimate to correct for the different pool and the different number of opportunities to give a better estimate of a player’s overall defensive value to the team.

  3. MGL said...

    Peter is 100% correct.  While it MAY be true that CF is more “difficult” (and you have to define what that even means), the reason for the positional difference, as he correctly states, is due to the pool of players at each position.  Imagine that for some reason, we knew that CF, RF, and LF were exactly the same in terms of difficulty AND number of opps.  If teams still put their best fielders in CF (there would be no reason to do so of course), then a CF moving to the corners would still gain “runs” because those runs are relative to the average player at that position (again, as Peter says).  That being said, I am not sure the CF IS more difficult to play.  In fact, it may be easier, as there are fewer balls that are severely sliced and hooked.  When I played baseball, I preferred CF to the corners for that reason.  Probably the only reason to put your best OF defender in CF is the number of opps, once again as Peter points out.  It is not even clear (to me) that because CF is deeper, that a better defender should be put there. 

    Same with the IF.  Is playing SS more “difficult” than playing 3B?  Tell that to a third sacker as he tries to field a bullet hit by Albert Pujols!

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