December 21, 2009

Ahead in the Count

When Bad Teams Land Good Free Agents

by Matt Swartz

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When the Orioles signed Mike Gonzalez on Friday, the collective sound of baseball fans' palms hitting their foreheads reverberated throughout the land. The Orioles have virtually no chance of competing in 2010, and they cost themselves their second-round pick. They simply will not have enough games to close, and those games will not push their team over the edge into the playoffs for this season. Instead, keeping the draft pick and concentrating their resources on scouting and development seems to make much more sense.

Similarly, when Gil Meche signed with Kansas City after the 2006 season in which the Royals had lost 100 games, many rolled their eyes at the absurdity of sinking $55 million into a pitcher who would only decline throughout the contract. Even if the Royals became good by the end of the contract, Meche likely no longer would be, and his contract would be an albatross as they tried to improve.

Nate Silver's graph of the marginal value of a win shows that teams on the cusp of the playoffs will benefit more by adding free agents, as those players have a high probability of pushing them over the edge and generating sufficient revenue to justify their spending. Thus, it would make sense that the best teams would be the ones who should be spending on free agents, and this is typically what we observe. On the other hand, we see exceptions like Mike Gonzalez and Gil Meche, who appear to be irrational signings.

The question that I have asked myself in this article is when it would be smart for a bad team to sign a free agent. The problem with signing a pitcher like Meche is that, at the end of the contract, he would be 32 years old and was very likely to have experienced an injury or suffered a decline in value. For teams that may improve over the life of the deal, it may be rational to add a young free agent who is likely to age well and get the value of his performance later in the deal. This is a simple example of when making such a signing could be rational.

On the other hand, signings like the Orioles grabbing Mike Gonzalez represent some of the worst situations-those in which a team loses a draft pick. The return on signing high draft picks is high, and such players can be the ones that make a difference in bringing a bad team to a competitive level. Therefore, it is a pretty good rule of thumb for bad teams to avoid signing players who cost them draft picks because they should value them more. Even though the first 15 picks in the draft are protected, a second-round pick still makes the majors frequently-nearly half the time, actually-so an early second-round pick is quite valuable.

The less obvious situation is one in which a bad team has a high probability of trading that player at the trade deadline for subsequent value. Late last July, during high Halladay season, many teams tried to grab Doc and other coveted players from teams with little hope of making the playoffs. At the time, many sabermetricians attempted to use trade value metrics commonly used during the offseason to approximate the value in prospects that the Blue Jays should expect in return.

However, I pointed out that these articles made a critical mistake in assuming that the value of adding Halladay in the middle of the season was simply his full-season value multiplied by the fraction of the season remaining. What I explained is that the return to a player is non-linear. As the marginal value of a win graph shows, a large portion of a player's value comes from increasing the probability that his team makes the playoffs. The marginal value of a win is essentially derived partly from considering the probability that one win makes the difference in a team's season multiplied by how many wins that player provides.

Much can happen during the baseball season that can change this probability, but for teams right on the cusp of making the playoffs, the odds of one game making the difference in their season increases. Last year, the team that I estimated to have the most value for adding a player like Halladay was the Tigers, coincidentally enough. Who thinks that adding Halladay would have helped them when they faced off against the Twins in game 163 last year, or during the series the previous week against the Twins? Indeed, it was more predictable in late July that the Tigers would need someone to put them over the top than it would have been the previous December. The value of adding a player increased for the Tigers during the season. Similarly, the Mets value for adding players fell dramatically by the deadline. Early in the season, they were right there with the Phillies and Braves, and there was a reasonable chance that one win might make the difference in their season. As it turned out, Joe Mauer could not have put them over the edge in 2009. It is tough to say whether you will be the Tigers or the Mets ten months before the end of the season, but with only two months to go, this crystallizes.

As my article explained, if you estimated the marginal revenue of having one season of Halladay in the previous off-season, you may have gotten approximately $27 million (I have since revised this number upwards in light of recent research by Sky Andrecheck). However, a number of teams still would have seen their marginal revenue of adding Halladay equal to about 65-70 percent of this in July despite only 43 percent of the season remaining.

This segues perfectly into my current question of when a bad team should sign a free agent. Suppose, for example, that a team with low odds of making the playoffs signs a player worth four wins above replacement to a one-year deal. Further, for simplicity, suppose that this player was not offered arbitration and would not cost any draft picks, and that the team could expect no draft pick compensation after the season. The cost of such a player who is a sure thing to produce for one year might be about $21 million. With 70 games remaining, such a team would already have paid him about $12 million of his contract, leaving $9 million to go. Despite the $21 million being fair value for his services at the time, the current $9 million remaining is far less than his value to those teams that find themselves on the cusp of making the playoffs.

Further adjustments to my model from last year that increase the value of a win ignoring playoff odds, and increase the values of making each stage of the playoffs similarly demonstrate that a team with a replacement level player would expect to get about 70 percent of the $21 million in revenue to be generated for them between the deadline and the end of the season if they traded for him. This is $14.7 million. Thus, the bad team has a player on their hands in July who is worth about $14.7 million and costing only $9 million despite the fact that they paid fair value and won the bidding war for his talents the previous December. If they trade him, they can acquire a prospect worth about $5.7 million, which would be a prospect ranked outside the Top 100 overall prospects but still representing a mildly decent chance of contributing at the major-league level. The question is whether or not it worth spending $12 million for that prospect. That depends on if the team the received $6.3 million worth of value for the first 57 percent of the player's season.

If the odds of making the playoffs are absolutely zero, this would probably fall short. Using an adjustment factor to increase Nate Silver's valuations of making the playoffs and valuations of a win with no impact of making the playoffs proportionally such that it represents the dollar value of a win as presented by Sky Andrecheck, the $1.35 million per win for the 2.27 wins provided would yield about $3.06 million in value. This would fall short of the $6.3 million cost.

However, for a team that is highly unlikely to make the playoffs as currently projected but still with some chance of lucking their way in, there actually is value to pursuing this strategy of signing a player that you expect to trade in July in all likelihood.

Consider a team projected to win 77 games in a division/league that would probably require about 90 games to make the playoffs. Suppose, for simplicity, that such a team in the playoffs would have a 45 percent chance of winning any game pitched by their current first three starters, a 39.3 percent chance of winning any game pitched by their current fourth starter, and a 50.7 percent chance of winning any game pitched by the prospective four-win pitcher. This team would have a 2.5 percent chance of making the playoffs before adding the four-win player, and after adding the player and increasing their win projection to 81 games, they would have a nine percent chance of making the playoffs. This team would only expect about $9.2 million from signing the player for one year if they could not trade him.

However, they would still find it advantageous to sign him. Suppose there was an 80 percent chance that they would basically be out of contention at the trade deadline. If so, they would have surrendered $12 million in services worth about $3.06 million to them and would get about $5.7 million of value in prospects back at the end of the deal, thus costing themselves a net $3.24 million.

If the team happens to be in contention, then the trade has paid off very well, though. They can now expect maybe a 60 percent chance of making the playoffs and getting $50 million on average. The 60 percent figure includes some sure-thing scenarios and some borderline cases where they are in contention enough to hold on to the player, and the $50 million includes some cases where they win series they had 40-45 percent chances of winning. In this case, they will spend $21 million over the year. The win value excluding the possibility of making the playoffs was worth $5.4 million, but the player would now be worth $30 million for playoff added value (60 percent of $50 million), and a total of $40.4 million at a cost of $21 million. The team would have netted $14.4 million.

Essentially, the team would have about an 80 percent chance of costing themselves $3.24 million and a 20 percent chance of making themselves $14.4 million. This is a profit of $300,000 in expectation. Adjusting playoff probabilities to consider the chance that the team may actually be good if they find themselves in contention, this number would get even higher.

Thus, we have found a very specific set of criteria for which a bad team should sign a free agent, even with little to no chance of making the playoffs during the duration of the contract:

1. The team should at least have some small chance of making the playoffs, rating as a 75-80 win team before adding the player.

2. The team should be allowed to trade the player easily. This means we rule out no-trade clauses, signing 10-and-5 players who have automatic no-trade clauses, and signing players to multi-year deals that grant the player rights if traded early in the deal.

3. The team should be in a large enough market that they would benefit from signing the player if they were a contender.

4. The team should not have to surrender draft picks for signing the player.

5. The team should expect to be able to find multiple possible trade partners if they fall out of contention.

The last rule is the tricky one that requires some explanation. Pitchers are the best example of a type of player that should generate multiple bidders if put on the trading block in July. Teams generally require four starters in the playoffs, and most team's fourth starter is no guarantee of a win. Nearly any team in contention would at least listen about trading prospects for a starter, and certainly at least two teams in contention would have nearly replacement level starters in their fourth starter slot. Outfielders who can play multiple positions typically have some value as well as corner outfielders who can become DHs on American League clubs. Catchers and middle infielders are other examples of players for whom there may not be a market midseason. If there is only one bidder for your shortstop at the deadline, then you will not get fair value for him. Thus, position players are often risky if they are not players who play multiple positions. Pitchers represent the best bet.

Therefore, when you see older pitchers signing one-year deals with non-contenders and wonder why these clubs would consider adding a player so unlikely to push them over the top, check back in July and see if they are looking to net a prospect or two for that same pitcher. The Mets, Astros, Brewers, Giants, White Sox, and Tigers are all teams that have outside chances of making the playoffs this season but are unlikely to do so. However, all six of them come from large enough markets that they would gain a lot of money from a pennant run. Although these teams may not find it worthwhile to sign a multi-year deal with a no-trade clause to Adrian Beltre, inking a pitcher such as Joel Pineiro or Jon Garland might pay off substantially even if they do not put them into the playoffs.

Matt Swartz is an author of Baseball Prospectus. 
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