In June, Eric Seidman and I discussed the Diamondbacks’ starting pitchers with some focus on Dan Haren, explaining that he was particularly unlucky. At the time of our article, Haren’s ERA was 5.35 and his SIERA was 3.08. Haren would be the ace of many pitching staffs in the major leagues, and is signed well below market value through 2012, with a reasonably priced option for 2013.

Fast forward to the day of Haren's trade to the Angels last Sunday, and his SIERA was almost exactly the same (3.16), while his luck had corrected itself and his ERA was already down to 4.60. Still, the Diamondbacks needed to shed payroll, meaning that his $27.5 million MORP was not an estimate of his value—not to them. MORP, or Market Value Over Replacement Player, is about the value of a player’s skills in a competitive market, which pretty much equates to the value to a contender.

It appears that the Diamondbacks failed to get market value for his skills despite an ample number of potential bidders. Roy Oswalt might have commanded more value despite having less contract remaining. Cliff Lee commanded more with only a half-season left on his contract, and his previous two trades and their seemingly weak returns are actually very explainable by the small amount of time left on his contract before reaching free agency. CC Sabathia only generated one major prospect due to his lack of remaining time under contract back in 2008, too.

However, Haren had 2 years on a reasonably cheap contract remaining at the time of the trade, and he nevertheless commanded a weak deal. I have some ideas about what happened in that trade, which I'll get to later in the article. But to start off, I'll discuss how to value Haren using the new MORP, and what we have learned about in-season value of players. In the second part of the article, I'll discuss why I think that Haren appeared to generate such a weak return.

Valuing the Trade

Given what we know about Dan Haren and DIPS, it's not hard to see him as a 5 1/2-win player. We have discussed recently that, due to the increased likelihood of a player affecting a team’s playoff chances late in the season, a player is worth about 50 percent more per game to a team on the playoff bubble in late July than he is worth when he's on the free agent market. Haren’s remaining pro-rated salary is market rate for only 0.4 WARP over 162 games (or WARP3), but he is likely to produce 2.1 WARP3—a bargain of 1.7 WARP3 for the expense of employing him

Let’s assume a modest 5 percent inflation to $5.25 million per WARP3 in 2011. If so, Haren’s $12.75 salary would buy 2.4 wins, but anticipating a projection of 5.0 WARP3 from Haren would make him worth 2.6 extra wins over his contract. If the market value of wins inflates again, say to $5.5 million per WARP3 in 2012, then Haren’s $12.75 million salary buys 2.3 WARP3, but his projected performance of 4.5 WARP3 would make his value 2.2 wins over his salary. Take this out to the end, and his $15.5 million option for 2013 would be worth 2.7 wins at $5.75 million per WARP3, so his 4.0 WARP3 would be worth 1.3 WARP3 above his market value. So, for this exercise Haren’s value in summary is

1.7 wins in 2010
2.6 wins in 2011
2.2 wins in 2012
1.3 wins in 2013
7.8 wins

In contrast, Joe Saunders, one of four players sent from the Angels to the Diamondbacks in the trade, had a 4.73 SIERA with a 3.41 ERA in 2008, a 4.89 SIERA with a 4.60 ERA in 2009, and a 5.08 SIERA with a 4.80 ERA in 2010. An ERA around 4.90 in 190 innings in the AL is worth about 2.0 WARP3; that would leave about 0.7 WARP3 for this year. At a pro-rated $3.7 million in 2010 with the aforementioned mid-season premium on talent, the Diamondbacks would only get 0.2 WARP3, so his contract nets them 0.5 WARP3 for 2010. The wins probably do not add much to the Diamondbacks in last place, but we are focusing on market value here, because the Snakes received Saunders instead of more prospects from the Angels, so they acted as though they valued him at least as much as the contending Angels did.

Saunders has two more years before he reaches free agency, but as his value regresses and his salary escalates, he's simply not worth that much relative to the market. Specifically, his likely approximated $6.5 million arbitration award would only buy 1.2 WARP3 on the open market in 2011, and he is likely to produce about 1.8 WARP3, only 0.6 more than what that salary could command on the open market. His 2012 value may be zero, because his arbitration award is probably about as high as his market value.

As far as the rest of the package, valuing prospects is difficult to do, because they may become stars, or they may never make the majors. Fortunately, analyst Victor Wang took a unique approach to this problem that can help us come up with an approximate value. Wang averaged the pre-free agency Wins Above Bench value of players ranked similarly, while treating players who never made the majors as worth zero wins. Wins Above Bench uses a higher replacement level than WARP, so there are only 808 Wins Above Bench each year, as opposed to about 1,250 WARP3. So I converted Wang’s estimates of Wins Above Bench into WARP3 by multiplying by 1,250/808 to reflect that relative scarcity. Keep in mind, however, that these are estimates of expected value, so they're not exact. However, they give us some bearings on what to expect.

Further complicating things is how low these prospects are ranked. Rafael Rodriguez is a potential middle reliever, so he’s not a special pitcher. According to Baseball Prospectus' Kevin Goldstein, he's not even a sure thing on that front. Given that middle relievers are only worth about 0.5 wins per year in many cases, and Rodriguez is not even a guarantee to reach this spot, my ballpark estimate for his value is about 0.3 wins per year, with arbitration eating away at his value late in his service time.

Tyler Skaggs was a borderline Top 100 prospect, per Goldstein, who also added that he suspects Skaggs would come up a bit short if he were to make the list now. Since pitchers ranked between Nos. 76-100 produced 2.88 Wins Above Bench in their first six years according to Wang’s research, that comes out to 4.5 WARP3; since Skaggs is a little below this level, I spread 3.6 wins out over six years. And since Tyler Corbin seems to be worth below even that, I simply cut Skaggs’ value in half to come up with an estimate of Corbin's potential value. That’s a rough guess, but it doesn’t change the final analysis very much. Assuming that Rodriguez’s value accrues during 2011-16, and Skaggs and Corbin produce during 2013-18, we get the following table with all players’ values to estimate the net movement of wins in the trade:


Player Value by Year








































Net Value to D’backs











Overall, this means the Diamondbacks are actually surrendering a net 1.6 wins total. In nearly every other trade I have analyzed this way, teams have valued future wins less than present wins, meaning that the selling team should come up with positive potential net gain in expected wins, despite coming up short in the early years. However, the Diamondbacks appear to come out very far behind using this method, even treating wins in the future as equal in value to wins in the present.

The issue is not that the Diamondbacks were losers in this trade. To one way of the thinking, the Diamondbacks are better off for making this trade than for not making it: even if they weren’t going to run out of money this year, those wins were not going to be utilized towards a playoff run, so they have less value to the Diamondbacks. Both the Angels and Diamondbacks did and should have preferred doing this trade to sitting on their hands. Even though the Angels are an increasing longshot in 2010, this sets up a potentially strong team very well for 2011 and 2012.

Instead, the issue is market value. In terms of how much these players are worth on the trade market, the Angels did not give the Diamondbacks as much as the Diamondbacks gave the Angels. The question is why the Diamondbacks got what they did anyway. I'll turn to a bit of economic theory to shine a light on this.

Why Such a Raw Deal?

Economists often use something called the "Efficient Market Hypothesis" to think about transactions. The Efficient Market Hypothesis, among other things, states that assets are priced according to their true value to buyers, that trades are of value to both parties, and that neither party could have done better than the deal they got—as long as a specific set of assumptions are true. No economists actually think this is fully true, because we all know the assumptions are simply too stringent.

However, the Efficient Market Hypothesis is a very useful tool because it gives us a location, a compass, and tells us what direction to go. We can figure out what assumptions are violated, and that can tell us whether the price is going to be too high or too low. Specifically, the EMH assumes that there is no asymmetric information and that there is perfect competition for players. If there is, that affects the price.

However, baseball teams employ dozens of scouts to acquire information that their competitors do not have, so the assumption that information isn't asymmetrically distributed is clearly violated.

The perfect competition assumption means that any business that is overpaying for a resource can be run out of business by a competitor who buys the same resource for less and undercuts the price to steal all of their customers. It also assumes that any business underpaying for a resource will be bid up by their competitors who value the resource equally. Clearly, there is no driving a baseball team out of business—you and I cannot go to Arizona and start up a new baseball team, named after a totally different kind of snake, and charge a few bucks less for tickets by not overspending on players. The hypothesis’ assumptions are absurd in that case, so we know it also won’t hold. A team can overpay for labor in baseball and not go out of business—that element of the Efficient Market Hypothesis does not work.

However, the other side of this does generally work. A baseball team will usually be vulnerable to the market force that eliminates underpaying. If one team was trying to pay less than a player is worth, they would be outbid in some instances—but only for free agents and for trades with multiple bidders. Players who are not yet eligible for free agency are not competed for, so they are not going to follow this law of perfect competition, because there is basically no competition.

However, Haren on the trade market was bid on by several teams, and the Diamondbacks chose the Angels' package above all others. As a result, there are a few possibilities to explain the low value received that I demonstrated up front.

Obviously, the first possibility is that sabermetricians are wrong, and that every baseball team is right, and that Haren’s ERA is a better approximation of his skill than his SIERA. That seems unlikely given all the research completed on this issue.

Another possibility is that the analysts are right, that SIERA is an awesome way to evaluate Haren, and that none of the dozen teams in buy-mode right now are as aware of that as they should be. That also seems unlikely—this isn’t a secret, and if PitchF/X is any indication of what scouts are seeing, his velocity and movement are the same as in previous years.

It’s possible that the Diamondbacks ignored all of the other teams bidding for Haren’s services, too—but why would they do that? The abundant rumors about various Yankees’ proposed packages suggest that the Diamondbacks did listen. It seems unlikely that all of these teams would simply give up and not try to outbid the Angels if everybody agreed that the package was so poor.

That leaves one other possibility, which is that the Diamondbacks just really liked what the Angels were offering. This is where asymmetric information comes into play, and asymmetric information is one factor that can make underpaying relative to an efficient market value possible. Every team has a different scouting report on every player, and it seems obvious that the team that ends up with a player is usually the one that values him the most. That is one of the reasons that you do not suddenly see every draft pick dealt one year after they are drafted, when they are first allowed to be dealt: teams value the guys that they picked in the first place.

Similarly, the fact that the Diamondbacks ended up with Saunders, Rodriguez, Skaggs, and Corbin indicates that they probably valued them more than other teams. In fact, given that they traded Haren for them, they probably valued these four players a lot. Although I have not seen them, I would bet that the Diamondbacks' scouting reports on these guys look more favorable than almost every other team in the game.

The question is whether the Diamondbacks are right. Are the Diamondbacks the only team to see the value in these players? Are they noticing something that other teams are not? Or is something else at play?

My guess is that this is actually symptomatic of The Winner’s Curse. The Winner’s Curse describes what happens when different people bid on something and they all have a different “signals,” or estimates, of its value. The average estimate among all 30 teams considering a player is probably about right on the mark, which means the team which does bid the most for that player is probably one with a signal for his value that is too high. I think that what is happening in this case is that the Diamondbacks placed the highest value on these players, and probably think that they got a better return than they did.

It’s tough to say whether they actually believe in winning percentage as a method of evaluating Saunders, or whether that was just something that interim general mnager Jerry Dipoto threw out to make the move sound palatable to the media. It’s tough to know whether they think that Goldstein's assessment of Rodriguez’s upside of becoming a middle reliever is way off, or whether the historically terrible -3.62 WXRL from this year's bullpen has messed up their assessment of what a middle reliever is worth.

Regardless, unless sabermetrics is just way off in its valuation of Haren, or every other buying team is clueless about it, then the Diamondbacks valued this package substantially more than everyone else. I am not convinced there is any reason to distrust everyone else’s opinions of these players in favor of the Diamondbacks' apparent evaluation. They may come to prove everyone wrong in the coming years, but it seems very clear that the majority of teams did not aggressively target these same players, and that tells me something about their likely value.

Thank you for reading

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Well done. It's fun to see someone use microeconomics to analyze trades!

However, wouldn't your comments apply to just about every trade? That is, every team that trades for a player (or drafts a player) is likely to encounter a Winner's Curse because they probably value that player more than any other team and therefore run the risk of having overpaid.

Woody Studenmund
Thanks. I agree that most teams are going to victim's of the winner's curse. The solution to the winner's curse is to value the players at a lower level than you estimate them to be, figuring that if you do acquire them, they are probably not as valuable as you thought they were. My belief is that the D'backs didn't do that here, or at least not as much as they should have.
seems like you are using a linear expected value for prospects, but that would imply high ceiling, low probability guys and low ceiling, high prob. guys are evaluated in the same way. but premium guys are way harder to find than the average guys, and i think there should be an adjustment to take into account of the higher value of a high ceiling "hit".
The problem with that logic is related to my articles on MORP where I determined whether it should be linear. What you're saying would be right if 4-win players were worth more than 2 2-win players, but as I showed in those articles, this is not the case. So, the expected number of wins from players is sufficient here. A high-prob low-ceiling guy can be worth as much as a low-prob high-ceiling guy as long as they are sufficiently high/low probabilities.
The political aspects of these sorts of things are often ignored. In part because they're unavailable to us. But DiPoto may well have been under orders to "get SOME-thing of immediate use back so as to help sell a couple extra tickets for next year". And thus 'over-valued' Saunders. My understanding of multi-millionaire owner types is that they do give such orders alot more often than we realize.
Agreed. This is the reason that I didn't totally write off the wins Saunders generates-- it's an evaluation of the market value of the package with an agnostic view about which parts of the package are most important.
Great article. In thinking about the Haren evaluation side of this (or the MLB scouting angle of this), I was very struck by something Dave Cameron wrote over at fangraphs: "To MLB teams, limiting walks and striking out hitters are nice, but you can’t be an ace if you give up a lot of home runs." What struck me was that perhaps MLB teams/scouts are confident they can accurately ID pitchers who are HR-prone; or to put a finer point on it, teams/scouts can ID pitchers that are and will continue to be HR-prone.

I wonder if this confidence on the part of MLB teams/scouts represents a divide between saber-oriented analysis.
Those same analysts/commentators/journalists had no problem calling homer-prone Curt Schilling an ace. I think its just bobbleheads making noise.
The form of this article is a step forward in SABER analysis -- not just to find a winner or a loser but to see how the result came about. The Wallace-Gose swaps and the PHI-HOU swap are similar examples in the gap between a WAR-based Efficient Market Hypothesis and what takes place in MLB transactions.

I bet negotiations and norms of business play a role in some of these outcomes as well, since we're dealing with a small number of repeat players. Buster Olney reported that other GMs were shocked with the results of the Oswalt deal - if only they had known $11M and the option (as opposed to the exercise requisite) were in the mix. But those details probably emerged well into negotiations with the Phils at which point business etiquette or close relations between parties or reputation effects may have kept them from turning to a third party for a better prospect package (or bigger salary dump).

Or maybe they just valued Gose very highly (or they knew how highly the Jays did).

Although I do wonder why non-contending teams seem to value league average (not all that inexpensive) pitchers so highly.
Could it be that valuing league average pitchers so highly is one of the ways to become a "non-contending" team?

This looks like a return to the days of yore here in AZ. It was most prevalent during the Joe Garagiola Jr. days -- he would overpay for the guy he really wanted in trade, and if he wanted a guy gone, the price ended up being pretty low. It's a focus on getting the deal done and not on making it a good deal. (To be fair, Joe G. did pretty well on Karim Garcia for Luis Gonzalez...)
Very interesting article. I should go back to read your earlier MORP articles about whether the value of player-wins is linear. I have always thought that the reason this might not be true is that concentrating value in one position has value itself. Otherwise, it would make sense to trade a 24-win player for 25 one-win players, but if a team did this it would finish below .500. The limited number of positions on the roster means that the high-value player in one position increases the ceiling of the team and allows for some other positions to fall short and still succeed as a team.
Matt, excellent article, as usual.

I'd offer the possibility that we all, as a community, overestimate the weight given to sophisticated statistical analysis in evaluating trades. I think that the decision makers still rely significantly upon players' reputations, scouting reports, and obsolescent-but-popular stats (such as ERA and RBI). That does nothing to counter your observation that "The Winners Curse" may apply here. It merely adds my perception that the people really making the calls (at the GM and ownershp levels) are stupider than we might choose to believe.