Yesterday, I posed a thought experiment that had recently been posed to me: if Mike Trout were to become a free agent but declare that he would only sign a one year contract, how much would you offer him for the 2014 season alone? 2,800 people submitted answers — well, a little north of 2,800 now, but I had to dump the data into Excel at some point — and the results are pretty interesting. Let’s get right to them.

As you can see, the most common answer was $40 million, but the distribution around that number skews to the left a bit, so the actual average of all the entries was $38.8 million and the median was $39 million. There are also notable spikes at every interval of $5 million, which just goes to show we have all been conditioned to think in terms of zeros and fives, and while not materially relevant to the study, I find that kind of fascinating. And, while the data isn’t normally distributed, the standard deviation was $7.6 million, for those who are into standard deviations on non-normal distributions of data.

I think the easiest way to look at the data is this: 70% of the respondents chose a number between $25M and $40M, with only 30% choosing a number between $40M and $60M. Essentially, the promise of having the game’s very best player with no long term risk was only worth about a $14 million premium over the established annual salary that is paid to most star free agents on long term deals right now. Not only did the crowd not price in a higher rate of dollars per win for a superstar, they actually deflated it.

This is actually pretty consistent with how MLB teams have operated as well, and shows that perhaps there is something of a mental price ceiling that drives us back towards established norms in per year salary even if the object we are bidding on is vastly more valuable than the ones that established the market in the first place. With all due respect to the 154 people who entered $25 million in the poll, I don’t actually see a particularly credible argument for values that low.

If we project Trout’s overall value for 2014 to about +8 WAR — well below what he’s done the past two years, but we have to account for the risk of injury — then a $25 million payout would be paying approximately $3 million per win. If you can make a rational argument in the comments section about why you think the best player in the game should go for about 60% of last year’s market rate when he would also come with no long term risk, I’d love to see it. I honestly can’t think of one, beyond the idea that all baseball players are overpaid and you’d rather give the money to schoolteachers and firemen. The idea that you could do better by paying $18 million per year to Jacoby Ellsbury — on a long term deal that comes with lots of risk in the future — and then make up the gap with $7 million left over doesn’t really pass the smell test.

Even if you decided to just cut the money in half and go for two $12 million per year players, last year that would have bought you Torii Hunter and Adam LaRoche, or Shane Victorino and Michael Bourn, or Nick Swisher and Angel Pagan. Would anyone really trade Trout for one of those pairs? I just don’t see a realistic argument that you could spend $25 or even $30 million in 2014 salary and come away with an expectation of +8 WAR unless you seriously backloaded multiple contracts and borrowed heavily from your future in order to subsidize the 2014 payroll.

Really, I think anything shy of $35 million or so is probably too conservative for an +8 WAR player, but 27% of the respondents said they would top out at between $25-$34 million. I can understand an argument that the market price for free agents is inflated because of the risks of signing aging players with uncertain health, but I don’t know that I see a great case for why a 22-year-old superstar on a one year deal is less valuable than what the market has been paying mid-rotation starters and solid role players on multi-year contracts.

For me, the bidding would have to start at $40 million, and I’d probably be comfortable going up a bit from there. The injury risk is a real concern, but adding Trout to an 81-81 team would make his wins about as valuable as they could possibly be, given the team’s spot on the win curve and the potential revenues that come from a postseason berth. The marginal value of wins from 87-93 are enormous, and adding Trout would create an opportunity to push the team right into the sweet spot where each incremental addition would bring back the largest possible bang for the buck.

Additionally, I don’t think we can undersell the value of the one year commitment. While a team would probably prefer to have a player like Trout under contract for more than one season, the flexibility to walk away in case of an injury or unforeseen decline is essentially baseball’s version of insurance. We’re all willing to trade a little bit of money now to insure against huge losses in the future — see car insurance, homeowner’s insurance, health care premiums, etc… — and a one year contract would simply allow a team to eliminate the chance of sustaining huge future losses, and should come with a premium that prices in that risk avoidance.

Even if you only value long term risk avoidance at a few million, there has to be some transference of cash to Trout to account for the risk he’s carrying and the team is not. So, I’d argue that if there was to be a non-linear aspect of $/WAR pricing at some point, it would come on one year deals, which should require a larger price to performance ratio to offset the lack of risk being carried by the big league team beyond the single season.

That’s why I think I’d end up around $48 million before I bowed out and let him go elsewhere. Yeah, at $6 million per WAR, I wouldn’t be getting much of a bargain relative to the market rate, but turning those market dollars into the best player in baseball on a one year deal would be worth a premium over what I could get by spreading those dollars around on multi-year contracts. I believe in the value of depth, and I don’t really buy into stars-and-scrubs as an effective model for most teams, but given the parameters laid out — already a solid team in place, $60 million in payroll space, no future risk — a Trout-and-sidekicks roster would look pretty darn good.

Assuming I also spent the remaining $12 million effectively, I’d head into the 2014 season with a roughly 90-92 win team, but wouldn’t have sacrificed any of the farm system or future financial flexibility in order to make a playoff run. If you could spend that $60 million more effectively, I’d love to hear how. This will be a fun thread to look back at next spring, after all the free agents have signed and we know what players generally cost, so feel free to lay out your plans on how you’d spend the $60 million. I’d be especially interested to see how those who think Trout isn’t worth more than $35 million for one year would reallocate those funds and come up with a better roster than what they could get by giving him a big slice of the available pie.

To everyone, though, thanks for participating in this thought experiment with me. It was a fun exercise, and I enjoyed going through the results. And the next time that someone tells me that we’re crazy for continuing to model $/WAR on a linear scale, I’ll simply point them to this post. Even a perfectly linear $/WAR model is too aggressive for most of our readers, and the risk of total loss seems to be a much larger driving factor in determining salary than the potential of maximizing total production.