Last week I looked at the 2014 free agent class and how some of the big contracts of the offseason stacked up against our idea of fair market value. Afterwards, I tried to use this model to predict contracts for Ubaldo Jimenez and Ervin Santana, but came across the problem of factoring in the draft pick compensation, which I left out of my initial article simply because of its complexity. Draft pick value is highly variable, and it gets more difficult to assign costs when a team surrenders multiple draft picks. Regardless, I wanted to take a closer look because of the impact it will have on the top remaining free agents.

Let’s assume that each team places a dollar value on their first unprotected draft pick ($X). In a vacuum, if a team evaluates a player’s performance as being worth a certain amount of money ($Y) over Z number of years without any draft pick compensation, then they should only be willing to pay $(X-Y) if they will be forced to surrender a draft pick. For example, if the Orioles think that Ubaldo Jimenez would be worth $60M over 4 years, but value their first round pick at $10M, then they should only be willing to pay him $50M for those same four years. Of course this isn’t really fair to the player, but those are the rules.

So, how much do teams value their draft picks at? There’s no way to know for sure, but some research has already been done on the matter. Andrew Ball at Beyond the Box Score explored this question last summer, assigning a dollar value to certain tiers of draft picks. For our purposes, the important ones are the 8-15 draft picks (worth an average of $15.2M of net value) and 16-30 (worth $7.17M). This sounds like it’s in the right ballpark, but seemed a little bit low to me. Sky Andrecheck calculated average WAR by draft pick back in 2009, and found that the 10th overall pick was worth an average of 6.2 WAR, while the 30th pick was worth 3.6 WAR, numbers slightly higher than the more recent study. We also have to account for the fact that a team will pay around 30-35% of a player’s market value while under team control, and that they have to pay an average of $2M to sign a player drafted in the mid-to-late first round.

Taking all of this into account, I’d estimate that the net value of an unprotected first round draft pick can range anywhere from $10-25 Million dollars. This may sound a little bit high, but with the cost of a win at $6-7M, even a player who produces only 0.5WAR per season and costs a total of $10M for those six years of team control can provide $10M of savings. Since the teams signing high-priced free agents are usually pretty good and therefore have a lower draft pick, we’re probably looking at $10-15M in most cases. (Early second round picks might be closer to $8M.)

While this is great in theory, how have the attached draft picks affected the signings so far this offseason? In the table below, I included a more standard model — $6.5M per win with 5% inflation and standard aging (from Jeff Zimmerman’s contract calculator) — along with a modified version of my previous model. I didn’t want to mess with the aging curves so I used the same as Zimmerman (-.5 WAR/year until age-32 season, -.7 WAR/year after), I bumped inflation up to 6%, and I didn’t want to push a win past $7M so instead I gave a slight boost to the players’ WAR projections (just 0.2 WAR). I think it’s fair to assume that the team with the highest bid also expects the player to perform slightly better than projected.

The first two columns show the player and their total salary (assuming no options are vested or picked up by the team). The next three columns represent the “Standard” projection, followed by my “Modified” projection. The top six players were extended qualifying offers, so the signing team had to surrender a draft pick. The bottom eight players had no such compensation attached.

Player Salary Standard: Wins/Salary Standard: Projected WAR Standard: Net Wins Modified: Wins/Salary Modified: Projected WAR Modified: Net Wins Robinson Cano $240 29.94 24.60 -5.34 26.75 26.35 -0.40 Jacoby Ellsbury $153 20.34 15.15 -5.19 18.38 16.55 -1.83 Shin-Soo Choo $130 17.13 11.50 -5.63 15.45 12.70 -2.75 Brian McCann $85 11.89 11.65 -0.24 10.84 12.65 1.81 Curtis Granderson $60 8.57 4.60 -3.97 7.85 5.40 -2.45 Carlos Beltran $45 6.60 3.30 -3.30 6.07 3.90 -2.17 Draft Pick: Total $713 94.46 70.80 -23.66 85.34 77.55 -7.79 Jhonny Peralta $53 7.66 6.80 -0.86 7.02 7.60 0.58 Matt Garza $50 7.16 8.00 0.84 6.56 8.80 2.24 Ricky Nolasco $49 7.01 5.00 -2.01 6.42 5.80 -0.62 Omar Infante $32 4.92 3.60 -1.32 4.15 4.20 0.05 Scott Feldman $30 4.80 4.60 -0.20 4.08 5.20 1.12 Carlos Ruiz $26 4.13 6.30 2.17 3.50 6.90 3.40 James Loney $21 3.32 1.80 -1.52 2.82 2.40 -0.42 Jarrod Saltalamacchia $21 3.32 3.75 0.43 2.82 4.35 1.53 No Draft Pick: Total $282 42.31 39.85 -2.46 37.37 45.25 7.88

Regardless of which model you use, the conclusion is the same: so far this offseason, players who have cost the signing teams a draft pick have actually made more than the models predict. Much more. On average, these six players have been overpaid by about $9 million, while players with no draft pick compensation attached have actually been underpaid by an average of $7 million. This is the complete opposite of what we would expect if teams are acting rationally when it comes to the cost of their draft picks. When forced to pay what is essentially a $10M fee, these teams not only didn’t penalize the player, but actually paid them more. This could mean one of a few things:

Teams are willing to pay a premium for “elite” talent. The six players with free agent compensation attached include the only four free agents projected to be worth at least 3 WAR in 2014, along with the two next-best available outfielders. While Dave Cameron has long espoused the idea that the cost of a win is linear and there is no “bonus” for elite players, the fact that these six players haven’t been penalized for the attached draft pick tells us that teams may be willing to pay more to land the big guns. This could have to do with elite players (and their agents) being unwilling to take a discount because of the attached draft pick and there being at least one team who will cave and give the big contract, essentially ignoring the additional cost. This brings us to the second possibility:

Teams are not acting rationally with their draft picks. No prospect is a sure thing, so it could be easy for a team to talk itself into giving up a hypothetical player who may never make the majors in order to get a stud on their roster for the upcoming season. There are a lot of other factors here, notably the fact that signing team is usually at a high-leverage spot in the win curve and doesn’t know where they will be when the draftee they are giving up would be ready to contribute. Texas, for example, has a few players locked up long term, but also has some key pieces (Darvish and Beltre) who could be gone in a few years. Positional needs also certainly play a role here, but even when a team is willing to spend big money to improve in the short term, it’s tough to argue that they couldn’t have allocated their money better by upgrading at several other positions for the same cost (as Dave Cameron argued earlier this week). The Rangers, for example, could have kept David Murphy (2 years, $12M), signed Chris Young (1/$7M) for outfield depth, improved behind the plate with Jarrod Saltalamacchia (3/$21M), and bolstered their rotation with Matt Garza (4/$50M) instead of signing Choo, saving $40M and a first-round draft pick. The last possibility is that…

Something is wrong with the model. The other difference between the six players with a draft pick attached and the remaining eight is the length of the contract (an average of 6 years vs 3.5 years). If the teams signing these contracts expect the cost of a win to increase faster than the 5-6% inflation rate we project, then the middle and later years of this contract look a little bit better, but not by much. The only way to make the draft-pick contracts look better is if the players age much more gracefully than the average player, a pretty big risk to take on a $100 Million investment. The model also doesn’t account for any impact the signings may have on ticket sales. Five of the six big contracts came from big-market teams with lucrative TV deals, and teams may be willing to pay a premium to invigorate their fanbase with the addition of an elite player that might not be accomplished by signing a few mid-tier free agents who might add the same total value to the team. While I can’t speak to the economics, we all know that at the end of the day, the most important thing for the fans is to win.

While this is an interesting phenomenon, it doesn’t help us predict the kind of contracts the remaining free agents will get. As we saw with Kyle Lohse last year, while teams may be willing to look past the loss of a draft pick for an elite player, they might not if player in question is closer to league-average. While the free agents with a draft pick attached have actually signed for significantly more than market value, I wouldn’t expect to see this trend continue this offseason. With most of the contenders’ rosters pretty much ready for the season, they’ll only sign that extra piece if the price is right, including the loss of the draft pick. When it comes to players like Nelson Cruz and Kendrys Morales who may only generate $20M of value (2-3 WAR) over the next two years, the $10+ Million valuation of a draft pick explains why the market for them has been so slow. While things worked out fine last year for all of the free agents who turned down their qualifying offer, we could see a couple players really suffer this year, which may make agents — and teams — think twice about the qualifying offer next offseason.