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February 22, 2010

Ahead in the Count

Evaluating Multi-Year Deals

by Matt Swartz

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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.

Matt Swartz is an author of Baseball Prospectus. 
Click here to see Matt's other articles. You can contact Matt by clicking here

29 comments have been left for this article. (Click to hide comments)

BP Comment Quick Links

Richie

Are you sure there's no 'plexiglass' principle in play here? That is, teams typically offer multi-year deals only to players coming off good years, who then naturally regress Year 1, and bounce back some Year 2.

I'd also be curious to see how much of Year 1 regression was injury-related. That is, a player has a good year in part by playing alot, signs his multi-year deal, wears out in Year 1 in part 'cuz of previous wear-and-tear, then regains some health for Year 2.

Feb 22, 2010 10:30 AM
rating: 0
 
Ben Solow

The health angle might have something to do with it, but the regression angle shouldn't. Regression to natural talent would explain why they underperform in Year 1 relative to Year 0 (the contract year), but not relative to Year 2. Year 1 and Year 2 performance are draws from the same distribution, so you wouldn't expect any pattern.

As an aside, Matt, this is addressed a little bit in shirking literature applied to sports. The Krautmann & Solow paper out now is bad, but there's a much more rigorous paper in progress by Elena Pastorino, Harry Paarsch and John Solow if you're interested.

Feb 22, 2010 11:05 AM
rating: 3
 
BP staff member Matt Swartz
BP staff

Richie, Ben's explanation here is correct. Think of it this way. If a coin comes up heads more than 50% of the time, it's bound to regress back to a 50/50 chance the next time it is flipped, but it's not anymore likely to come up heads or tails the next time after that.

Ben, those sound like some papers I ought to have a look at! Thanks for letting me know about the literature. That's definitely relevant stuff for me to read.

Feb 22, 2010 13:51 PM
 
bpage18

Or... a team rewards a player who has been on the team for a few years with a new 2-year deal (presumably worth a lot more $$ than he was making previous), and he loafs around in that 1st offseason as he just "hit the contract jackpot", and has a lousy year. Then, in Year 2 (otherwise known as the year right before impending Free Agency), he comes back very strong again! It seems some of this has to be due to the "Playing for a Contract" year phenomena a little bit.

Feb 22, 2010 10:55 AM
rating: 1
 
BP staff member Matt Swartz
BP staff

Very possible. I don't know if the playing for a contract explanation covers all of this, especially the divide between re-signs and new signings, but it definitely could explain some. A valid point for sure.

Feb 22, 2010 13:52 PM
 
doncoffin
(422)

I wonder what would happen if you used the binomial theorem. Suppose that we know that 57.5 30 year-old players decline in their age 31 season and that 62.5% of 31 year-old players decline in their age 32 season (I am obviously making tjose numbers up). What percentage of players would be expected to improve in their age 32 seasons compared to their age 31 seasons? What percentage of players actually improve? Is the difference statistically significant? Just reading your essay would lead me to think that the difference between expected and actual is not statistically significant, especially when you restrict your sample to players signing 2 year contracts.

Feb 22, 2010 11:52 AM
rating: 0
 
BP staff member Matt Swartz
BP staff

The difference actually seems statistically significant. 39 of 71 two-year deals showed improvement instead of decline. The confidence interval on improvement from that is (43%, 67%), and certainly I would guess that less than 43% of this age group of players improve overall. This is more dramatic for re-signed two-year deals, of which 26 of 39 saw improvement. That's a (52%, 81%) confidence interval, and certainly fewer than 52% of players in that group decline overall. Thanks for highlighting this issue, though.

Feb 22, 2010 13:55 PM
 
cbirkemeier

Do players in the second year of a two-year contract beat expectations more than a player normally does in a contract year?

Feb 22, 2010 12:10 PM
rating: 1
 
BP staff member Matt Swartz
BP staff

I'm not sure the details of contract year performance, but I don't think that this difference is enough to explain this jump. This is certainly a valid question to ask though. I just don't have the data on it to answer it thoroughly, so all I can say is that my understanding of this research is that the contract effect is more subtle and largely related to age at the time players reach six years of service time.

Feb 22, 2010 13:56 PM
 
Asinwreck

Is there a Pirates exception, one where a GM offers a Pat Meares or a Kevin Young a multi-year contract for no apparent reason?

Feb 22, 2010 12:23 PM
rating: 0
 
BP staff member Matt Swartz
BP staff

Well...the rule is supposed to apply to GMs having knowledge of players not contained in the numbers, so as much as that rule doesn't apply to the Pirates, maybe...

Feb 22, 2010 13:57 PM
 
John Carter

Some teams will ride a pitcher at the end of his contract. This accomplishes two things. It ups his stats, so he becomes a Type A free agent and it eats up innings saving that team's younger pitchers from overwork.

Feb 22, 2010 13:42 PM
rating: 0
 
BP staff member Matt Swartz
BP staff

Definitely possible, but the pitcher improvement was pretty modest: 52% of performance in the second year. The real gain was hitters who provided 64% of their value in the second year.

Feb 22, 2010 13:58 PM
 
tbwhite
(361)

It still sounds like age may be playing a role. An average age of 35 for guys with 2 year contracts is pretty old, a lot of lesser players would have been weeded out by then. Maybe good players decline more slowly than mediocre players, and with an average age of 35 the mix is more tilted towards good players. Lots of guys flam out in their early 30's which is the extact time period that seems to be covered by the longer deals.

Feb 22, 2010 15:07 PM
rating: 0
 
BP staff member Matt Swartz
BP staff

I think that the research on aging says that particularly good players decline more slowly but tend to peak closer to 31, but not such that they are better at 36 than 35 as seems to be the case here. Certainly it is selecting sampling on aging, but there is something else mixed in too that seems related to re-signings in some way especially.

Feb 22, 2010 18:12 PM
 
tbwhite
(361)

Have you looked at the breakdown by individuals to see what is driving the gain in the second year of two year contracts ? In other words, in general does everybody improve some, or is it mostly noise with a few outliers driving the disparity between the 1st and 2nd year ? The sample size is pretty small. You're talking about only a 12.5 WARP improvement spread over 71 players, it wouldn't surprise me if the improvement was being driven by handful of players.

Feb 23, 2010 16:36 PM
rating: 0
 
BP staff member Matt Swartz
BP staff

It was 39 of 71 individuals who improved in the second year of two-year deals, and 26 of 39 of those re-signed two year deals. The biggest jump was Mussina from 1.1 to 5.0 in 07 and 08. It didn't look like outliers to me at all.

Feb 23, 2010 17:22 PM
 
WaldoInSC

The humility underlying this piece was refreshing. Great job, Matt.

Feb 22, 2010 18:26 PM
rating: -2
 
Darsox64

Would contractual status be added to PECOTA projections in an attempt to proxy the information the general managers have?

Feb 22, 2010 18:54 PM
rating: 0
 
Berselius

Matt - how would you go about calculating the percent value with a player who posted negative WAR in one season? E.g. someone who posts a -0.5 WAR in the first year and 0.5 in the second, for an aggregate of 0 WAR

Feb 22, 2010 19:12 PM
rating: -1
 
BP staff member Matt Swartz
BP staff

Good question. I avoided this by just aggregating WARP3 for all players in a group. Otherwise, the only issue is 0.0 total, because even -0.5 and +0.7 would be summed as 0.2 and the percents could be -0.5/0.2 = -250% and 0.7/0.2 = +350%. Clearly, you've hit on why I aggregated rather than trying to average the outlier percent scores.

Feb 22, 2010 20:53 PM
 
Dan McKay

Fantastic article. Lots of food for thought.

Feb 22, 2010 22:04 PM
rating: 0
 
Mark_Kieffer

I don't think this too suprising at the core. We talk about guys in their "contract year" often performing beyond what most expected. The 2nd year in the 2 year deal is that "contract year" and said player wants to look attractive when they hit free agency.

I think the more interesting thing to look at is why players underperform often times in the first year? Is it lack of motivation, or trying too hard to prove their worth, or what?

Feb 23, 2010 07:57 AM
rating: 0
 
joepeta

Matt, Very intersting article. I think there is one obvious question left hanging out there though: Who are the players entering year 2 of a 2 year contract this year? Jamie Moyer(gulp)comes to mind. Is there any way possible your work can give hope that that contract albatross, which can be at least partially be blamed for lack of a Halladay-Lee-Hamles rotation, can have some value?

Feb 23, 2010 08:10 AM
rating: 2
 
Lassaller

Matt, how did your study define option years? In other words, if a team pulls the trigger on a one year with an option, do you count this as a two year deal?

Feb 23, 2010 10:47 AM
rating: 0
 
BP staff member Matt Swartz
BP staff

I took out option years because that would definitely be a biased sample.

Feb 23, 2010 17:23 PM
 
Matthew Knight

While players may have "improved" in year two of a two year deal, I'd be interested to see how this compares with what they might have been expected to produce before the contract was signed. Say a player averaged 5 WARP in 2005-2007, then signed a two year deal and had WARPs of 2.5 and 3 in 2008-2009. It would look like he improved in year two, but really both years were a disappointment compared to what might have been expected by the signing club.

I also think you need to look at the contract year effect and compare how well players perform with how well they might be expected to perform. Then you could also include one year deals. Retro-PECOTA cards would be great for that!

Feb 23, 2010 12:43 PM
rating: 0
 
BP staff member Matt Swartz
BP staff

This is an interesting idea. Thanks!

Feb 23, 2010 17:23 PM
 
hjw099

This doesn't bode well for the New York Mets or for Jason Bay. Good read.

Feb 24, 2010 20:26 PM
rating: 0
 
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