By Eno Sarris

The court of public opinion is currently debating: Was Jon Singleton's contract too team-friendly? $10 million for five years of a young player seems like a steal these days, and that's why you have people like Bud Norris and Mark Mulder chiding the young man for his payday. 

But the economics of baseball are not so simple, as anyone who watched the first day of the amateur draft -- with its rules about bonus pools and slot values -- knows. Arbitration suppresses young player's salaries, for one. And then you have to deal with the fact that though Jon Singleton looks like he'll succeed -- he's got the bat flip down at least -- we don't know that he will. There's a non-zero chance that he busts. And if he busts, that's $10 million down the drain. 

That's still not a ton of money for a major league team, at least not spread over five years, and that's why the team was interested in doing this. If he works out, they get him on three options that'll likely be under market value by that time. That's another reason they like it. 

But it does make sense to look at the math. How many Jon Singletons do you have to sign, and how many have to succeed, in order to make the Jon Singleton contract a good idea? 

To answer that question is fairly complicated, but much of the heavy lifting has been done for us. Here are the concerns involved with evaluating the deal: 

1) How likely is Jon Singleton to succeed?
2) What is the most likely outcome for Jon Singleton on the field?
3) How much would Jon Singleton's output fetch on the open market?
4) How much will that cost per production change over the next five years? 

Once we have that, we can put together a probability matrix that outputs the the median surplus. That will help us understand how good of a deal this was for the team -- and give us an idea of how good these deals are, in general. And we won't have to do any of the math ourselves. I promise.

As fresh-faced and homer-happy as Jon Singleton is right now, it's hard to believe that he has a bust rate associated with him. But he ended last season as the 82nd-best prospect by Baseball America. And position player prospects ranked in the 70-80 bust about 70% of the time.

Perhaps that's unfair. The big first baseman was once ranked as highly as 27th on that same list, and he spent the beginning of the year mashing in Triple-A. He cut his strikeout rate some, too, and that's the biggest negative on his record. If we could rehabilitate his prospect status -- if the Baseball America ranking came out today -- he might be as high as the top 20. Then he'd carry a 40% bust rate. If you add in his plate discipline, as a 23-year-old with a high walk and strikeout rate in Triple-A, it looks like his bust rate should be around 60%.

Listen to Matt Eddy from Baseball America, one of the list-makers, and maybe it makes sense to settle in with a 40% bust rate: "Speaking as a fan of Singleton's ability and profile, I had only modest concern about his outlook after a poor year at Triple-A in 2013. The man has 70-grade raw power, a sweet lefty swing and enough feel to hit to make it work as a big league regular, probably of the first-division variety." 

Projection systems take minor league numbers, put them through the wringer, and produce a line based on what other players in similar statistical situations have produced. Dan Szymborski's ZiPs projections are among the best. He provided a five-year projection for Singelton that makes the first baseman look like he'll be a league-average producer:

2014 0.237 0.324 0.434 0.5
2015 0.252 0.329 0.479 1.2
2016 0.249 0.330 0.473 1.7
2017 0.247 0.331 0.476 1.8
2018 0.247 0.334 0.483 2.0
2019 0.247 0.337 0.490 2.1


That's a high-K, high-walk guy with 20+ homers a year and possible platoon issues. That lines up with our scouting report, and tells the story of the bust rate too: if he's purely platoon and can't rein in the strikeouts, he might find playing time scarce. If he does both, he'll outperform the projections.

But at least we have numbers that provide us the most likely outcome now. And an idea of how likely that outcome is. So how much is it worth? 

There's some back and forth about how much a free agent win above replacement is worth. Some prefer to use projections -- after all, when a player is signed, the team doesn't know what they will get, they only know what the player is projected to produce. Some prefer to use retroactive results to see what the market paid. One approach says that it's about six million per win on the market, the other says seven. Let's use $6.5 million for our calculations here. 

It's not as simple as adding up the WAR in the projections and subtracting the contract. In that scenario, the Astros make out like bandits as they get more than seven wins for just over ten million dollars by 2018 -- and then have three options that could help them lock down a league-average player for what would surely be a bargain of $20 million over three years. If you count those years and continue out his league-average projection, they'd pay around $30 million for 13 wins. Still a great deal. 

But we have the risk in Singleton's production. And we have inflation in the cost of a win. So Sky Kalkman made a calculator that you can use if you want to change the numbers to fit what you think is most likely. In this calculator, you can see different scenarios for Singleton's outcomes, all the way from a .5 WAR of a bust up to an All-Star first baseman. The genius of this calculator is that it includes the different team actions for each Singleton outcome -- they only pay $10 million for the busted Singleton, but they go to $30 million for the best Singleton. 

Since "bust" in the study above was defined as less than 1.5 WAR per year, we have a bust rate of 35% as the default in this calculator (scenarios A and B added together). Change that to 40%, add in a $6.5 million price per win, with 7.5% inflation if you want to follow along with the analysis here. Subtract the cost of the contract (less in the bust scenarios, where the options won't be used), and you get surplus values for each trajectory scenario. Give each scenario a probability, and you get a most probable outcome. 

In other words, given the state of the market currently, and the particular skill set and talent level of Jon Singleton, the median outcome is that the Astros get a $10 million surplus on this deal. 

Of course, much of that is due to the arbitration system, but it's an interesting number. It's the cost of the contract itself. 

In other words, this is a good idea for the Astros. If you sign two Jon Singletons, the one that makes it pays for the one that busts. At least. If the one that makes it becomes an All-Star, he gives you over $30 million in surplus, and you can afford two other busts. This is why the Rays have been doing this from Wade Davis to James Shields to Evan Longoria. 

You'll see more of these deals, even if they produce some stinkers. The ones that make it just provide their teams enough value to shrug off the busts. 

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Eno Sarris writes about baseball at FanGraphs most of the time. He also started BeerGraphs for the beer nerds out there. He doesn't always play daily fantasy, but when he does, he plays it at