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.

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.

After Matt Garza reportedly signed with the Brewers for $52 Million over 4 years today, the initial response was that it was a steal. Baseball writer Joe Sheehan tweeted that the signing was “Grand Theft Pitcher“. Sure, a day after the Yankees spent $175 Million on a big question mark, the price for Garza looks like a bargain. Upon closer analysis, however, the deal appears to be pretty close to what we should expect given what we know about the cost of a win, inflation, and aging curves. This can be seen by using the same model that Dave Cameron writes about so frequently.

This model assumes that in 2014, a win costs $6 million dollars, and that the cost of a win will increase by 5% each year. Steamer projects Garza for 2.8 WAR in 2014, and I subtracted 0.5 WAR each year to account for age-related decline. As with the Kershaw contract, the model pretty much nails the cost for four years of Garza. The deal appears to be slightly team-friendly, with the Brewers getting 0.13 wins of value over the course of the contract. Put in money terms, they saved about $800K for Garza’s expected production. His health concerns (he has totaled 259 innings in the past two seasons) mean extra risk for the team, making it tough for me to get really excited about the contract. According to the model, the Brewers pretty much paid market value for Matt Garza.

But despite the numbers in front of me (and you), the contract does feel like a bargain. Why is this the case? This brought me to the greater point of this article, which was to try to find out the real market value for the 2014 free agent class. To do this, I applied the same model explained above to the 14 major contracts that have been signed this offseason by MLB free agents. These contracts are all include at least 3 years and $20M guaranteed, and total nearly $1 Billion. This leaves out relievers (which never quite fit into the model), injury-prone bounce-back candidates like Josh Johnson, and of course Masahiro Tanaka (since he’s extremely difficult to project). Ten of the fourteen players are between the ages of 29 and 31. For 2014 WAR, I used an average of Steamer and ZiPS (where available), and in the few instances where there was a team option or buy-out, I included the cost of the buy-out in the final year of the contract, as players in their mid-30s are rarely worth the cost of the option year. Lastly, rather than projecting the money a player should have earned, I simply calculated the WAR that a player is being paid to be worth (Wins / Salary) and compared it to their projected WAR for the duration of the contract. Without further ado, the table:

While your first instinct may be to declare most of these contracts huge overpays, the fact of the matter is that if everything appears to be an overpay, we need to adjust our baseline. According to the model, teams have paid for 146 wins, but are only projected to get back 124. What could account for the difference between the model and reality? On one hand, we have to consider the fact that every team values a win slightly differently. The Yankees have a huge incentive to put together a competitive team or they risk alienating an impatient fanbase. A win is worth more to a team on the brink of contention than a team sitting at the bottom of its division. This could be driving much of the variation, but is impossible to fully account for.

This leaves us with four factors that could cause the discrepancy between the model and the market that we can adjust for. First is the initial evaluations of the players. For instance, Shin-Soo Choo is coming off of a 5.2 WAR season, but is projected for just 2.9 WAR by Steamer. If we pencil Choo in as a 3.5 WAR player in 2014 (Oliver has him at 5.4), then he is set to produce 14 WAR during his 7-year contract, and be worth “only” -4.55 wins relative to his contract. The second is player aging. Taking off half a win each year is a quick and relatively accurate way to calculate future WAR for players who are already around 30 years old. However, some research has suggested that elite players may peak later and/or decline slower, which could affect many of these high-priced free agents (at least for the first few years of the contract).

The third and fourth variables are the cost of a win in the present and in the future. We’re using $6 Million per win, but other research has suggested that a win may cost more like $7 Million. In addition, the model increases the cost of a win by 5% each year, and some teams might suspect that rate to be higher with all the additional money flowing into the league.

After fixing the biggest outlier of the table (by projecting Choo for 3.5 WAR in 2014), these are the adjustments that would have to be made to a single variable (with all others held constant) to give us a model that properly values this free agent class so far:

Player Evaluation: The team signing the contract expects the player to perform roughly 0.23 WAR better than the Steamer/ZiPS projects in 2014.

Player Aging: The team signing the contract expects the player to decline at roughly 0.37 WAR per season.

Present Cost of a Win: One win (+1 WAR from a player) is currently worth $6.9 Million on the open market.

Future Cost of a Win: The cost of a win is expected to increase by 11.5% each year for the life of the contracts.

As is usually the case, the truth probably lies somewhere in between, with a little bit of each. In some cases, the driving force may be different for each team and each contract. The Mets may have signed Granderson believing that he can be worth 2.6 WAR in 2014 (as opposed to 2.2 from the projection systems), while the Mariners may have agreed with Steamer and ZiPS that Robinson Cano will be worth 5.35 WAR in 2014, but might project him for a slightly slower decline.

Just for fun, I’ll take a shot at modifying the model with a few minor adjustments so that the expected wins purchased matches the expected production. For my updated model, I’ll use the following parameters: Steamer/Zips are accurate measures of current talent, the players signed will decline 0.45 WAR per season after 2014, a win currently costs $6.4 Million, and the cost of a win will rise by 6% in the foreseeable future. Here’s the adjusted table:

Reducing the rate of decline and increasing the cost of a win helps out the longer contracts quite a bit, so Robinson Cano’s contract starts to look a lot better. However, the net benefit is largely offset by committing such a massive amount of money to a single player who could get seriously injured or decline sooner than expected. With the new model, the Garza deal looks more like a bargain (although I would still hardly call it a steal), and a few contracts that looked like a market value or a slight overpay appear to be more team-friendly than initially anticipated (McCann, Peralta, Infante, Feldman, and Saltalamacchia). Carlos Ruiz looks like a downright steal. Keep in mind that even just netting half a win translates into an extra $3 Million of value, so we’re talking about a pretty significant savings here.

In closing, Cameron’s quick-and-dirty model works quite well, but given the contracts signed so far this season, appears to require some minor adjustment. It’s impossible to know which of the factors require adjusting and how they vary from one team to another, which is what makes projecting these contracts and determining whether a contract is a bargain or an overpay so difficult. As is always the case, only time will tell, and as more free agents sign we’ll be able to see if the new model checks out and make necessary adjustments.

All projections are from Steamer and ZiPS. Contract information is from Fangraphs and Baseball-Reference.