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Talking Chop Baseball Analysis Primer: Surplus Value

MLB: Miami Marlins at Atlanta Braves Brett Davis-USA TODAY Sports

Most of this primer has been focused on production, that is, considering what a player does for his team on the field. But, modern baseball (perhaps sadly), isn’t just about production. Instead, with vast differentials in team revenues, baseball analysis has incorporated another avenue of assessment: value.

Before diving in further on this topic, it’s important to clarify exactly why value matters. First, we start with the idea that teams want to win. If they didn’t want to win, they wouldn’t care about production, which is to say that they wouldn’t care about WAR. So, let’s say we have a field of teams who want to win. It’s the offseason, and there are a host of players that are free agents. These players can be signed for any amount that both the player and team agree on, but it’s a completely free market: each player can negotiate with, and sign with, any team. For any team that wants to win, if that team had infinite resources, that team would sign literally every player (if they could). There’d be essentially no downside to it. However, teams don’t have infinite resources. Every team’s payroll is limited, even if it doesn’t always feel like that to fans of small-market teams who simply can’t compete in the free agent arena. So, instead what happens is that teams compete in the free agent market, trying to maximize their future production (that is, WAR) within their budget level. This maximization is what sets the free agent market.

Unsurprisingly, we find that the free agent market generally makes perfect sense on a WAR basis: players who are expected to produce more WAR generally get paid more money than those expected to produce less WAR. Because of this, we’ve seen the outline of a pattern emerge, where buying a “unit of WAR” on the free agent market costs a specific amount. The discussion of this pattern is wide-ranging and complicated. While it suggests that the price of WAR on the free agent market is linear, we also see a lot of indication that this isn’t quite true. After all, if the price of WAR is, say, $7 million per unit, and a six-win player hits the market, chances are he’s not going to get $42 million per year (or is he?). Similarly, under this same assumption, it’s unclear why a team would commit $7 million to a 1 WAR player who is, in essence, a bench player not worthy of getting regular starts. The way I think of dollars per WAR is that it’s a central estimate that breaks down at either end, while being pretty reasonable in the middle.

But, here’s the cool thing about this discussion: in many ways, what the actual “dollars per WAR” amount is doesn’t matter. In order to see why not, we first have to talk about why we care about dollars per WAR at all.

One of the reasons why understanding WAR prices matters is because it helps teams plan for the future. Let’s say a team thinks that its current roster has 30 WAR present on it. We know from the WAR discussion that 30 WAR plus the replacement-level baseline of a 47 to 48 win team means that the team can expect to win 77 to 78 games in the coming season. That means the team is somewhere around seven or eight games out of the 85-win threshold that we think of as what’s necessary to be a contender for a playoff spot. If the price of WAR is $5 million per WAR, then the team would need to have $35 million to $40 million in its budget available to compete. (The team could also trade future WAR to add to its current WAR amount, and lower the budget space necessary to compete, but in the end, to the extent the team wades into the free agent market at all for upgrades, dollars per WAR gives it an idea of how much those upgrades will cost.) Note that in this scenario, if many teams want upgrades, and there are fewer potential upgrades available than desired, the price of WAR will go up as teams outbid one another. Also note that if the team’s 30 WAR is the result of having players at every position, buying a 2 WAR player will give the team less than two extra WAR, but still cost $10 million, because chances are there’s some team that would indeed see a full 2 WAR upgrade from signing that player, and therefore would be willing to pay market price for him.

The other reason, though, is that using a dollar price per WAR lets you translate everything into dollars. This then helps you assign value to everything, including players not available on the free agent market. In order to do this, we first need to make the assumption that WAR is indeed available on the free agent market for some price, which given the discussion above, seems like a perfectly reasonable assumption. Under this assumption, you can always buy WAR at its price, just like how replacement-level players can always be gained for essentially nothing (but don’t help you win games at all). But, buying WAR is expensive. If you need 37.5 WAR to field an 85-win team, and the price of WAR is even $5 million per, it would cost you $187.5 million to field an 85-win team, assuming that entire team was bought on the free agent market. But, the price of WAR probably isn’t $5 million per anymore, it’s probably closer to $10 million per. Is any team fielding a payroll of $370 million or so? Of course not! That’s because free agency is not the only way (or even a major way) to build a team. Instead, teams have all sorts of players providing WAR at below-free agent market rates. If a player only earns $1 million but gives you 2 WAR, and the market price of WAR is even $5 million per WAR, that player has basically “freed up” $9 million of your budget that you can now use towards free agents.

Baseball’s weird economics are what govern this entire system. Teams control players they call up from the minors for six or seven years, depending on whether they manipulate their service time for that extra year of control. Depending on a player’s service time, he is eligible for either three or four years of arbitration; the remaining years see him earning a league-minimum salary under $1 million. Even the arbitration-eligible years represent a substantial discount over what a similar player would earn in free agency: the rules of thumb for arbitration-eligible compensation are 25 percent, 40 percent, and 60 percent of free agent market value for a similar player for players eligible for three arbitration years (that’s a discount factor of 2.4 relative to free agent prices) and 20 percent, 33 percent, 50 percent, and 70 percent of free agent market value for a similar player for players eligible for four arbitration years (that’s a discount factor of 2.3 relative to free agent prices). See here: for more.

Functionally, then, surplus value is basically just how much a given player “frees up” his team’s budget relative to a free agent that would provide similar production. The implicit assumption here is that free agent deals don’t have any surplus value -- because they’re the default, freely-available deal on the market. In other words, if the price of WAR was $5 million per, and you had a 2 WAR player making $10 million per year, if you made him and his contract vanish, you could replace him for that same $10 million per year on the free agent market the next day. What you couldn’t do on the market, though, would be to get a 2 WAR player for only $5 million per year. To do that, you’d need to trade with another team, and you’d have to give that team something. Meanwhile, there’d be no reason to trade with another team for a player already making $10 million and providing 2 WAR, because once again, you could just sign that player for the same amount yourself.

So, that’s the general idea: surplus value is the player’s production [WAR multiplied by the price of WAR] less his salary obligation. If the two are equal, the player has no surplus value; you could get the same production for the same price on the free agent market at any point. If the production exceeds salary, the player is freeing up your budget for other things relative to the free agent market, and has positive trade value as a result. If production is below salary, I’m sorry. That player is actively sucking resources from your team worse than a free agent with the same production would have. Better luck next time; you’ll need to give other teams something of value to get them to take the player off your hands.

Even though it seems like all of this suggests that the specific price of WAR matters a lot, that’s not the case. If you have two players with different surplus values, and you change the price of WAR, one player will always be more valuable than other. The degrees to which he’s more valuable might move around a bit, and changing the price of WAR may make one or both contracts underwater. But so long as the same number is used to evaluate each player, the conclusions aren’t really going to change.

Prospects and Surplus Value

Generally, if a team wants to add wins, it has two choices to acquire players from outside the organization. It can sign them on the free agent market (no surplus, but you get your wins), or it can trade prospects for them. This means it’s important to be able to value prospects in order to understand whether it makes sense to just pay dollars for a player, or to trade future wins (the prospects) for present wins (the currently-productive player). While MLB teams do all sorts of things, the trading of prospects for major league players is the dominant trading paradigm, because it allows teams to either trade future wins for current wins, or trade current wins they don’t need or can’t use for future wins that might be more helpful in a pennant chase later on.

The real detail of valuing prospects could require more words than the rest of this primer. Luckily, the last few years have seen many of these words already written, and numbers already crunched. As a result, we now have not just one, but myriad ways of valuing prospects. At its heart, all prospect valuation considers the same parameters:

  • How good the prospect is, often expressed as an “FV” score. FV stands for “future value” and reflects a scouting assessment of the potential future production of the player. 50 FV is average, and can be equated to a 2 WAR player in many respects; each five points above and below 50 is akin to half a win above or below 2 WAR.
  • Whether the prospect is a hitter or a pitcher. This matters, because the parameters discussed below vary substantially between these two groups.
  • The bust rate of similar past prospects, i.e., the likelihood the prospect never provides major league value. In this case, “similar” generally means prospects with the same FV score and pitcher/position player grouping, though it can mean some other things depending on the methodology.
  • The production for non-busted similar past prospects.
  • The salary obligations for non-busted similar past prospects.
  • (Depending on how fancy the methodology gets with it) Inflation in the cost of WAR over time, and applying the time value of money to discount future wins relative to present wins.

I recommend all of the following to learn more about this topic:

The general takeaways of all of this work include the following:

  • Position player prospects are notably more valuable than similarly-ranked pitching prospects.
  • Once you get past the “50 FV” tier, prospect values tend to nosedive. Teams tend to have tons of 45 FV, 40/45 FV, and 40 FV prospects, and these players have high bust risks and/or low ceilings. They’re not going to headline deals for good major league players. You’re going to have to give up good stuff to get good stuff in most cases.
  • Rather than being just an academic exercise to see whether you can value prospects (the answer to this is yes), valuing prospects in this manner actually lines up with trades we actually see occur. While not all trades are going to tick-and-tie to prospect values perfectly, nearly all trades are in the ballpark, and when they’re not, there are either special circumstances that can’t be captured in a straight value-for-value framework (like no-trade clauses that reduce team leverage) or the trade is widely thought to be one-sided.

One-Minute Trade Evaluation with Surplus Value

Now that you have an understanding of surplus value, let’s apply it to see how it can be used to evaluate potential trades.

Player Production

First, pick a player.

If that player is a prospect, his value is going to be somewhere around the various published estimates of that value from one of the links in the prior section. If he’s not on any list where his value is published directly, find his FV grade (or grades from multiple sources), and apply the standard valuation for that grade based on whether the player is a position player or a pitcher. If the player has multiple grades from multiple publications, or if you feel it’s not appropriate to use only a single publication’s value, average them as you see fit. Just be clear about what you’re doing and why. You’re done; prospect surplus values are already surplus values (i.e., production less salary), you don’t need to do anything else.

If the player is not a prospect, we need to think about production first. There are many ways to think about future production. One way is to use a projection system. Steamer and ZiPS projections for the current/following year are generally available on the Fangraphs player pages. You can also do something else, like just using the player’s most-recent single-season WAR value, or averaging the WARs of his last three seasons, or something else like this. Note that the player may be under team control for multiple years. If this is the case, you want to consider his production for every year he’s controlled, not just the current/following year. If a player is projected to be a 2 WAR player but is controlled for three total years, that means he could be expected to produce six total WAR over those three years.

But, watch out for aging. As noted in the aging section, you may want to lop off 0.5 WAR per season from a player in his age 31 through 35 seasons, and 0.75 WAR per season in his age 36 seasons and onward. For example, if a player is projected for 5 WAR and is controlled for eight years, and turns 30 next year, you may want to consider a WAR path like: 5.0, 4.5, 4.0, 3.5, 3.0, 2.5, 1.75, 1.0. There’s an 0.5 WAR per year decline starting at age 31, which becomes an 0.75 WAR per year decline starting at age 36.

Once you have that total WAR, you can just multiply it by the dollar per WAR parameter of your choice. Values around $9 million per year are commonly used right now, but what’s important is that you be consistent, especially if you are using published prospect surplus value estimates from a source that was already based on some specific dollar per WAR figure. Once you’ve multiplied “expected production over life of contract/team control” by “dollars per WAR,” there’s your production figure, in dollars.

Player Salary

If the player has a major league contract that pays him specific dollar amounts in specific dollar years, great. Very easy! His salary is just what’s owed to him under that contract. Don’t forget to include buyouts for team options that will likely be declined, too.

If the player does not have a set contract, but is under team control, calculating salary is a little more annoying. First, consider whether the player is, or will be, arbitration-eligible next year. You can look up player contract status using Cot’s Contracts: Specifically, select a team, and click the link for payroll obligations, which will give you a spreadsheet. This spreadsheet will give you the player’s contract status if he’s owed a set amount, a blank cell if he’s owed a league minimum amount, or something that says “A1” through “A4,” which denote arbitration-eligible years. (The first year that the player is eligible for free agency will have “FA” in the cell.) If the player is going to be “A1” next year, you can probably look up his estimated arbitration-eligible salary on MLB Trade Rumors, which uses a model made by Matt Swartz to publish really accurate arbitration-eligible salary estimates. If this is the case, then forecasting salaries is fairly easy.

  • If the player is “A1” this coming year and his control spans “A1” through “A3” only, then for future years, just scale that salary up using the 25-40-60 or 20-33-50-70 rules of thumb. For example, if a player is “A1” and the MLB Trade Rumors model estimates he’s going to earn $3 million in arbitration this coming year, then he will earn 40/25 x 3 = $4.8 million as “A2” and then 60/25 x 3 = $7.2 million as “A3,” for a total of 3+4.8+7.2 = $15 million.
  • If the player is “A2” this coming year and his remaining control spans “A2” through “A4,” and there’s no available MLB Trade Rumors estimate for his arbitration-eligible salary next year, then you can just take his past year’s salary (when he was “A1”) and scale up by the 20-33-50-70 rule of thumb as needed. So, if he made $2 million last year, then 33/20 x 2 = 3.3, 50/20 x 2 = 5, and 70/20 x 2 = 7, for a total remaining salary of $15.3 million over three years. Or, if MLB Trade Rumors did publish his salary for the coming year (say at $5 million), then you’d only scale up the remaining years, so 50/33 x 5 = 7.6 and 70/33 x 5 = 10.6, for a total of 5+7.6+10.6 = $23.2 million over three years.

If the player has any league minimum years left, those can be valued at $0.6ish million per season. Where you may need to do some extra math is if the player is still making league minimum, and isn’t hitting arbitration eligibility soon. If this is the case, to forecast his salaries during those arbitration-eligible years, combine his projections with the arbitration salary rules of thumb. So, if the player is projected to be a 2 WAR player going forward (and his arbitration-eligible years all occur before he turns 31, to avoid any aging effects), you’d do $0.6 million in salary for each of his league minimum years, then 0.25 x 2 x dollars per WAR for the first arbitration-eligible year, 0.4 x 2 x dollars per WAR for the second arbitration-eligible year, and so on. (If the player was a Super Two, that is, eligible for four years of arbitration, you’d do 0.2 x 2 x dollars per WAR, then 0.33 x 2 x dollars per WAR, and so on.)

Surplus value and matching the package

Add up the production. Add up the salaries. Subtract the latter from the former. That’s your surplus value for one player. Do the same for all players in the deal. If the two sides are pretty close, the deal is fair. If they’re not, then it’s not really a fair deal. Yes, discounting and inflation in the price of WAR may also matter, but they don’t move the needle very much, and this is supposed to be a one-minute trade evaluation exercise. Even though it may not seem like all of this only takes a minute (it took you longer than a minute to read, that’s for sure), if you practice it a few times, you’ll see it goes by very quickly.

Other considerations

The main thing to think about here is that surplus value in the trade evaluation context is useful as a benchmark, not as a supreme overlord. I think of it as something like going car-shopping. You want to know the relative price of your current car (to trade in) and the car you want, but that doesn’t mean everything you see will be exact. You might be able to haggle either your trade-in up or the price of the car you want down. Or maybe there won’t be too many cars in your area like the one you want, so your choices are limited and you end up paying a bit more. It’s a guide, not destiny.

Why isn’t it destiny? Well, it’s because all of the parameters might move around a bit. Maybe one or both of the teams involved in the deal project a given player differently for the future. Maybe one prospect is considered a 45 FV by one team, but a 50 FV by another. Maybe a team was ordered by ownership to trade one player, or trade for some player. All of these things can mess with the value that changes hands from our perspective. But just like you wouldn’t go around telling people you’re going to buy a used car that usually goes for $20,000 for $13,000 because you’re absolutely certain it’ll work out that way, it doesn’t make sense to consider hypothetical trades where the two sides are far apart in value. Sure, it might happen. But lots of weird things happen, like the trade where the Braves moved Shelby Miller for two top prospects and a player as good as Shelby Miller himself (Ender Inciarte). It doesn’t make it prudent to bank on those sorts of things happening again.

We also see a few other trends in trades that might be worth considering:

  • The trade market for defensive wizards who don’t gain as much value from hitting is potentially fraught. These players aren’t traded that often so it’s hard to tell definitively whether they are discounted on the trade market, but it’s worth thinking about. Using the methodology above, I estimate that Ender Inciarte has upwards of $70 million in surplus value (at $9 million per WAR) in the 2018-2019 offseason. Would teams value him this way? Who knows.
  • Many teams don’t want quantity-over-quality returns. You generally see deals of prospects-for-major leaguers involve a headliner prospect that constitutes about half of the prospect package’s overall value. Again, this doesn’t always happen. But if you’re trading for a player with $30 million in surplus value, it doesn’t really make sense for the deal to include 10 40/45 FV players valued around $3 million in exchange; the deal is probably going to include a prospect valued somewhere between $10 million to $20 million, and then another prospect or two to make up the difference.
  • In general, if the two sides have surplus value packages about 10 percent apart, that seems essentially close enough for the deal to be fair, given the general uncertainty in everything baseball-related. However, for hot commodities, or packages where only prospects are going one way, or other considerations, it makes sense for the package that doesn’t include the “desirable thing being acquired” to be something like 10 percent higher than the package going the other way, to account for needing to overpay to win the bidding. This is even less of a rule of thumb than the other considerations, it’s more a signpost that teams should be prepared to go a bit above fair value in some deals.

tl;dr takeaway for surplus value - surplus value is a way of considering how much benefit a player gives the team by freeing up budget to be able to buy additional wins at free-market rates. It puts everything on a dollar basis, which is also helpful for evaluating trades (both hypothetical and real).

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