# Why a replacement-level player isn't valuable

An arguement that I continue to encounter is that the replacement-level player still has some value to a team – that he has real hits and home runs, and that those still contribute to real wins in some way. Viewed in this light, it’s silly to say that a replacement-level player has no value. Isn’t it?

What we want to look at is the full universe of a team’s options – not just guys who have played in the majors, but guys that could play in the majors — roster filler at AAA, prospects at AA, and free agents looking for so much as a minor league invite. So for that, we’ll use Rally’s CHONE projections, which looks not only at major leaguers but a whole slew of minor leaguers.

This is an illustration, and not a study – so I used Rally’s R150 to estimate runs, and his projected playing time measured in AB. I also ignored defense. If we wanted to study the issue in-depth we could tighten up a lot of assumptions there.

So let’s look at the graph:

The x axis is R150 – how many runs a player is above/below average in 150 games on offense. The y axis is at bats – how many at-bats that player is expected to have. Not all of those at-bats are projected at the major league level, obviously – some of them will occur in the minor leagues.

The light red line indicates the cutoff for average. The dark red line indicates the cutoff for replacement (commonly around -18 to -20; I used -20 for the purposes of this graph).

The purple line? That represents the playing-time cutoff. In the past 10 years, MLB has averaged roughly 166,000-167,000 at bats a season. And so the purple line is the point at which projected playing time for players of that caliber meets or exceeds the number of available at-bats.

At the far right of the curve, there is no competition for playing time – all of those guys are going to find at-bats. As you start to move left, competition increases. And by the time you get to the replacement-level players, what you discover is that you have enough players to cover a full third of the at-bats in all of MLB, and that you really don’t need that many. Essentially by definition half of the at-bats in MLB are being used by players who are average or above, right?

Once you get down to the replacement level, you’re dealing with a lot of available players for very few availabe at-bats – the vast majority of ABs have been taken already by better players. There’s very little reason for a team to keep around a guy who’s below replacement, because the competition for playing time at that level of play is so severe.

And this is why the marginal value of a replacement player is zero – he isn’t any more valuable than a dozen other players who are rotting away in bus leagues, he’s just more fortunate. In measuring a player’s value, the question (at least as far as I’m concerned) is, “How many games would a team win without this player, as opposed to with him?” If one of our replacement-level players gets injured, how many fewer games would team win?

And the answer is zero, because there’s another guy out there just like him who the team can get to replace him.

(As an aside – the graph would continue to rise on the left-hand side if Rally included guys in A ball and the rookie leagues. You could go further, adding in college teams, high school teams, your beer league – the population of pro baseball players is really just the rightmost edge of the population curve of all able-bodied people.)

### 20 Responses to Why a replacement-level player isn't valuable

1. Peter says:

It might just be my browser, but in Firefox 3 the y-axis scale in your graph is partially covered by your sidebar, so it looks like 10, 20, 30 …
Just letting you know. Keep up the good work; I really enjoy the articles this site provides.

2. Peter says:

Following up my previous comment:
The graph looks just fine when looking at the individual post (at http://statspeak.net/2009/01/why-a-replacement-level-player-isnt-valuable.html), but the scale is cut off in both Firefox and IE on the main page (http://statspeak.net).

3. Dan Novick says:

It looks fine for me in Firefox

4. Dan Novick says:

It looks fine for me in Firefox

5. Colin Wyers says:

It’s probably an issue of screen resolution, not browser. I can try to shrink the image a bit for the front page.

6. Millsy says:

I don’t think it really matters all that much. The graph doesn’t say anything about how a player is worth zero. It’s a very pretty way of saying bad players don’t get lots of at bats. Unfortunately, it doesn’t address the questioning of how there is no value in filling the 25th spot on the roster. It also doesn’t address why we would take into account ‘zero value’ for the first X number of runs for a mid to higher level player. They will always have leverage to demand their MRP or close to it from a team if there are multiple suitors bidding.
For another view on shortcomings of VORP I would refer anyone to the discussion at Hardball Times under Colin’s article “Eating the Rich”.
Colin–I would post the same here (as it is a more appropriate forum/article for the discussion)…but may be redundant.

7. Colin Wyers says:

Millsy, I’m not advocating specifically for VORP (look around the site and you should find my “The Trouble With VORP” piece from a while back, for instance.) I don’t want to tie this specifically to any one implementation of a replacement-level metric.
I also don’t want to discuss it merely in terms of MRP – that’s very important for the THT article but not necessarily relevant to all use-cases of a replacement-level metric. And there’s a common misconception that rep-level requires thinking of it in terms of salary and I really don’t think that’s true.
Essentially, because of the talent curve above, your replacement level should be set at the point at which a player’s likely backup is no worse than he is – he has no marginal value to his team because they’re not any worse off with the next guy on the depth chart. This works because at the margins, the supply of 0 RAR/WAR players exceeds the possible demand.
This is the principle behind replacement level. If you discover this isn’t true for some specific rep-level metric – be it VORP, or WARP or Fangraph’s player value – it’s because they’ve incorrectly figured the replacement level.

8. Dan Novick says:

Millsy, I see you found you way over here…
Bad players (replacement level players) don’t get lots of at bats because there are a large number of players freely available who can duplicate that same performance. Colin’s definition in paragraph 3 of his comment is the same thing.

9. Millsy says:

I completely understand the idea that there are large numbers of players at this level. I may have misinterpreted your implications of VORP. I’ll continue to read and check out the ‘Trouble With VORP” article.
The actual replacement level players have little value because of this fact, I understand. But I’m worried that when evaluating bigger guys, the statistics put up within this replacement level are not taken into account. The fact that the player plays for the team in itself gives the player value, however. The actual player himself may not be worth much given the supply, but the final roster slot on the team is worth a significant amount, given the team needs 25 players.
I agreed that VORP, however, does work AT the replacement level…just not far beyond, given the rarity of players beyond that level. Thanks for your comments…it’s an interesting debate that I’ve seen before.

10. Colin Wyers says:

As a fundamental rule of baseball, a team has to send up a batter for every plate appearance. You can’t simply NOT bat. And because of the talent curve that I showed at the top of the article, you have to presume that that player is likely a better than .000 OBP true-talent hitter. So there literally is no such thing as a team that scores zero runs – such a thing is not possible given the distribution of talent in MLB.
Because of that, it makes little sense to give credit for the first run above zero, or the second run above zero, or the third – it doesn’t tell us anything meaningful about a real baseball team.
So in explaining a player’s contributions to team wins, what we want to know is not how many games a team will win but how many more games a team will win, compared to how many games they’d win without that player. And it’s against the rules of baseball to suggest that those plate appearances simply will be left unused, and simply unrealistic (and uninformative) to assume they’ll be filled by someone who can’t hit the ball or walk no matter how many PAs they have.
The replacement-level baseline tells us who is filling those plate appearances at bare minimum – these are the worst players an MLB team is willing or able to accept over any meaningful sample of playing time.

11. Millsy says:

It’s very interesting to think things in this way…and the innate need to put meaning on that bottom level sometimes overwhelms our logical thinking (intercepts in regression come to mind). It’s obvious I can’t portray how basic economics works to you, so I’ll pose a challenge:
Create your own MLB franchise, convincing MLB that you have no need for a minimum salary component, because you think they’re being quite charitable to these ‘replacement’ players by paying them upwards of \$390,000. Pay your replacement level players \$0. We’re going to assume you are equal with the average team in producing players from your minor league system. See how well your team does…keep an eye on your revenue stream, and let me know. If I’m wrong, I will buy you a 12 pack of the beer of your choice (National Bohemian, I hope).
🙂

12. Sean says:

You aren’t going to pay the player zero. You’ve got to be competitive with minor league salaries and pay enough that the player doesn’t find another line of work. But say \$50,000.
I really don’t think there will be any noticeable difference between your replacement level players and the rest of the league’s. You are still paying competitive wages to your above replacement level players.
Your scrubs, say the last 3-5 guys on the roster, will wish they were playing for one of the 29 400k teams, but given a choice between playing for 50k and not playing at all, they’ll play. And there is just a ton of such players to choose from.

13. Colin Wyers says:

The salary truly doesn’t matter for the sake of the arguement that I am making.
The equation for value I am using is essentially:
Wins With Player – Wins Without Player = Value
You can make eight figures and not have much value at all (Ken Griffey Jr. has been doing his best to do that for years.) You can make the leage minimum and have tons of value. (Look at Evan Longoria or Geovany Soto.) We’re starting from the premise of value absent salary concerns right now.
The reason a replacement player has no marginal value is that his replacement is just as valuable as he is. The reason we only count a player’s production above replacement when assigning value is because a player is not replaced by NO production but by replacement-level production.
I don’t see how claiming this makes me incapable of understanding basic economics.

14. Millsy says:

The problem is that there is value based solely on being on the roster…being the one putting up the statistics. My argument really has nothing to do with the minimum salary. It has to do with the fact that, despite others being able to produce withing replacement level, there is still value in those statistics.
If you’re a salesperson, and you sell \$50,000 worth of merchandise, even when the bad sales person sells \$20,000, you’re worth \$50,000 (we’re simplifying this…no other expenses, no intangible attributes of job or employee). If the company is offering you only \$30,000 (value over replacement), you’re going to go somewhere else. Someone is going to say ‘hey…there’s a lot of surplus in that guy, we’ll give him \$30,001.” Would you let him go? No. You would offer him \$30,002. Better players will have every reason to demand this from bidding teams. Assuming your team has equal revenue and payroll as your competitor, you’re going to lose the player. That’s all I’m saying. Maybe this breaks down for the last 15 to 30 players in the league.
My point isn’t that there is no variability in player assessment (for example, your Ken Griffey, Jr. anecdote). Under the assumption, as Sean pointed out, that players would be ‘happy to play for \$50,000″, I guess maybe it works. But that’s not how negotiations work in the real world, and if you can’t figure that dilemma out, you’re probably in trouble when bidding for very good players.

15. Colin Wyers says:

We are apparently having two seperate conversations, and I’m starting to conclude that I’m an idiot for assuming you’re ever going to join the conversation I’m having. I’m going to try again anyway.
There are two parts to the compensation model, MRP, whatever: how much a player is worth to his team in runs/wins/etc. and how much those runs/wins/etc. is worth to the teams in dollars. To put it in economist-speak, I’m only talking about MP right now, absent any concerns of MR.
Because, simply put, there’s a lot of questions where we’re talking about a player’s value where we don’t care about marginal revenue. The MVP award, the Hall of Fame – there is a great interest in baseball as a game, not as an economic enterprise.
I’m trying to explain how team wins occur in a way that is useful to a variety of arguements, some that deal with marginal revenue and some that would prefer to think about baseball as though it wasn’t a business at all. If that doesn’t interest you, then you’re missing out on a lot of what makes studying baseball fun. And you’re missing out on a lot of what baseball is.
But, fine, let’s discuss MRP. There’s a certain percentage of revenue for MLB that is simply not related to team wins – revenue sharing, obviously. National TV contracts and merchandising, obviously. But even some attendance is completely unrelated to the product on the field. Father-son trips, corporate skyboxes, drunken frats in the bleachers, and family vacations – to a large extent these things are unaffected by single-season win-loss records. (You don’t believe me, check the Cubs’ attendance during some of their bad years in the 90’s.)
You can rake in a certain amount of revenue simply by fielding a team of AAA scrubs. Consider that your initial capital. You then decide to invest some of this money into more wins to draw in more customers. If you initially invest \$1 million in a fund, and you have \$1.1 million in the fund now, the fund did not earn you \$1.1 million, it earned you \$100,000.
The key word here is marginal – we want to know the DIFFERENCE in wins, revenue, etc.

16. Millsy says:

I’m sorry if you took anything as an insult…it’s all in good fun. I enjoy the discussion.
I’m not an economist, nor would I ever, ever claim to be. The reason I pick the dollar amounts is that it’s easier to understand and use corrolarries in things outside myopic baseball statistics. I understand there are other revenue sources outside the winning, I was just simplifying it. When we start talking about this other stuff it becomes very difficult to say what’s what.
My ORIGINAL reference to MRP and salary was more so to your post on The Hardball Times, which absolutely did talk about why players are valued so high. I apologize that I misinterpreted this specific article.
However, I still disagree. Based solely on the fact that these guys are AAA scrubs, they have value. They’re not AA scrubs, they’re not A scrubs. These rosters all have a need to be filled at each level. When we discount the ability to put up even replacement level numbers at the MLB level, we forget that these are still very rare skills. Once a player finds out that their participation is resulting in a profit for an owner, they are going to want a piece of it. You are right in that the discussion of how much better Alex Rodriguez is than Willie Bloomquist is a different topic, though related. Unfortunately, we could replace a 25 man roster with the following lineup:
Dan Novick
Colin Wyers
Millsy
Sean
Peter
Dave Berri
Nate Silver
Joe Paterno
Phil Birnbaum
Now, while this may be extremely silly and have the effect of a circus freak show (how far can Josh Hamilton hit the ball off of Millsy?…I could answer that…REALLY FAR), it gives us a starting point. The stats would essentially be 0. Because MLB is at this higher absolute level, people pay to see RELATIVE competition AT this level. The price of being able to provide this is not 0, and neither are the statistics. There is OF COURSE, something to measuring things at a relative level and at it’s margin…but, as you remember, my first small comment was in the context valuing Tex using his stats above replacement (on THT), when it won’t work because, as we have seen from the recent CBA, the MLBPA and its players will demand more, as they should.
On a second note, I LOVE baseball. After playing it for 20 years, I couldn’t love anything more. Because I’m not very good on the relative MLB level (that’s an understatement), I have to find something else to occupy my time. I love talking baseball, but understanding it completely is even more meaningful.

17. Brian Cartwright says:

Millsy, yes, replacement level players have value. Willie Bloomquist will get an extra base hit in some seasons. It’s that they have no MARGINAL value. They don’t add anything. They are no better than dozens of other guys who are not in the majors.

18. Millsy says:

And with that snarky comment…I’m done here. Thanks for reminding me I have a life outside trying to have an actual discussion on a forum which is dominated by a club of pompous hand-holding buddies.

19. Brian Cartwright says:

I made fun of Willie Bloomquist, whom Tom Tango describes as the definition of replacement level. I was not trying to insult you in any way.

20. Millsy says:

Thank you for the clarification. It’s obvious we have different views on how this works. If it wasn’t meant as an insult, I misinterpreted it and I apologize.
I assumed you were claiming Bloomquists only value was due to variation in his performance. However, if Bloomquist has value outside simple variation season to season(simply assuming he’s replacement level, which may be a mistake), and you agree, then the title of this article is incorrect.
The marginal value above replacement for a replacement is obviously zero. But this does not mean there is no marginal value above what really could be out there. The idea is that, because there is a team, and because that team makes money (whether it’s tied directly to winning or not) based solely on the fact that the team exists, works, and plays, it makes it problematic to value players without valuing their entire workload. There is a reason we pay less to watch minor league games, college games, high school games, and little league games. That’s all. Simply treating everything as relative within MLB forgets about who these guys really are, and why fans show up to the games.