How Big a Bump?

In the Yankee Analysts' big prediction shindig, the lone blogger to choose the Yankees as AL East winners was William J., who defended his selection (not that it needed defending) in the comments:

I can understand why the Red Sox are so fashionable, but when I balanced both sides of the equation, I didn’t see the drastic shift so many else do. Sure, Crawford and AGon are great additions, but I don’t think people realize how good Beltre was. VMart was also very good. Also, too much is being made of Youk and Pedroia being healthy. Not only did those two play 175 games last year, but both were having career years. Boston will gain a bump from having them all season, but not as much as people are implying. Also, how Youkilis handles the switch to 3B could be an issue.

This is something I alluded to in the big post about Fangraphs' new aggregate defensive measure, but it was overlooked in the resulting continuation of the Jeter brouhaha, so I want to address it as a separate item here:

Is it true that having Adrian Gonzalez and Carl Crawford on board will essentially offset losing the value of Adrian Beltre and Victor Martinez, especially when considering the likely defensive dropoff from Beltre to Youkilis at third and Youkilis to Gonzalez at first?

At first blush, this makes a lot of sense. No one, not even Beltre, is repeating Beltre's 2010 performance, after all, and it's not like Gonzalez is replacing a scrub at first; he's replacing a slugger who is arguably as good with the bat and better with the glove at that position. The Sox may actually decline offensively and defensively at the corners, while Crawford basically replaces Victor Martinez's production with the bat and simply helps make up for the likely shortcomings of Martinez's replacements.

Let's try to quantify some of this feeling.

(I want to note quickly here that this post isn't meant as a strict rebuttal of William's points; I've been meaning to do this post for a while, and his comments provide as good a jumping off point as any.)

Here are some 2010 numbers, all courtesy Fangraphs, since we'll be using their defensive data:

[Quick glossary: OPS you know; wOBA is weighted On Base Average, a measure that combines most offensive contributions and scales them to on-base percentage, with .321 being league average in 2010, by using linear weights); wRC+ is weighted Runs Created Plus, or wOBA adjusted for park effects and league average and scaled so that 100 is league average, essentially to wOBA what OPS+ is to OPS; Runs Above Average takes those wOBA numbers, adjusts for park and league and converts them to the runs/wins-added format. The defensive stats I've gone over before, but they are Defensive Runs Saved, Total Zone, Ultimate Zone Rating and Aggregate Defensive Rating. I think we all know RAR/WAR, Runs and Wins Above Replacement, which totals all these values, adds or subtracts value for playing time and position, and converts the runs into wins. The Runs Above Average I use under offense is offense-only and park adjusted. The RAA I use in the total is the total of offense, defense and position credit as calculated for WAR, which means it uses UZR only for the defensive component, not the ADR hybrid I prefer.]

Adrian Beltre

• Offense: .918 OPS, .390 wOBA, 141 wRC+, 33 RAA (offense only)
• Defense: +10 DRS, +10 TZ, +13 UZR, +11 ADR
• Total: +48 RAA (offense, defense and position as measured for WAR), +68 RAR, 7 WAR

Kevin Youkilis

• Offense: .975 OPS, .419 wOBA, 160 wRC+, 32.5 RAA
• Defense: +4 DRS, +3 TZ, +1.5 UZR, +3 ADR
• Total: +26 RAA, +40.5 RAR, 4 WAR

Now the catch here is that Youkilis missed the final two months of the season, affecting all the runs-based numbers we see here. Even so, he still provided essentially the same offensive value as Beltre did over the whole year, and he would have finished, assuming he had kept the same level of production over the final two months, within 1 WAR of Beltre, the difference accounted for solely by the difference in the fielding adjustment between the two. They provided equal value in a vacuum, but one played first base and one played third, so the third baseman understandably is the better asset to have.

On offense Youkilis has provided +35.5, +39 and +32.5 (possibly +43 if healthy) runs above average over the past three years, matching or exceeding Beltre's 2010 every time. Simply average the last three seasons together, and you get roughly +36 runs, three better than Beltre's 2010. Average the first two with the prorated version of 2010, and you get +39, six runs better than Beltre. I think it's safe to say that a healthy Youkilis in 2011 has a slight edge on offense over the 2010 Beltre. 

However, Youkilis on defense can't touch Beltre, who has better defensive numbers at the harder position than Youkilis does at the easier one. ADR had Beltre as a +11 defender in 2010. Youkilis over his career at third has been a +4 defender. He was -1 in the infinitesimal sample size of 15 innings last year, but a +6 and a +2 in far more substantial (though still limited) playing time replacing Mike Lowell in 2008-09. UZR rates him a +7 defender per 150 games over his career. I wouldn't go that far, but calling him league average seems fair.

Add that all together, ignoring durability and position credits (we're assuming everyone's going to be healthy, and we're not comparing across positions) and you get this for the Sox' third base situation:

• 2010 (Beltre): 33 RAA (offense) + 11 ADR (defense) = +44 RAA 
• 2011 (Youks): 38 RAA (proj. offense) + 0 (proj. defense) = +38 RAA

The Sox lose six runs by replacing Adrian Beltre with Kevin Youkilis. But what about replacing Youkilis with Adrian Gonzalez?

As a refresher, I've reposted Youkilis' 2010, so we don't have to keep scrolling up.

Kevin Youkilis

• Offense: .975 OPS, .419 wOBA, 160 wRC+, 32.5 RAA
• Defense: +4 DRS, +3 TZ, +1.5 UZR, +3 ADR
• Total: +26 RAA, +40.5 RAR, 4 WAR

Adrian Gonzalez

• Offense: .904 OPS, .378 wOBA, 143 wRC+, 38.5 RAA
• Defense: 0 DRS, +9 TZ, +1 UZR, +4 ADR
• Total: +26.5 RAA, +51 RAR, 5 WAR

 Youkilis had the better rate stats — yes, for all the excitement over Adrian Gonzalez, he may be the Red Sox' second-best hitter — but the lost playing time for Youkilis means Gonzalez provided more value. The question, as it has been all offseason, is to what extent Petco Park depressed Gonzalez's numbers (and, secondarily, to what extent his shoulder injury affected his hitting in 2010). Setting aside that discussion for now, Gonzalez has produced +30.5, +48.5 and +38.5 batting runs above average (park adjusted) in the past three years, compared to Youkilis' +35.5, +39 and +32.5 (+43). Very similar, except for Youkilis' injury, which actually happened and therefore means Gonzalez is likely to outproduce in 2011 the value Youkilis provided in 2010, especially considering he seemed to have reached a new level two years ago. Nevertheless, average them together, and you get Gonzalez +39, Youkilis +36.

On defense, Gonzalez has posted an ADR of 0, +10 and +4, while Youkilis has been +2, +7, +3, essentially the same, each with an average around +4.5. That gives us this:

• 2010 (Youks): 26 RAA (offense) + 3 ADR (defense) = +29 RAA 
• 2011 (A-Gon): 39 RAA (proj. offense) + 4.5 (proj. defense) = +43.5 RAA

So the six runs the Sox lose from replacing Beltre with Youkilis is swamped by the 14.5 runs they gain by replacing Youkilis with Gonzalez. That's a net gain of 8.5 runs, very close to one full win of improvement. That's more because Youkilis was hurt last year and will be replaced by a slightly worse but hopefully healthier hitter and nearly identical fielder in Gonzalez, while the healthy Youkilis will replace the lesser-hitting, better-fielding Beltre at third.

Figuring out the Martinez-Crawford situation is trickier. We could just look at each player in a vacuum, but they play different positions and are replacing/will be replaced by different players, who themselves provide(ed) value. So let's tackle left field first.

The Red Sox essentially split 127 of their games in left field between three players who are not on the 2011 Opening Day roster: Daniel Nava, Bill Hall and Jeremy Hermida, with another 30 games going to this year's fifth outfielder, Darnell McDonald. Those four played 157 of 162 games. Crawford played 154 games last year, so I don't think it's unfair to take the line of all Red Sox left fielders in 2010 and compare them against Crawford alone in 2011.

McNavahermihall (and friends)

• Offense: .695 OPS, .312 wOBA, 88 wRC+, -10.5 RAA
• Defense: -17 DRS, -5 TZ, -8.5 UZR, -9.5 ADR (self-calculated)
• Total: -34 RAA, -4.5 RAR, -0.5 WAR

Yeah, that's brutal. The Red Sox received replacement-level performance out of left field for the entire season.

Carl Crawford

• Offense: .851 OPS, .378 wOBA, 139 wRC+, +32.5 RAA
• Defense: +14 DRS, +10 TZ, +18.5 UZR, +14 ADR
• Total: +44 RAA, +66 RAR, 7 WAR

Crawford in 2010 was more than seven wins better than the Red Sox' left fielders. That's the difference between 89 and 96 wins, or a game better than the gap between the third-place Sox and the wild-card Yankees.

Of course, Crawford had a career year last season. On offense, he's been worth +18.5, -2, +23.5, +32.5 runs over the past four seasons. I'm inclined to throw out 2008, as it's clearly not indicative of his talent level (the only season in six years below +16.5). Averaging the other three, we get +25 runs above average. That seems about right to me.

Defensively, Crawford hasn't been rated as anything but elite for quite a while: +15, +18, +14 in the past three years, a +15.5 average. 

• 2010 (Slop): -10.5 RAA (offense) -9.5 ADR (defense) = -20 RAA 
• 2011 (Craw): +25 RAA (proj. offense) + 15.5 (proj. defense) = +40.5 RAA

Even dialing back Crawford's career year, he is expected to be an astounding six wins better than the horrendous Sox left fielders of 2010. If the Red Sox changed nothing about their team other than adding Crawford, they would have made up the gap that existed in 2010 between them and the playoffs.

But they didn't "change nothing," and they lost a significant piece in Victor Martinez, who will be replaced by a platoon of Jarrod Saltalamacchia and Jason Varitek.

Victor Martinez

• Offense: .844 OPS, .364 wOBA, 123 wRC+, +16 RAA
• Defense: -7 DRS, -8 Fans Scouting Report, -6 BtBS (no other metrics measure catcher defense)
• Total: +20.5 RAA, +38.5 RAR, 4 WAR

It's worth noting here, too, that Martinez would have provided more value, probably another win, had he not missed a month with a broken thumb. The combination of his and Jason Varitek's simultaneous injuries led to the Red Sox receiving sub-replacement value from their replacements.

There's no good way to judge the prospects of a player who has needed three seasons to compile a full year's worth of plate appearances. Likewise, Varitek's first season as a part-time player was just last year, and he spent part of it on the DL with a fluke injury. I'd go with straight projections, except that Salty's vary widely, from an 82 wRC+ courtesy of ZiPS to a 105 projected by Bill James. Varitek's are a little more stable.

The Sox plan to use the two largely as platoon partners, with Saltalamacchia posting a .765 career OPS against righties, and Varitek with an .860 career OPS against lefties (including .800 or better each of the last four seasons). That would appear to maximize their strengths, so forgive me if I cherry pick a little and select the most optimistic of both players' projections. The fact remains that no one is projecting them as any better than league average, so I don't feel like we're doing an injustice to Martinez here, especially considering both players would have to underperform their career platoon averages to meet these projections:

• Salty 2011 (James): .745 OPS, .329 wOBA, 105 wRC+, 2 RAA
• Varitek '11 (James): .710 OPS, .314 wOBA, 95 wRC+, -1.5 RAA

On defense, Saltalamacchia has been rated around -3, -4 over the course of his career, while Varitek has also been considered slightly below average. Both men were considered essentially average last year by both DRS and the Beyond the Box Score rankings. They'll be splitting time, so I'm going to give them both -2 for a combined total of -4, which would be a drop of seven runs from their combined totals in 2010, according to BtBS, four from their combined DRS rating and even with the Fans Scouting Report assessment from last year. Martinez, meanwhile, was at +0.5, -7 and -2 over the past three years, numbers that broadly agree with a contention that he is not as bad on defense as usually assumed but still below average. That's an average of -3.

[You can argue the metrics are especially unreliable regarding catcher defense, and that these ratings are too optimistic, but let's not forget that if they are too optimistic about these two, they are also likely too optimistic about Martinez, who looked terrible early in 2010. I think in this case the Sox are will likely not receive defense much worse than what they received from Martinez.]

• 2010 (VMart): +16 RAA (offense) -7 ADR (defense) = +9 RAA 
• 2011 (Saltytek): +.5 RAA (proj. offense) – 4 PSF (proj. defense) = -3.5 RAA

The Sox drop 12.5 runs by going from Martinez to a platoon of Varitek and Saltalamacchia — not insignificant but nowhere near the increase of 40.5 runs they gain from replacing the sub-replacement dreck of 2010 in left field with Carl Crawford. In all, dropping Martinez and "replacing" him with Crawford nets the Red Sox 28 runs — nearly three wins.

To summarize:

• Beltre 2010 to Youkilis 2011: -6 runs
• Youkilis 2010 to Gonzalez 2011: +14.5 runs
• Martinez 2010 to Salty/Tek 2011: -12.5 runs
• Filler 2010 to Crawford 2011: +40.5 runs
• TOTAL 2010 to TOTAL 2011: +36.5 runs

That's between three and four wins gained, in order of significance, by

1. Replacing four replacement-level left fielders with Carl Crawford.
2. Replacing an injured Youkilis' production with a healthy Adrian Gonzalez.
3. Kevin Youkilis being healthy all season long and offsetting the significant loss of Beltre's production at third.

In short, the massive upgrades in health and production at first base and left field more than offset the downgrades at catcher and third base — and are only part of the reason why the Sox are expected to be a much-improved team in 2011.