It’s free agent season, which means it’s time to complain about whom your favorite team is signing. Or not signing. Or reportedly thinking about signing. Or reportedly thought about signing and whom you would have complained about if they had signed him, but now that you know that they are not signing him, you’re angry that they didn’t have the courage to do it. In the eyes of their fans, all 30 teams will do so much to damage their potential for a World Series championship in the next three months. And they’re mostly right. There will be 29 teams that will fail to win the World Series next year. Teams are really bad at this.

This winter, someone will do something big like signing Robinson Cano or Clayton Kershaw to a contract that will end when my oldest daughter is a tween and that has more money in it than the entire annual GDP of the nation of Kiribati. And someone will do something silly like giving a four-year contract to a 30-something-year-old player that will pay him as if he were assured to be a four-win player for those years, even though he’s showing sure signs of decline and hasn’t been worth four wins in three years. It’s easy to look at every signing and declare it an overpay, especially when the only guideline for a “proper” amount of payment is the handy “5 or 6 million per win” rule. If only things were that simple.

I worry that the rule of $5 million has gotten a little too ingrained in analysis of free agent contracts. It’s not a horrible shortcut, but like any shortcut, it’s bypassing consideration of a lot of other important factors. So, as we enter the heart of free agent season, let’s look at the rule of $5 million and why it seems that teams are always “overpaying” for free agents.

Reason no. 1: We’re Looking at the Problem All Wrong
We often lose sight of the fact that the point of the exercise is not to have the best ratio of dollars spent to wins generated. A team filled with players making a million each and who all put up half a win above replacement value will have a ratio of $2 million per win (What value!), and can point that fact out to their fans as they lose 110 games. Teams are looking to augment their roster in free agency. The goal might be to maintain respectability and patch a hole during a rebuild so that a hotshot prospect can have more developmental time, but usually, it’s the same thing we do every offseason, Pinky. Try to make the playoffs.

In general, analysts do seem to have some awareness of this. There’s some manner of absolution given to teams that “overpay” if they are on the bubble of playoff contention and the signing will pull them a lot closer to that goal. Making the playoffs comes with a fantastic revenue boost, and going from the 89th win to the 90th is more likely to result in a playoff appearance than going from 65 to 66.

But let’s also consider that teams with a lot of potential talent due to arrive in two years might sign a free agent to a four-year deal with an eye toward treading water in years one and two, and then having a complementary piece already in place for years three and four (at this year’s prices!) when the young talent comes to the big club and matures. This seems to have been the basic idea behind Jayson Werth’s contract with the Nationals after the 2010 season.

There’s also the case that not all two-win free agents are created equal. (Huh?) The key here is variance. Suppose that you had one steady player who is guaranteed to give you two wins—nothing more, nothing less. Another is more volatile and might give you one win or three. The reality of a baseball season is that a lot of things have to break right for you to make the playoffs. All of the 2013 playoff teams had risky moves that paid off, and guys who came out of nowhere to provide surprise value. If you have a team that is pretty much guaranteed to win 82 games, congratulations: you have no shot at making the playoffs. If, however, you have a team that might stumble to 77 wins, but has a realistic chance to win 87 if things go well, you at least have a chance at a playoff spot. Teams aren’t trying to buy marginal wins as much as they are trying to increase their chances of making the postseason. Sometimes that means using a high-variance strategy. In that case, the volatile player might have more value to a team and be worth the extra million.

Reason no. 2: Free Agents Are Not Sold in Grocery Stores
Every Sunday night, I go to the grocery store. When I get to the banana stand in the produce section, I’m faced with a couple hundred little clusters of bananas. Some are riper than others. Some have two bananas in the cluster. Some have seven. I can choose which cluster to buy based on how many bananas I think my kids will eat this week and when they will need to be ripe. And at the grocery store, I pay by the pound.

The rule of $5 million assumes that free agency operates like the bananas in a grocery store; in other words, that I’m certain to find a suitable free agent who has the correct number of wins that will ripen at the correct time, if I just poke around. But really, free agency is more like shopping for bananas after my fair city (Atlanta) gets word that a giant snowstorm (two inches) is on its way. There might be five bunches left by the time I get there. One of them has seven bananas, and I need only (and have enough money to buy) five. But the next-biggest one has only four bananas, and they’re already a little spotted. There are a couple more that have two bananas each, and both look fine. Then there’s the other bunch that has three good bananas and a fourth one that has a little crack in the peel. Which one should I choose?

I could sacrifice buying grapes this week, and shift some of that money over into bananas and aim for the bunch with seven. The problem is that there’s another guy next to me who also wants that bunch, and either we have a knife fight for it or we could do the civilized thing and bid up the price per pound. Maybe I should instead buy a smaller bunch of bananas and put some of that money into more grapes. Maybe there’s a good bag of grapes that fits my needs there, but because of the giant snowstorm and people panicking, there are people already roaming in that section of the produce aisle. I need to think quickly. Maybe I should pay market price for the bunch of four bananas and hope that it will do. It’s entirely possible that even if I did massive reconnaissance before coming and mapped out exactly what my produce choices would be, I’d still be stuck. The only way I can fill my family’s fruit needs in the store is to bid against the other guy for the bunch of seven bananas. Either way, someone’s going to end up paying more than market price is supposed to be. And if the agent for that bunch of bananas knows what he’s doing, he’ll make it snow.

In the hipster’s paradise (Weird Al, are you out there?), there’s always a bunch of exactly five locally grown, organic, fair trade, just-ripe-enough bananas being sold by a guy who is running this fruit stand as a way to get seed money to start a non-profit that will end human trafficking and who will mention you in his TED talk. That would be nice, but baseball teams live in the real world, not Brooklyn. My children are hungry for a third baseman, er, banana! The ideal option isn’t always there. (And yes, I went all food metaphor on you.)

Reason no. 3: Willie Mays Has No Value
Suppose that Willie Mays were a free agent this year. Willie will turn 83 in May of next year, so he might be a little bit past his peak years, but let’s rewind the tape to age-29 Willie and drop him on the market. To whom would the Say Hey Kid have the most value? In terms of the marginal return, it would be the team that had the weakest center fielder. While the Angels apparently have gobs of money to spend, they also already have a 10-win center fielder on the roster. (Okay, so if this were real, Mike Trout would play left.) There would be no value for them in adding Willie Mays!

But what about a team that doesn’t have a decent center fielder currently under contract, and where the farm cupboard is rather bare in the outfield. If they stick with what they have on the roster right now, they might expect to get a return below replacement level out of center field next year and in the years to come. Willie Mays is the perfect solution. (There surely are other options, but let’s forgo those for a moment.) The problem is that our rule of $5 million is denominated in wins above replacement and assumes that what we’d be replacing a replacement level player. In this case, we’d be buying the 10 wins that we believe Willie Mays is capable of, but also the fact that we don’t have to go into next season (and future seasons?) with a below replacement level player in center. Willie is worth a little extra there. This is why elite starting pitching often fetches such high prices. The marginal guy who will be dumped is not the team’s current ace, but the fifth starter, who’s usually a dud.

Reason no. 4: Rise and Run, But No Intercept or Exponents?
The rule of $5 million is basically set up as an equation that says salary = $5M * expected wins. You may recognize this from high school algebra as the general equation of a line (remember y = mx + b). It’s just that we’ve artificially set “b”, which is the intercept—or in this case, what we should pay a replacement level player—to zero. J.C. Bradbury has previously warned against this, and his piece on the subject is a must-read for anyone who analyzes free agent signings.

In addition to payroll, there’s another finite resource that teams must conserve in the free agent signing process: roster spots. A six-win player has more value than two three-win players because he consumes one less roster spot. Maybe those two roster spots weren’t doing much anyway, in which case it’s a wash, but the more quantity you sign, the more chances you have to displace someone who was actually providing value. Even if those two roster spots are completely empty right now, signing a six-win player for one of those spots means you have another chance to make a value-add move this off-season. There’s exponential value in being really good.

There’s a counter-argument to this. The six-win player is going to cost a lot, and that may use up the other limited resource, cash. The other move might have to be “promote Smith from Triple-A because he’s making the minimum.” As we saw last week, about a third of those minimum-wage guys provide negative value to a team. Plus, by signing the six-win player, you are concentrating a lot of injury risk into one human body. You could look at “sign two lesser guys” as a risk-hedging strategy. That’s reasonable. Then again, you might prefer the riskier strategy and hope that your marquee signing stays healthy and the rookie puts up two unexpected wins for little cash. Both could happen. You plays your games and you takes your chances.

There’s a general sense that this sort of value is actually priced into the market. High-end free agents often get salaries that generally approximate the $5 million per win expectation, but for more years than we can reasonably expect them to sustain that level of performance. The common line is that a team will get good value now and pay for it on the back end of the contract. In a rational market, high-end free agents should be able to ask for more than $5 million per win because of this extra value they provide in saving a roster space with which the team can work. I’d argue that teams recognize this value (and the bid-up premium), but generally choose to amortize the cost into extra years.

Reason no. 5: Hedging Your Bets
It’s worth noting that the six-year, $100 million contract has both risks and rewards for both sides. On the team’s side, they are betting that a similar, cheaper player won’t come along in the next six years. And while teams are very aware of the aging curve (how could they not be?) they are also aware that salaries inflate. By signing this free agent now, they lock in the price for that sixth year. It might still be an overpay at the end if he’s lost most of his mojo, but some of that loss will be inflated away. Maybe he’s the magic guy who sustains his performance for all six years of that contract, even though the last one will be at age 37. There’s risk and there’s potential reward.

From the player’s side, signing a long-term deal has its own risks. He is giving up on the chance to cash in on those potentially inflated salaries down the road. If he signs a three-year deal, he might have another chance down the road at another big payday. He might also be rehabbing from Tommy John surgery at that point.

But then there are other benefits to long-term deals. One is that a marquee signing isn’t just a player on the field, but might make a nice instrument to use in branding the team to the community. Maybe there’s a small uptick in sales of $25 t-shirts that cost $2 to make. From the player’s point of view, signing long term means stability. Let’s not forget that these guys are humans, some of them with families and young kids. It’s awful to have to move young children from city to city all the time. (Take it from a dad of three!) What’s an extra $5 million when you already have 100, if it means uprooting the kids?

Everyone takes on risk in free agent deals, and risk doesn’t feel nice. It would be wonderful if your team could sign all of its players to one-year deals for $1 million each and they would all be guaranteed to put up five-win seasons and then politely re-up for another million next year. It’s easy to let that risk make you snarky, and yes, this contract might backfire spectacularly. But before you start snarking, consider that some amount of risk is inevitable.

Reason no. 6: Shane Victorino’s Walk-Up Music
Don’t worry, about a thing.

No. Every little thing won’t always be alright, Mr. Marley. But it’s tempting to think that it will. In the previous six reasons for “overpaying” free agents, I’ve made the case that our models are too simplistic and that teams need to be given more credit. There is one case where I think that teams most certainly could fall prey to wearing rose-colored glasses. It’s called optimism bias. It’s the belief that things will be okay, mostly because it would be nice if things really did turn out okay. Yes, we should all plan for the worst, but few actually do.

Again, the biggest critique of free agent contracts is usually “You’re gonna hate that contract on the other side” with projections of players who are barely replacement level at the end, and still making $20 million. There is reason to believe, at least with hitters, that good hitters (the ones who would be getting $20 million dollar salaries to begin with) actually have a longer peak and a slower decline than lesser hitters, but even then, there probably will be a mismatch. Of course, there are also examples of players who maintained much of their glory into their late 30s and even 40s. It’s not a law of physics that players decline, and humans are very good at convincing themselves that this time will be different.

The Tyranny of the Average
I understand why the $5 million rule exists. It’s an average of what teams seem to be paying for free agent talent, and ideally you want your favorite team to be doing better than average. Baseball is, after all, a game of relative advantages. The problem is that teams sign only a couple of free agents each year, and within very specific contexts. Using a one-size-fits-all measure is easy, but reality is just so much more complex. If we’re going to give GMs a fair shake, we need to at least take some of those issues into account.

I’d suggest that a new framework (and maybe with some enterprising research, a new formula) be used that looks at what a more fair price for free agent wins might be. It should include

  • A reasonable projection of the player’s future contributions, as well as for the player he would ostensibly replace. In the near-term, this can be derived from looking at who’s already on the roster or in the minors. For longer-term evaluation, some idea of how often new cost-controlled value is generated and what salaries might do in a few years.
  • Where the team is on the win curve (and perhaps what other moves they might make in concert with this one) and where they are in their building/winning cycle.
  • An understanding of how this signing affects the team’s chances of making the playoffs, rather than how many marginal wins it creates. Those are different things.
  • What the other alternatives are to signing this guy. It’s hard to do a full counter-factual, but it would be nice if we tried.
  • An understanding that this is all done in real-time, not with the benefit of the hindsight that makes us all geniuses.

Mostly, we need a rejection of the yes/no nature of the rule of $5 million. Too often, things get boiled down to “It’s more than $5 million per win, therefore it’s a bad deal.” There is risk, good and bad, in every single free agent deal for both the team and the player. The goal is to take the best risks that you have available and to balance those risks appropriately. Yes, there are really bad free agent signings, but sometimes good things happen to bad GMs and things work out unexpectedly. We have to allow for that. Instead I’d ask for a system that leaves a little bit of room for those shades of gray and for the fact that not all free agent signings are the same.

Thank you for reading

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Another thing to mention is that $5 million isn't the average of what teams have been paying free agents per win. I think the average went over $7 million a year or two ago.

Having said that, it's useful to have a benchmark, but it's good to remember that each team has its own benchmark...and that it probably varies by position and year.
It depends on how you measure it. In 2013, the number paid per win was roughly 5.2M for hitters and 7.4M for pitchers, but that includes salaries from contracts signed in 2012, 2011, 2010...

If we're looking only at new contracts, it seems that number really is creeping closer to 7M.
Intercepts: For a $/WAR rate, shouldn't the intercept be the league minimum salary, as that's what you'd have to play a 0 WAR player?

On reason 3: Isn't the point of replacement level that you can reliably get players of that level for minimum cost? If aces (or Willy Mays)can have value greater than their WAR because they're replacing a sub-replacement level player, that sounds like an argument that replacement level is set too high.

Also, if Willy Mays is replacing, say, a 4 WAR center fielder then, in addition to the 6 WAR improvement, you also have a 4 WAR trade chip. Maybe you won't get full value for him, but you can't just consider that 4 WAR to be lost.

On volatility: Yes, this came up recently in a discussion of a suggested Tigers/Mariners trade. Overall the trade looked reasonably fair to me except that the high-volatility players were going to the Tigers and the low-volatility ones to the Mariners, which struck me as exactly the reverse of what should happen. Fringy teams need volatility, clear favourites need certainty.
It's more than just setting the intercept to the league minimum (500k). It's that when you suppress the intercept, it messes with how the line is best fit to the data. (Click on the JC Bradbury link for more info.)
Right, it changes the slope. I actually tried this on someone's $/WAR study and it dropped the result from $6m/WAR to about $5.6m.
Also, re: the 4 WAR CF becoming a trade chip, you can flip him for something else, but with reduced leverage. The other team knows that he's surplus to parts, so why should they pay full price?
True, though if you have more than one team interested you could in theory get them to bid against each other up to the full value (or at least the second-highest perceived value plus a bit). Though that would depend on persuading Team A that you're telling the truth when you tell them you've got a better offer from Team B.
That's the point of replacement level. It's also a fundamental flaw of the approach and why its important to look at WAR/WARP as illustrative but not precise measures.
I would add two other aspects. One is the belief of many teams that they have to do 'something' to generate publicity and therefore sell tickets. So say $5M for a win and $2M for the all the news stories it spawns. Second, is simple irrationality. Owners sometimes ignore the value equation and do things for their own ego, eg. Willie Mays is my new BFF! or I have a new toy and I want to play with it!
Loved this article. A lot to think about.
Great article; it should be must reading for fantasy owners.
What should teams pay per win? Is $5M/win too high? Is $7M/win still worth it?

Historically, what is the return on investment of going from 80 wins to 85, or 85 to 90? Obviously, with more success comes playoff revenues, increased attendance, more merchandise, etc.

That might also be a case for the non-linear value of a top player-- adding one 6-win guy will move more seats and merchandise than adding three 2-win guys that casual fans have never heard of.
Thanks--just the latest in a series of terrific articles over the last few months. You are becoming my #1 reason to read BP.
I disagree about the bananas - often you don't even have to go to the store to get them, they're already right there in your kitchen. Val Pascucci, Craig Wilson, Tyler Moore, etc... there are hundreds of examples over the years of guys who could have produced as well as or better than the overpaid free agents their teams acquired to play their positions.

It seems like teams would rather label their own low-cost internal solution as a "4A guy" or a "bench guy," never giving him a shot at seeing what he can do with 500 AB, and view some overpriced free agent as a "proven guy" because he had one 3 WAR season 5 years ago. Pay the "proven guy" $10MM and watch him produce a 0.9 WAR, or some other level far less than your "bench guy" could have provided with consistent AB's.

I had to laugh out loud: "There will be 29 teams that will fail to win the World Series next year. Teams are really bad at this."
Grab the 7-bunch of bananas, tear off two, and head to checkout.

... What? Atlanta doesn't do that to free agents?
The overall point is well-taken, but one quibble: Swartz's whole point when he calculated the $5M/WAR number was that the nonlinear effect doesn't really exist. Even the best teams have a handful of players, even starters (esp. when you consider pitching) that are worth ~0 WAR. As they will tend to spend their resources addressing those, everyone ends up paying at a basically linear rate.
Re not assuming the intercept is zero or the MLB minimum ... I just found the regression analysis I did for the 2006-07 free agent starting pitchers. The R^2 is .96. The equation for projected AAV is 5.5 + 2.6 * VORP wins (last 2 years weighted 70/30) +/- 0.4 years of age below / above 32 - 0.7 if re-signing. That's right, the intercept was $5.5M (95% confidence interval $3.5M - $7.5M). Talk about paying for "proven talent."

I do think I saw this come down in a subsequent season, but I've never forgotten that.
Russell: Great job. Exctremely illuminating on the thought process and the factors that need to go into it. Thank you.
This is the type of outstanding stuff that makes BP worth paying for. Here is one more thought, completely anecdotal I admit. I thought of the 2004 Tigers, who followed their historically bad 2003 by spending a bit of money on players like Ivan Rodriguez, Rondell White and (shudder) Jason Johnson. I remember some criticism along the lines of "Why pay for anyone when you're terrible." It didn't work out that great, but I remember the narrative at the time being about sending a message that they wanted to win, turning around a losing culture, etc. They at least managed to win 72 games and you have to assume that being in the neighbourhood of respectability somewhat helped them attract talent in the ensuing seasons, get fans believing in the team again, etc. So there has to be value in going from 43 to 72, even if it's difficult to measure.