December 8, 2009

Ahead in the Count

Shifting in the Third-Base Market

by Matt Swartz

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The recent signings of Placido Polanco and Chone Figgins by the Phillies and Mariners came in at relatively inexpensive deals compared to what the recent value of their performances might suggest. Polanco certainly seems like at least an average hitter for a third baseman, and is likely to play at least average defense at third as well. As I'll get into, the typical market rate for a third baseman of Polanco's abilities as a 34-year-old would be for about $25 million for a three-year deal. However, Polanco signed for $18 million plus a mutual option.

Performance Analysis

Valuing Polanco at $25 million involves first predicting his performance, and then valuing that predicted performance. His last three years seem to indicate a pattern of decline, but that is mostly a BABIP-related phenomenon. Although his EqA has fallen from .292 to .272 to .254, this is because of a lucky 2007 in which he had a .346 BABIP, followed by a .319 BABIP in 2008 that is more typical of his skill level (and close to his .314 career BABIP), and then followed by a .295 BABIP in 2009. His power skills remained steady with an ISO that barely changed (.110 in 2008 and .112 in 2009), and his K/AB was 7.4 percent in both years as well. He also got approximately the same number of walks (5.7 percent vs. 5.5) as well. The only real difference in production was his BABIP.

Of course, as players age many of their skills decline, so this could just be aging. There are a few reasons that BABIP declines with age. Most often, a BABIP change that is a skill-level change associated with age will come with a change in batted-ball rates. This is unlikely to be true of Polanco, as they all stayed more or less the same for him. Another reason is that players slow down. They have more trouble beating out infield hits, so infielders play back and they have trouble getting balls through the hole to the outfield. Indeed, Polanco's BABIP on ground balls fell from .273 to .237. However, his infield hit rate went up, from 4.4 to 8.1 percent. This increase in infield-hit rate coupled with his equivalent seven stolen bases and his EqBRR going only from 3.0 to 1.4 seem to imply that Polanco is no faster or slower than 2008. Polanco instead hit fewer balls into the hole-only 16 percent compared to his average over 2005-08 of 22 percent. Of course, another reason that BABIP tends to go down with age is that hitters lose their ability to hit the ball hard. However, Polanco's ISO have been very steady, going from .118 to .110 to .112 over the last three years, after hitting 10 home runs for the first time since he was a Phillie back in 2004. His line-drive rate actually went up this year, from 20.7 to 22.3 percent. Simply put, Polanco is probably not hitting the ball any softer than he used to, or getting to first any slower than he has in the past.

He also is unlikely to be losing much bat speed as his infield pop-up rate dropped from 6.8 percent to 6.0. Polanco's BABIP on line drives went down slightly, but line-drive BABIP is most closely associated with power. In fact, with Polanco's ISO staying constant and a slight uptick in home-run rate, his (albeit mediocre) power seems intact. His fly-ball BABIP took a small drop as well, but with similar power results and similar infield pop-up rates, as well as no major changes in how often he pulled the ball, this seems to be a small change that should correct itself in 2009. My BABIP model that I developed last year would predict him at around .319 in 2010. That seems likely to happen given all this information. With similar walk and strikeout rates, and a small uptick in homers due to Citizens Bank Park's friendly dimensions that strongly favor right-handed hitters, and it seems reasonably expect a line of approximately .305/.340/.420 from Polanco, good for about five runs or so above average with the bat.

Defensively, the various metrics seem to show a consensus that Polanco has been a plus fielder at second for the past three years, with his UZR going from 9.2 to 2.1 to 11.4 runs above average, and Baseball Info Solutions' Total Runs Saved attributed him with 11, 11, and 7 runs over the last three years. Both metrics seem to agree that when Polanco regularly played both second and third in 2002-2005, he was roughly an equivalent fielder at each position, but to be safe, let's project him as an average defender at third base, seeing as he has not played there for four years.

Valuation

Thus, we have a player who seems like a reasonable bet to be around five runs above average at the plate, and who plays average third base defense. To value this, there is some disagreement in the sabermetric community as to how to approach positional adjustment, particularly as it relates to second and third basemen. On one hand, Baseball Prospectus' VORP and WARP statistics evaluate positional adjustments by looking at how second and third basemen actually performed on average. The average OPS among third basemen from 2007-09 was about .020 points higher than the average OPS among second basemen (although this fell to about .005 points in 2009). Thus, VORP treats a second basemen's offense relative to a lower baseline than a third basemen's. However, Fangraphs' valuations treat second and third basemen with equal positional adjustments, on the basis that the average second basemen who moved to third, and vice versa, have historically performed about as well at each position. Thus, the scarcity according to that argument suggests that they are of equal value as players can be moved between positions if a team so chooses.

In reality, both are only models, and the best way to approach scarcity is to consider what the current opportunity costs are for teams out there. For the Phillies, the immediate alternative is Greg Dobbs, who would be about 5-10 runs below average at both hitting and fielding, and is a couple of runs below average at baserunning as well, so he could be about 20 runs, or two wins, worse than Polanco at third base. Taking Dobbs out of a pinch-hitting role would also require his being replaced by weaker hitters, which could put the Phillies at about 2.25 or 2.5 wins worse with Dobbs at the hot corner and Andy Tracy getting the pinch-hitting chances against right-handed pitchers than they will be with Polanco at third and Dobbs getting the pinch-hitting chances against right-handed pitchers. The third basemen on the free-agent market that are currently likely to sign deals for the major league minimum or so include a series of guys who hit and field about as well as Dobbs. Thus, within this exercise, the opportunity cost to signing no one for the Phillies was really about 2.25 wins.

Valuing this is tricky. Many sabermetricians currently estimate the value of a win on the free agent market by about $4.5 million. However, a recent article by Sky Andrecheck suggests that the average player with over six years of service time got about $6 million per win this season. The difference between the two models is that the $4.5 million estimation only looks at the first year of free agency. This is not a particularly useful way to look at multi-year deals, however, since most players decline in value over the course of a contract and treating all declines equally is misguided. Simply looking at Polanco's value in the first year of the deal and then multiplying by $4.5 million would get you to the opinion that he is worth $10 million per year. However, at 34 years old, he is likely to decline more rapidly over the three year contract than the average free-agent signing. Thus, Andrecheck's $6 million figure would seem more appropriate. Andrecheck has commented recently that $6 million was abnormally high for recent years, and these numbers suggest that perhaps $5.25 million may be a more reasonable estimate for the dollar value of a win given all of this, with about eight percent inflation in baseball salaries being a reasonable estimate for the following two years.

A simple estimation of Polanco's decline would say that his value may go from 2.25 wins this year to 1.50 wins in 2011 and 0.75 wins in 2012, and with the $5 million per win figure with eight percent inflation, that puts his value right around $25 million. Of course, the replacement level for third basemen may tick back up, and the mutual option for 2013 may have some value to the Phillies as well, so the value of the deal should fall close to $25 million on average.

By way of comparison Chone Figgins' deal is reportedly for four years and $36 million, with a vesting option to turn it into five years and $45 million. However, the Mariners surrendered a first-round draft pick in the process. Doing a similar analysis to the one above, I believe that the typical market for Figgins would have netted him over $10 million a year for a four-year deal, with a similar vesting option and as a Type-A free agent. Adrian Beltre does not have an obvious suitor at the moment, although a few other teams certainly seem possible. The economy is too simple an explanation for this phenomenon of players signing team friendly deals at third base. The reality is that salaries do not deflate by 20 percent for many other professions during a recession, so why should those of third basemen? The explanation is more subtle.

The Imperfect Market For Free Agents

The typical laws of supply and demand that you may have been taught in your college microeconomics class are ill-suited to explain a market like that of free agents. The primary assumption of the introductory model of supply and demand assumes that neither buyers nor sellers can affect the price of labor, which is not true in this case due to the size of the market. There are only a few third basemen and a few openings in any given offseason, so the market is determined differently. Free agents are bid for in an auction format where typically the highest bidder wins the auction for a player's services. The amount that a team is willing to pay is based on the marginal gain in wins that the team would get by adding the player multiplied by the dollar value of a win to that team.

The dollar value varies greatly from team to team. The Yankees certainly gain more by increasing their win total by one than the Royals. Going into the season, the Yankees increase their odds of making the playoffs by about five percent by adding a one win player to their team; the Royals probably add about one percent to their playoff odds by adding one win to their team. The primary gain in revenue from improving your team is from getting to the playoffs, so the dollar value is different and market sizes are different, too. Similarly, the Twins and Rays behave as though a win adds fewer dollars even though they are typically on the playoff cusp as well. Therefore, the major buyers to be considered are teams that have a legitimate shot at making the playoffs and mostly those from the so-called larger markets.

The teams who should actually be considered buyers can be further limited to teams who would actually stand to gain from adding the player. The Cardinals were simply not going to be players for Mark Teixeira last offseason, no matter how much their marginal dollar gain from adding a win is, simply because Teixeira does not add wins to their club by replacing Pujols. The Cardinals' "replacement level" for first base is quite a bit higher than the level that the Yankees considered when inking Teixeira to his eight-year deal last winter. Pitchers actually have more stable prices for this reason-because the average fifth starter for teams is relatively similar, so the gain in wins by adding John Lackey will not vary as much among contenders as the gain in wins by adding, say, Adrian Beltre.

The market for position players is a little different due to this subtlety. The replacement level for each team at third base is different. The Mets do not stand to gain much by adding Beltre even if they do have a reasonably good chance of being competitive next year and thus have a higher dollar value for wins added (though, I should note that if I find the voodoo doll collection I used last season, they may not actually be competitive after all).

Instead, if there were three legitimate free-agent targets out there at third base, the replacement level used to determine the baseline from which calculations will be counted will be approximately equal to the production value of the team with the fourth-worst internal option out there as teams bid for free agents.

Manipulating the Imperfect Market

Last offseason, for example, the number of corner outfielders and designated hitters available far exceeded the number of openings out there for competitive, large-market teams with usual "replacement level" designated hitters, and left and right fielders. As a result, the prices came way down and Adam Dunn ended up signing with the Nationals according to their value of him-which was far less than he would have received in a different market. The Phillies targeted Raul Ibaņez as their left fielder, and paid a price higher than they would likely have paid if they waited. Of course, Ibaņez had a strong enough year that it is hard to question the Phillies for choosing him as a target, but it is likely that they paid the market rate from the previous year's market rather than the rate at the time.

This season, the Phillies did something quite different. General manager Ruben Amaro Jr. seemed to have this in mind when he recently said:

There are going to be a lot of free agents, and I don't know how many teams are going to be pouncing on the third basemen. I don't know how many third basemen are needed around the league... I just think there are more players than there are seats in this offseason. We could have misread the market, but we feel like there are more third basemen available than there are third-base positions to be filled.

The competitive teams in reasonably large markets that could stand to upgrade at third base going into this offseason are the Phillies, the Mariners, and perhaps the Cardinals and Angels (although David Freese and Brandon Wood, respectively, represent somewhat reasonable options that may be preferable to play instead). The Twins do not behave as though they have a very high marginal dollar gain per win, and so they are unlikely to pay the typical market rate for third basemen. The Astros and Orioles certainly could have openings at third base, and have occasionally behaved as though they believe they will be competitive. However, it seemed that the obvious third basemen on the market were Chone Figgins and Adrian Beltre, and the obvious openings for competitive teams were the Phillies and Mariners, and perhaps the Angels and Cardinals. This seemed like a typical amount of supply and typical amount of demand, where the replacement level for third basemen is approximately two wins below average. The internal options for the Phillies and Mariners were almost certainly right around there, and the Angels were perhaps not far behind them. The Cardinals seemed to have a better alternative, however, and among the Cards, Orioles, and Astros, they were unlikely to push the bidding all that high.

The relatively simplified model of free agency that I have described above assumes that the supply of free agents at each position is fixed in any given offseason, and that certainly is how Amaro described the model he has in mind above. However, many players play multiple positions, and this year's third-base market contained three guys who could play multiple positions. Placido Polanco has played both second and third base, and Mark DeRosa plays both of those positions and the outfield. Figgins has played a few positions, too, but after providing outstanding defense at third base last year, he seemed unlikely to switch, winding up 16.3 runs above average according to UZR, and 31 runs above average according to Baseball Info Solutions' Total Runs Saved.

Early rumors this offseason stated that the Phillies were craving DeRosa to play third base for them; then they added Polanco instead. The second-base market is relatively weak this offseason, and by effectively enticing Polanco to be on the third-base market-and then signing him-the Phillies ended up moving the replacement level that the market interpreted at third base upwards and thus the price downwards. Soon after they did, the Mariners signed Chone Figgins at a good deal for themselves, and now the bidding for Adrian Beltre is pretty much based on how much the Angels, Cardinals, Astros, and Orioles want him. That is quite different than if Polanco had signed as a second baseman, and the Phillies were in the midst of the bidding for Figgins and Beltre. By acting early, I'd argue that the Phillies got themselves a deal. They also got the Mariners a deal as well, and whoever signs Adrian Beltre may get a deal if Scott Boras does not have any tricks up his sleeve. What the Phillies did was add to the supply of third basemen by changing Polanco's position, and when they supply increases, the price goes down.

The Phillies typically give nonsensical reasons for which players they want. Amaro credited Polanco for being a professional hitter who makes "quality outs" in his announcement of the signing, and multiple sources cited the Phillies' desire for University of Pennsylvania graduates as a leading reason that they wanted Mark DeRosa. Were those the reasons the Phillies really wanted the market to treat those guys as third basemen? It is hard to believe a team that has won the past two National League pennants would be so foolish in their free agent evaluation-really hard to believe.

Matt Swartz is an author of Baseball Prospectus. 
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