How Do Baseball Teams Discount the Future?

This is Matt Swartz’ fourth piece as part of his July residency at FanGraphs. A former contributor to FanGraphs and the Hardball Times — and current contributor to MLB Trade Rumors — Swartz also works as consultant to a Major League team. You can find him on Twitter here. Read the work of all our residents here.

The most distinct feature of my approach to calculating the cost per WAR on the free-agent market is my inclusion of the draft-pick-based costs to signing free agents, in addition the more obvious monetary costs. This requires a greater collection of assumptions than a simple focus on the dollars spent on free agency, but provides a more robust estimate of what teams give up when they dip into the free-agent market. It also requires a logical economic framework, including opportunity costs, so it also requires estimating the foregone costs of draft picks that a club could have received had they not re-signed their own players.

The gap between my actual estimates of the cost per WAR and the same calculation absent draft-pick compensation is not trivial. While it normally is only around 7%, it reached as high as 20% in 2015. Of course, with the new CBA lowering draft-pick compensation, this difference is likely to drop, making this part of the analysis somewhat less important. However, it remains essential to consider changes in draft-pick compensation to understand changes in cost per WAR over time. What may appear, in some years, like a collective decision by clubs to spend more aggressively in the free-agent market is frequently just a product of lower opportunity cost of foregone draft picks, leading teams to pump more dollars into free-agent contracts.

The biggest challenge when utilizing this framework is determining the appropriate discount rate to use. This isn’t easy to do and can easily vary from team to team and over time, as well. This article won’t pin down a perfect number; it’s almost certain that a better estimate of the discount rate requires a more detailed analysis of trades and other decisions that teams make when considering how to value player performance at different points in the future. It’s also challenging to use this approach to determine if the discount rate that teams use has changed, because it appears that the method of estimating said rate is noisy enough that it varies over time within a very large range. However, it’s worth understanding the approach.

In this article, I attempt to present that approach. Before I begin, one note: some of what follows is rather technical. I feel much of it is necessary, though, to establish the entirety of my methodology before moving on, in later posts, to actual illustrative cases.

The simpler part of using this analysis is looking at draft-pick bonus money saved. While this pales in comparison to lost WAR values from missing out on draft picks, a full picture does require netting out how much a team saves by not paying bonuses on those draft picks. I’ve performed a slightly more sophisticated nonlinear approach to estimate bonuses for this series than in my previous work, basically assuming that bonuses paid to draftees have the same exponential structure (relative to pick number) as the WAR they produce varies by pick number. I’ve also found better estimates of the specific slot values for draftees by pick, leading to a better estimate.

Of course, the larger issue is analyzing the picks themselves. While the average pick surrendered has been around roughly the 30th overall, this has varied significantly and has been higher (at times) in the past. It also will certainly be lower in the future due to the new CBA rules. To estimate the value of picks, I continue to use the Draft Pick WAR Calculator developed by Sky Andrecheck way back in 2009. While the precise outputs have possibly changed over time, they probably haven’t changed much, and Andrecheck’s model is certainly the best publicly available one.

In addition to this estimate of the WAR produced by players according to their draft pick, I’ve also found (in my own research) that prospects tend to debut roughly three years after being drafted. Therefore, a player’s WAR tends to accrue to the team who drafted him from three to nine years after said player is drafted, after which the player is a free agent. That’s roughly equivalent in value to all the WAR accruing exactly six years after the player is drafted, so that’s what I use in my estimate. I also had to net out the actual salaries through arbitration that successful draft picks will eventually receive, knocking down the net value of the WAR created by about 20%.

I decided to continue using a 10% discount rate (meaning that teams currently value the ability to obtain future WAR 10% less each year into the future). This is still my best guess about how teams are valuing draft picks. This means the team values the WAR 56% less than they would if it all came right away. And since they have to pay roughly 20% of market value due to arbitration in the latter years, they value the WAR 20% less than that.

In the three tables below, I’ve split the free-agent market data I have available into three time periods: 2006-09, 2010-13, and 2014-16. I’ve looked at all players who earned salaries at least $2 million in excess of the league minimum and compared the cost per WAR for those free agents with and without draft-pick compensation attached.

So, for 2006 through 2009, there were 398 player-seasons for free agents with no draft-pick compensation attached and a salary of $2 million greater than league minimum. These players earned $6.11 million per WAR. Depending on whether I used 5%, 10%, or 15%, the 388 player seasons with draft-pick compensation attached earned anywhere from $5.43 to $5.90 million per WAR. What this means is that, even assuming a very high valuation of the future (and the associated low discount rate of 5%), it appears that we still get a better bargain on free agents with draft-pick compensation attached. Using anything less than 5% seems unreasonably small.

This is especially true, considering the fact that, when we look at 2010 through 2013, the players with draft-pick compensation seem very costly. In terms of discount value, this means that even using a very forgiving 15% discount per year on lost draft pick’s production, the cost is too high.

Does that mean that we think teams were extremely patient in 2006-09 and then impatient for 2010-13? This seems unlikely, especially because they seem very patient again from 2014-16. Note that even the 5% discount-rate column below suggests that players with draft-pick compensation attached cost less than those without.

Obviously, the market is probably not this volatile and most of what we find here is noise. It certainly is possible that teams have gotten more patient since I did this analysis, but I would guess this is not true, given that they seemed to get less patient in 2010 to 2013 than in 2006 to 2009 using the same methods. I decided to keep using a 10% discount rate in these articles, which aligns pretty well with the appropriate average value across these time periods.

It’s important to remember that a 10% discount rate doesn’t quite mean that teams are irrationally impatient. There’s a good reason why teams would value current wins over future wins. Every year teams become significantly more valuable according to both public estimates of values as well as actual team sales. The rate of return for teams is extremely high, and winning sooner can probably capitalize on much of this. I suspect that the value of winning a World Series sooner is much better for a club because they’re able to sell off season tickets sooner and then those sales are persistent going forward. I would be skeptical that “smart” teams discount any more patiently than “dumb” teams, but they probably do estimate the future impact of their decisions more accurately.

With the completion of this article, I now feel comfortable that we have the right framework to review some of the market inefficiencies that I found in earlier research. The market does seem to behave in roughly the same way in aggregate, with teams discounting the future and the cost per WAR remaining linear across all average annual values (as we found in the last piece). That means that we can consider whether teams are getting smarter over time and, if so, what that means for the free-agent market. The subsequent articles in this series will review exactly that.