“Replacement-level.” In certain corners of the baseball internet, it’s a dirty word. In other corners, it’s a given. But what does it mean, truly, to be a “replacement-level hitter” in 2020? Is “replacement-level” a provable concept? Do you need an advanced math degree? Are there real examples of such hitters? Read on to find out!

To answer that question, I devised a quick study. (THANK YOU, temporarily-free Play-Index from Baseball-Reference.com!!!! Seriously, if you haven’t enjoyed the benefits of the P-I before now, *this is the time* to look into stuff, because the P-I is disappearing in favor of something better soon.)

Anyway, the study is simple. I want to know what a replacement-level player is. So I looked over the last five years at all non-pitching players with 1-100 PAs. You have to manually remove some pitchers who also played the “position” of pinch hitter, but that’s not too hard. And you’ll get some false positives, sure – 2019 Giancarlo Stanton, for sure, was no replacement-level hitter. But I figure the benefits are worth it. These are, essentially, the guys who MLB teams want *just enough* to carry them on the roster, either just in September or when there are injury problems. Yet, they’re not the guys who actually *play*. So how do they hit?

Here are the data for the last five years:

**2019*** – 185 players batted .197/.264/.318 in 8125 PAs (7324 ABs, 3438 G), with a secondary average of .230 and a run average [(R+RBI)/AB] of .212

Best-fit player: Pat Valaika, COL (86 PA)

Worst-fit player: Lane Thomas, STL (44 PA)**2018** – 182 players batted .204/.268/.321 in 7226 PAs (6554 ABs, 3261 G), with a secondary average of .221 and a run average [(R+RBI)/AB] of .208

Best-fit player: Michael Hermosillo, LAA (62 PA)

Worst-fit player: Rowdy Tellez, TOR (73 PA)**2017** – 190 players batted .204/.269/.313 in 7710 PAs (6970 ABs, 3494 G), with a secondary average of .213 and a run average [(R+RBI)/AB] of .197

Most prototypical player: Richard Urena, TOR (75 PA)

Worst-fit player: Jeremy Hazelbaker, ARI (61 PA)**2016** – 196 players batted .209/.269/.318 in 7545 PAs (6870 ABs, 3496 G), with a secondary average of .207 and a run average [(R+RBI)/AB] of .201

Most prototypical player: Ben Paulsen, COL (97 PA)

Worst-fit player: Hunter Renfroe, SDP (36 PA)**2015** – 192 players batted .207/.268/.312 in 7130 PAs (6488 ABs, 3398 G), with a secondary average of .203 and a run average [(R+RBI)/AB] of .199

Most prototypical player: Darrell Ceciliani, NYM (75 PA)

Worst-fit player: Jarrett Parker, SFG (54 PA)

The total five-year average is based on 945 player-seasons (some players appear more than once, but are counted separately here), who had 37,736 PAs and 34,206 ABs over the course of 17,087 G. Their slash was .204/.268/.316 with a secondary average of .215 and a run average of .204

**I did choose to keep 2019 Michael Lorenzen in the “non-pitchers” group, since he appeared in 29 games as an outfielder. This was, weirdly, the only borderline call in the entire five-year span.*

So… why do this study? Well, for one, it was a fun project (for me). For another, it was a way to take advantage of the P-I while it’s still free (and still exists). But more importantly, I genuinely wondered what we should expect of these guys who occupy our benches, but we rarely see enter a game. Tom Tango is very fond of saying that there’s no such thing as a replacement hitter – just a replacement *player*. But offense is pretty easy to measure, and these guys are ALL bench players, whether they’re there for their glove or their bat. So you can survive as a ML hitter at just about the Mendoza line if you can add 64 points of OBP and a little more than one “secondary” base per *actual* base. Plus, let’s not take something like the concept of “replacement player,” and act as if it’s not worth re-testing every once in a while.

WARNING: Math below! The section below also assumes familiarity with the Pythagorean Record, so if you’re not familiar with it, now’s the time.

So what on earth does this study teach us about what replacement level might be? Well, given a line like this, we can use what we know to determine how many runs they scored; if we know that, we can estimate how many runs an average team might allow defensively, and then we can estimate how many games such a team would win. We know, for example, that a major league team uses roughly 4131 batting outs (AB-H; roughly 25.5 per team game; aka 25.5*162. This average is remarkable stable over time, regardless of team quality). If we know that this hypothetical team bats .204, we can set up a system wherein *x*=H and *y*=AB. We know two things: that .204*y*=*x*, and that *y*–*x*=4131. A little quick math substitution tells us that *y-*.204*y*=4131, therefore .796*y=*4131, thus we’re dealing with 5190 ABs, including 5190 ABs and 1059 H. We can use similar math to determine that this hypothetical team would’ve had 5710 PAs, 1532 times on base, and 1640 TB, in addition to 1057 R+RBI. Using the a pretty standard R:RBI ratio for the era (about .955 RBI:R), we can estimate 541 R for this team.

But hold the phone; another method to check would be to run the Runs Created formula, developed by Bill James, which is essentially OBP*Total Bases. James is fond of saying that runs in baseball are geometric, not linear. Of course, this is a nonsensical way to say: if you take *standard* statistics, and put them in a *non-standard* lineup, they will skew funny. A player with a .268 OBP will score more runs on an average team (with a ~.320 OBP) than a player surrounded by other .268 OBP-players. Anyway, if you do the basic runs created formula, our team only scores 440 runs. That’s… really big to reconcile. We’re talking about a difference of 100 runs, or 20-25% of our team’s total. So I say, let’s split the difference, and call this team a 480-run team. Hope that works for you. I would love to hear the argument one way or another, so if you’ve got quibbles, please let me hear them. But I’m going to stick with 480 R for the remainder of this exercise.

Anyway, all this is taking place in an environment in which the average offense scored 734 runs. If we assume that you have to be *at least* average defensively in order to stay in the league if you’re this brutal of a hitter, guess what? We can use the Pythagorean theorem with 480 R scored and 734 R allowed:

480^2/(480^2+734^2)=.299.

What do Fangraphs and Baseball-Reference use as Replacement level? .294 – a difference of less than one W/year! (FYI, prior to 2013, B-R used .320 as replacement level; if you go back and use 1.8 as the exponent for the Pythagorean theorem, long the Baseball-Reference standard, you get .318 as replacement level!)

So there you have it, folks. Replacement level, explained – at least at a basic, understandable level. So *is* there such a thing as replacement level? Yes; certainly. Can you determine what it is, using objective standards? Yes, absolutely. Can you then quibble with someone over what standard they used? Most *definitely*! I mean, if you assume our team scored 541 and allowed league average, and you prefer the 1.8 exponent on the Pythagorean theorem, they’re a .366 team; if you assume 440 R and an exponent of 2, they’re a .264 team. That’s a difference of 16 wins over the course of a season. Point is, either way you slice you, you’re probably not going to get them much *worse* than winning a quarter of their games, and you’re not going to be able to get them to winning 40% of their games. So you can find a place in the middle there that makes you happy – but the fact of Replacement Level is pretty undeniable, pretty easy to prove, and consistent with the level used by Fangraphs and Baseball-Reference.

*(For what it’s worth, by the way, in case you want to know my own personal preference, I’ve always assumed that, at the team level, you can be both 20% worse at scoring runs, AND 20% worse at allowing runs and still be a replacement-level team; do that math, and you get a Pythagorean winning percentage of .307. But I’ve inundated the readers here with enough nonsense over the years; I don’t want to go through all that again. But just try the Pythagorean theorem with a team that’s 20% worse than average at each scoring and allowing runs, and you’ll see that it holds. Also, 20% worse on each is a 50-win pace in a 162-game schedule, and 50 is a nice, round number, so I’m personally partial to the .307 number, for reasons partly mathematical, and largely aesthetic.)*

The point is, however you slice it, the Replacement Level set at two of the internet’s greatest baseball sites is pretty dern good. Feel free to discuss below, as you’d like. I would love to hear community feedback on this.