How Good is Harrison Bader’s Defense?

It’s apparently Harrison Bader week here at Viva El Birdos, as stlcardsfan4 wrote about him on Thursday and I’ve got this follow-up today. Mine, I regret to say, doesn’t have any more idea than his about why scouts missed Harrison Bader’s defense. It really is one of the great mysteries of this Cardinals season- apparently Kevin Kiermaier was just hanging out on the bench and nobody knew about it. Instead, I’m trying to answer a slightly more nebulous question. How good is Harrison Bader’s defense, really? How good is it in the larger sense, the going-forward sense?

This season, Harrison Bader is quite possibly the best defensive outfielder in all of baseball. By Ultimate Zone Rating (UZR), one of two publicly available advanced defensive metrics, he’s been the second-best outfielder in baseball on a rate basis, narrowly behind the aforementioned Kiermaier. By Defensive Runs Saved (DRS), the other popular defensive statistic, he’s the best outfielder. Not too shabby for a rookie weighed down by all those flowing locks of his.

Defensive metrics are, to put it lightly, kind of confusing. They don’t always match the eye test. Jhonny Peralta was a great defensive shortstop by pretty much all rating systems, but he looked like he could barely move on some nights. You know what’s not confusing? The new Statcast defensive metrics. Their flagship metric, Outs Above Average, essentially just figures out what percentage of outfielders make a catch for a given distance from starting position and hangtime. There’s not much subjectivity to that- it’s literally just a measure of how quickly they can get from point A to point B and how efficiently they run there. You know who leads all outfielders in Outs Above Average? Well, Billy Hamilton. That really ruined my narrative flow. Harrison Bader is second, though! He’s only one run behind the consensus fastest man in the majors. What does that look like? Baseball Savant has two excellent visualization tools for it. First, there’s a scatterplot of how long each ball hung in the air, and how far the fielder had to run to get it:

The lower and the further right on this chart, the faster you have to run and the better jump you need to get to the ball. That’s a pretty great visualization. That’s not all Baseball Savant has, though. Want to see an outfield with the landing places of every ball Bader either caught or didn’t get to, along with his starting position? Great news!

Gotta love the bonus compass. In this graph, the red lines show the outermost perimeter of the plays Bader has made this year. It’s a good thing the Cardinals can’t clone two more Baders, because an outfield of Baders would be running into each other in right-center a surprising amount. The man can fly.

If nothing else, hopefully these graphs give you an idea of just how crazy good Bader’s defense has been this year. I don’t want to focus on that today, though. Let’s take as a given that Bader is a great defender this year, one of the best of the best. What does that tell us about how good of a defender he’ll be next year? How about the year after that? Well, I’m going to level with you. It’s not the easiest question to answer. Look at those dots up above. There are a lot of them, but there aren’t that many right on the margins. It would be unrealistic to think that we know all there is to know about Bader’s true defensive talent level just from a year of data.

With that disclaimer out of the way, I’m still going to try! How am I doing it? Well, I put together a bunch of random statistics, a priest, at least three swords, a license to ill from the Beastie Boys, three Ouija boards, and a squeegee. Obscure Eminem reference aside (hi Rihanna!), what I actually put together was a long history of defensive metrics recorded by rookies. Why rookies? Well, I don’t want to color the information set we have with previous data. If 2017 Andrelton Simmons has a great defensive season, we tend to believe it. Some of that is because it’s clear to see from watching him that he’s great. Some of it, though, is because we know he’s always done it. You can look at his past stats, as well as his past play, and make some reasonable guesses about the future. If 2017 Trevor Story has a great defensive season by UZR, we’d be a little more skeptical, because he’s never done it before. Thus, rookies only. I wasn’t able to find scouting reports for all of these guys, which would have been helpful when it comes to figuring out which guys are closest to Bader, but I do have a database of every season worth 10 or more runs per 150 games played since 2010 according to UZR (Bader’s defense rates out at a little under 20 runs per 150 games on the metric). I eliminated everyone who had played at least 500 innings in the field in a previous season, because we want guys about whom we truly had no prior information. That leaves the following 20 players:

There are some interesting names in this table. The predictable glove-first guys are there- your Billy Hamiltons and Jose Iglesiases (Iglesii?). There’s a lot of star power too, though. This isn’t really in the purview of this column, but I find it pretty interesting that the likes of Giancarlo Stanton, Bryce Harper, and Mike Trout all put up elite defensive seasons in their rookie years. That’s not a tremendous surprise- superstars tend to be great athletes. It’s interesting either way, though. In any case, these guys are the cream of the crop, the rookies who put up the best defensive seasons in my sample. As a whole, they were 14.4 runs above average at their respective positions in their rookie years. If you’d like to think about it in wins, that means they were worth about 1.5 wins to their teams relative to an average defender at their spot. That’s pretty incredible if you stop to think about it. If there were a dead average major leaguer who played a dead average position on defense, he’d be worth 1.85 wins per 600 plate appearances (I’ll get into the gory mathematical details in a footnote). If you instead gave that player one of these elite rookies’ defense, he’d be a 3.5-win player, an All-Star many years. That’s some serious value.

Okay, we have a cohort for Bader. They might not all be as good as him on defense, but they at least provide a starting point for analyzing great rookie defenders. How did these guys do in their second seasons? Remember, the only information we have about them is that they were excellent defenders (by the metrics, at least) in their rookie season. Here’s season two:

Let’s be generous and call that a mixed bag. There’s definitely some regression to the mean, reasonable in a sample of standout seasons. The group are still above-average defenders on average. Their level of defense, however, declines meaningfully. In response to this evidence, you might say, well, obviously. Some of these guys aren’t actually good defenders. Well, you say that now. The truth is, it’s hard to tell in the moment who’s going to be great and who’s going to be good or even average. For a very real example of this, consider the case of Bryce Harper. His rookie season was 700 innings of center field with well-above-average defense. He was a giant, fast guy- as recently as 2015, he showed off a 28 ft/sec sprint speed that would play just fine in center field, and that was after four years of bulking up. He’s also always had a plus arm and good instincts. The next year, however, he was back to being only marginally above average. The point is, we just don’t know who’s going to be a great defender and who is just a flash in the pan. In terms of standard deviation, you’d do just about as well guessing every player would be league average as guessing their first-year defensive numbers would hold up. How does year three look?

Well goshdarnit. These are still pretty middling. The good news is that this group, as a whole, is still above average at defense. If you’re curious, they averaged 6.4 runs above average in season two and 7 in season three. That’s not really what gets the people going, though. “Harrison Bader is better than average at defense” is not a sentence anyone came here to read. It’s probably the best you can say with a read of UZR, though.

There are some things that this analysis doesn’t consider, can’t consider. First of all, Bader is fast. No, faster than that. Faster than faster than that. He’s FAST. I simply don’t have a good database yet for how well speed in year one predicts defense in year two, but it’s encouraging to see that Lagares and Hamilton mostly held onto their defense. In terms of things I could actually do, I considered folding in DRS to look at players who were good by both systems, but this was going to add a lot of work without adding much to the analysis that I could see- DRS only really disliked Whit Merrifield and Jose Iglesias relative to UZR. The real answer, I think, is that we’ll just have to wait and see. A reasonable estimate for Bader next year is probably something like eight to ten runs above average as a centerfielder. That’s absolutely fantastic. There have only been 15 centerfield seasons better than ten runs above average in the past three years. It’s probably a little early to think he’s actually as good on defense as he’s playing right now, though. Let’s not build him a statue just yet.

Appendix 1: Some WAR Methodology

I said that an average player was worth 1.85 WAR per 600 plate appearances up above. Why am I so stupidly precise? It comes down to the definition of WAR, which you can find here. There are 1000 available wins above replacement by definition, of which hitters get 57%, again by definition. We know that each team plays 162 games, and there are roughly 38 plate appearances a game. Thus, there are 30 * 162 * 38 or 184,680 plate appearances in a year, and the value of all those plate appearances is worth 570 wins. All we have to do is divide 570 by 184,680 to get the average wins created per plate appearance, then multiply that by 600 for the 600 PA season we’re talking about above. Et voila!

You can do some interesting math once you have that value. For example, in 2017 teams scored 22,582 runs in 185,295 plate appearances, or .122 runs per plate appearance (we’re ignoring park factors in this analysis to make the math a little cleaner). Thus, over a 600-PA season, a 100 wRC+ player would create 73.2 (600*.122) runs. If Bader hits for a 90 wRC+, that would make him 7.3 runs below average, roughly .8 wins. Since we are projecting his defense to be worth something like 11 runs (9 runs plus a 2.5-run positional adjustment for centerfield), this would leave him about 4 runs above average, something like a 2.2 win player. Throw in another half a win for baserunning, and that gets him up to 2.7 wins. We can use this value to figure out how truly awful he’d have to be as a hitter to be valueless. At 1.85 wins for a league average hitter (and 9.3 runs per win) and with 16 runs of defense plus running, a 100 wRC+ Harrison Bader would be worth 33.2 runs more than a replacement level player. Subtract 33.2 from that 73.2 league-average runs created, and then divide the result by 73.2, and you can see that if Harrison Bader is an elite centerfielder and runner, he’d need to be a 55 wRC+ hitter to be replacement level. Neat!

There are some caveats here. One, he’s probably not going to be worth 5 runs of baserunning value if he’s really running a 55 wRC+. Two, a replacement level outfielder is not really what we want, so it’s not a tremendously valuable conclusion. It does let you do a little mental math to see how much hitting is worth, though. Every 13 points of wRC+ is worth a win over a 600-PA season. Think Bader’s a 100 wRC+ hitter? Bam, he’s a 3.6 win player. 87 wRC+? He’s a 2.6 win player. Please note that I reverse-engineered this all through the Fangraphs glossary, so there’s some chance I’m marginally off on the details, but I think the math works close enough.

Appendix 2: How I picked the defenders

I looked for all players who exhausted their rookie eligibility in a season they put up 10 UZR/150. Then, I added all players who exhausted their rookie eligibility the year before they put up 10 UZR/150, but who compiled less than 500 innings at their position while doing so. I ended up adding Christian Yelich, who played 505 innings in left field, because he was the only one of the bunch anywhere close to 500 in his rookie season, and I wanted an extra data point if possible. I figured he fit the spirit of the search well enough.

Second, which UZR did I use for outfielders? Well, wherever possible I used the same outfield position, rather than their overall OF UZR, to compare like for like. For players who changed positions, I used their new dominant outfield position. For players who split time across the whole outfield, I just used their overall outfield UZR.

Appendix 3: The most important article about WAR you’ll read this year

It’s here. If you are interested in baseball analytics, read this. The issue Carleton addresses is one of the key potential weaknesses of a WAR-based model. If positions aren’t fungible, WAR needs a re-think. This always kind of intuitively makes sense in the extremes- an average shortstop is probably not a +20 defender at first base (looking at you, Ian Desmond). The specific data has always been hard to come by, though, and this is a great dive into it. If you rely on WAR as a tool to analyze baseball, knowing its limitations is tremendously important, and this article does a great job of tracing some of those limitations.