Each year, about 25 players receive two-year contracts. The inevitable question that analysts ask is whether it was smart to commit to the player for a second year, or whether the team should have stuck with one year. But did you know that most players receiving two-year deals in recent years actually do better in the second year of their contract? Players who receive three- and four-year deals produce similarly in the first two years of their deals as well, instead of declining as many people believe.

Similarly, when the PECOTA cards are released you will be hard-pressed to find a lot of players in their 30s-and the vast majority of players receiving two-year deals are in their 30s-that PECOTA projects to perform better in 2011 than 2010. This is logical, because most players do decline in their 30s, but players receiving two-year deals improve more often than they decline. This is particularly true for players who were re-signed to two-year deals with their old teams, as opposed to players adjusting to new environments. This is relevant for evaluating contracts in general, because it shows some of the extra information teams have when they decide to offer these contracts, and the importance of context when looking at projections on PECOTA cards for 2011 and later. Aging curves are certainly different by player, and therefore it is important to analyze contracts with this in mind, especially with evidence that teams are more knowledgeable about individual aging processes than previously believed.

Even the most hardcore sabermetricians have no problem admitting that there is more to analyzing baseball players than just looking at numbers. We often get pigeonholed as having this mindset-I recently received an e-mail from a friend asking me to explain the logic behind sabermetricians’ “belief that mental factors do not exist in sports.” There are plenty of factors, physical as well as mental, that the numbers just don’t reveal. An interesting analogy to a team’s insider knowledge about players they sign is the bonuses given out to prospects. PECOTA uses draftee signing bonuses as an aide to developing projections for them. If you feed PECOTA Stephen Strasburg’s college statistics, it might expect him to do good things, but once you tell it that the Nationals were willing to guarantee him $15.1 million, it will expect him to do great things, because from the program’s point of view, he’s more likely to be something special than if the Nationals were unwilling to part with that much cash.

The same rule applies to multi-year deals. Once we know that a decision has been made, we need to update our expectations based on this fact. I can look at John Lackey‘s recent injury history and think that he is a health risk. However, once I know that the Red Sox looked at his medical records and determined what type of aging trend he might have-and still offered him five guaranteed years-then I have to assume that the team has some private information. I certainly would start to doubt his ability to succeed if he couldn’t find anyone to offer him a decent contract.

When evaluating team decisions, we cannot look at these choices as natural experiments. Looking at Johnny Damon‘s PECOTA projection without knowing that teams have passed on him one by one will probably overstate his value. Looking at Chone Figgins‘ without knowing that the Mariners‘ front office gave him four years will probably understate his value. The reality is that once we saw Pat Burrell struggle to find anything better than a two-year contract from the Rays, we should have wondered if teams knew something bad about him that wasn’t common knowledge, especially because the Phillies and their strong scouts couldn’t hide from him fast enough after letting him lead their World Series parade on Halloween in 2008. It seems like all 30 teams realized he was unlikely to repeat his 4.4 WARP* from 2008.

Last year, the Nationals resigned Cristian Guzman to a two-year deal for 2009-10, but were disappointed to see him decline in 2009 after a stronger 2008 performance. But the question now becomes what the Nats should expect from Guzman in 2010, during the second year of his deal. Should they consider him an older player bound to get worse? Maybe, but more likely not. Russell Carleton reminded us last week that players all have different aging curves, and it seems like teams have some ability to detect this.

Looking at all 71 two-year deals inked in the 2006, 2007, and 2008 offseasons as I work on the re-development of MORP, I came upon a curious phenomenon. As I noted at the outset, players get better during two-year deals. It’s not by a small margin either: those 71 deals delivered 51.5 WARP during the first year, and 64.0 during the second year, meaning that they delivered 56 percent of their value during the second year.** This phenomenon is not unique to pitchers or hitters, either, though it is stronger for hitters. Pitchers got 52 pecent of their WARP during the second year of their two-year deals, while hitters got 64 percent of their WARP during the second year of their two-year deals.

Interestingly, the same pattern did not emerge when looking at the three- and four-year deals during the same time period, although teams did seem to identify players who could hold their value pretty well. The Braves certainly seemed to have a beat on oft-injured third baseman Chipper Jones, when they signed him to a three-year deal after the 2005 season. He only produced 4.4 WARP3 in 2006, but improved to 7.1 in 2007 and 7.7 in 2008 as a 36-year-old. The Padres certainly did not look smart in 2006 after re-signing Brian Giles to a third year. His .283 EqAplus was far below his career average that year, but he maintained an identical EqA in 2007, before looking like his old self in 2008 with a .319 EqA, producing 4.8 WARP.

Gathering all 50 three-year deals from 2005, 2006, and 2007 together, players generated a combined 86.8 WARP in the first year, 79.5 in the second year, and 50.1 in the third year (representing 40, 37, and 23 percent of their WARP). It is clear, however, they these players do seem to hold their value for at least the second year of their deals. Pitchers on three-year showed a steeper decline than hitters too, generating 48 percent of their WARP value in the first year, 37 percent in the second, and 14 percent in the third. Hitters held steady in their second years, going from 36 percent to 36 percent to 27 percent over their three-year deals. (Similar patterns emerged using WAR.)

Players held up during four-year deals as well. Among the 19 four-year deals, players generated 47.4, 49.8, 42.4, 39.0 WARP in each of the four years respectively, representing 26 percent, 28 percent, 23 percent, and 23 percent of their value. Even though they declined during their four-year deals, players receiving them clearly held their values very well. This indicates another element of team knowledge about the players they sign to these deals, even if there is a small decline. If you look at the next four years on PECOTA cards for most players with six years of service time, they will certainly not be projected to have similar numbers 2013 as 2010, but that seems to be the case for the subset of players who are offered four-year deals. What seems to be happening is either that teams have been ridiculously lucky, or that they have an intelligent sense that these players are going to hold up. There are players like Billy Wagner and Tim Hudson who get hurt near the end of deals, but there are also plenty of guys like Guzman and Damon who produce more in the last year of their deals than the first, second, or third.

In a helpful discussion with Eric Seidman and Tommy Bennett on this issue, they suggested that age may be correlated with deal length. This seemed reasonable, but players receiving two-year deals apparently do better in their second years are older on average: players getting two-year deals were 35 on average, compared with players on three-year deals who were 32 on average, and 31 on average for players on four-year deals (with standard deviations of four, three, and two years, respectively). There was something about these players on two-year deals that made teams want to sign them for two years but not three, and it seems that these teams were not making a random decision.

Although older players were more likely to decline during their two-year deals, many players in their early- and mid-30s improved during their deals. The seven players between 25-29 in the first year of their two-year deals got 55 percent of their value the second year, but the 22 between 30-33 generated 71 percent of their value in their second year, and the 23 players between 34-36 got 65 percent of their value in their second year. It was only for players older than this that we start to see the expected decline in the second year of two-year deals. The 10 players between 37-39 in the first of their two years got 43 percent of their value in the second year, and the nine players over 40 got 44 percent of their value in the second year of their deal. So, we do see some element of aging for these players, but even players in their early- and mid-30s are improving during their two-year deals.

My suspicion as I gathered this information was that teams have inside knowledge, but another possibility is that players need to adjust to new teams, cities, and leagues. The easy way to tell the difference is to check whether players who re-signed with their old teams did relatively better later in deals or if players who signed with new teams did relatively better later in deals. The answer was pretty clear-among players who re-signed to two-year deals with their old teams, they produced 39 percent of their WARP in the first year of their deal, and 61 percent in the second year of their deal. Players who signed two-year deals to new teams produced 63 percent of their WARP in their first year, and only 37 percent in their second year deal. It certainly seems that teams who re-signed their players had better information on their players. Looking at players who signed three-year deals produced 36 percent, 34 percent, and 30 percent of their WARP in each of their three years, respectively-maintaining constant value for sure-but players who signed three-year deals with new teams declined from 45 to 39 to 16 percent of their WARP in each of their three years, respectively.

There were just 19 four-year deals, and only six were players re-signing with their old teams, so it is tougher to analyze four-year deals. However, there is some evidence of improvement at least early in their deals among re-signed players, even if they tapered off at the end. Among players who re-signed with their old teams for four-year deals, their production by year broke down as 20 percent, 33 percent, 29 percent, and 17 percent, while players signing four-year deals with new teams broke down as 29 percent, 25 percent, 21 percent, and 24 percent.

What appears to be happening is that teams seem to have some sense of the aging curve of individual players, especially if they are already in their organization. There are probably a variety of reasons that this subset of players aged well, but the team knowledge about the player’s medical and scouting information appears to contribute to the decision to give a player two-year deals. This is important to keep in mind when we hear of a player signing a new contract and look to a projection system to figure out how smart the deal was. Chances are that there is additional information-especially about aging-which teams have that we may not.

*: For this exercise, I’m using what’s currently shown as WAPR3 on player cards; this is WARP2 per 162 games.
**: This is not limited to some quirk of WARP measurement; using FanGraphs’ WAR, they averaged getting 57 percent of their value during their second year, further validating this result.