Baseball's Most Valuable Players through April and May

We are now two months into the 2012 season. Matt Kemp's incredible April, Albert Pujols' miserable April, Josh Hamilton's dominance in his contract year, and many more stories have been all over baseball's headlines. Instead of writing a boring re-cap of those stories that everyone has read before, I set out to discover which players have been the most valuable over the course of April and May.

**Spoiler Alert: It's not Josh Hamilton**

To calculate a player’s overall value I used two measures, WAR (wins above replacement) and salary. WAR’s page in Fangraphs’ sabermetric library, describes the statistic as a calculation of "the value a team would lose if they had to replace that player with a ‘replacement player’." At this moment in time, WAR is the best statistic for incorporating a player's entire impact (value) on the diamond.

Players get paid for their on-field contributions. Sometimes, very often in fact, there is a discrepancy between the amount of money a player gets paid, and his actual output in games. Thus, the most valuable players in baseball are the ones who contribute the most on the field value (high WAR), for the smallest amount of pay (low salary), essentially WAR/$. Baseball Prospectus already employs WARP/$ as a statistic on their team compensation tables. However, they do not offer leaders in that statistic across the 30 teams in baseball. I also prefer Fangraphs' calculation of WAR over the BP's version of the statistic.

So I created my own leaderboards based off of fWAR. I split the respective top-10's into batters and pitchers. WAR is a statistic that was created not only to incorporate every aspect of player's performance, but also to make the comparison between batters and pitchers as close to "apples to apples" as possible. Thus, a leaderboard for all players would most likely work, but I decided to separate the positions anyways.

Batting Leaderboard:

Hitters	WAR	Salary ($ in Mill.)	WAR/$
1. A.J. Ellis	2.5	$0.49	5.10
2. Austin Jackson	2.5	$0.50	5.00
3. Mike Moustakas	2.3	$0.49	4.72
4. Giancarlo Stanton	2.1	$0.48	4.38
5. Josh Reddick	1.9	$0.49	3.92
6. Mike Trout	1.8	$0.48	3.75
7. Alejandro De Aza	1.8	$0.50	3.64
8. Jason Kipnis	1.7	$0.48	3.53
9. Jose Altuve	1.7	$0.48	3.52
10. Mark Trumbo	1.7	$0.50	3.40

A.J. Ellis has been the most valuable hitter through the first two months of the season. Wait, what?

The Dodgers' catcher has come out of nowhere to be one of the best players in baseball. The 31 year-old career minor leaguer has posted an outstanding OBP (.430, 1st among catchers) and wRC+ (154). His 16.3% BB-percentage leads all catchers, but his walk rate was helped by him spending a good portion of the season hitting in eight spot of Los Angeles' lineup, ahead of the pitcher. It will be interesting to see if he'll continue to walk at such a high rate as the Dodgers have now moved Ellis out of that spot in their lineup. Ellis' start was listed among BP's top 11 Surprising Early-Season Stats, earlier this month.

Jackson was on pace to lead this list, but he went on the DL with an abdominal strain on May 17th. Jackson is known primarily for his defense, but his wRC+ (170) ranks second among CF's, only trailing Hamilton.

Early this month, Bradley Woodrum of Fangraphs labeled Moustakas the luckiest hitter in baseball, based on the huge difference between his BABIP (.337) and his xBABIP (.244) at that time. Since then his BABIP has moved down closer to his xBABIP now at .295. Luck or no luck, the Royals' third baseman has had a very productive start to this season.

Reddick has looked like Billy Beane's best acquisition of the off-season. His 1.9 WAR is more than that of Seth Smith, Jonny Gomes, Yoenis Cespedes, Collin Cowgill, and Coco Crisp combined. He's also hit 14 of Oakland's 40 home runs.

If the season had started in May, Trout and Stanton would sit comfortably atop this leaderboard. Stanton's health caused his April to become a quasi-spring training; his value has come entirely from May (-0.1 WAR in April). Trout was not called up to the bigs until April 27th and he still has yet to accumulate enough PA's to be a "qualified" hitter, but since his call-up Trout has been as good as anyone in baseball. The 20 year-old's combination of speed (8 steals, 4 infield hits), defense (4.9 UZR), and bat (146 wRC+) have been lethal.

De Aza's game is completely built on speed, most of his value comes from his work on the base paths and range in the field. Two of the last three players on this list are hitting like elite second basemen. Altuve and Kipinis rank second and fourth respectively among second basemen in wRC+, ahead of household names like, Robinson Cano, Dustin Pedroia, Ian Kinsler, Ben Zobrist, and Brandon Phillips. Trumbo jumped onto this list this morning, after homering last night for the fourth night in a row. The now-utility man has found the ability to couple patience with power this season, leading to some startling results.

Pitching Leaderboard:

Pitchers	WAR	Salary ($ in Mill.)	WAR/$
1. James McDonald	2.1	$0.50	4.18
2. Chris Sale	2	$0.50	4.00
3. Lance Lynn	1.4	$0.48	2.90
4. Brandon Beachy	1.4	$0.50	2.83
5. Wade Miley	1.1	$0.48	2.29
6. Felix Doubront	1.1	$0.48	2.27
7. Juan Nicasio	1.0	$0.48	2.08
8. Jake Arrieta	1.0	$0.49	2.05
9. Bud Norris	0.9	$0.51	1.96
10. Madison Bumgarner	1.0	$0.56	1.79

The batting leaderboard boasted a good deal of familiar names, or at least names that are rising in popularity; while the pitching leaderboard really does not. Sale gets talked about a fair amount mainly because of his see-sawing between the White Sox' bullpen and rotation, and his unbelievable 15 K performance this week against the Rays. Sale has been very good, but he hasn't been the most valuable pitcher through the first tow months of this season; that title goes to the Pirates' James McDonald.

McDonald has received very little attention, in all likelihood because he plays for the Pirates. The only story I can recall reading about him was by Baseball Nation's Grant Brisbee. Brisbee noted that McDonald's trade from the Dodgers to Pittsburgh may have been the worst trade of the last five years. I think most readers would be surprised to see McDonald near the top in a bunch of statistical categories based on just on-filed performance and don't take into account his low salary. He is 4th in fWAR (2.1), ERA (2.20), and FIP (2.41). Also t-17th in xFIP (3.29 same as Clayton Kershaw, Dan Haren and Johan Santana).

Lynn and Beachy have gotten off to scorching hot starts. Lynn won his first six decisions and has posted a 2.54 ERA and 3.02 FIP to boot. Beachy leads baseball in ERA (1.77), but the fact that his K/9-rate has dropped by almost four strikeouts from last season makes me wary that his success is sustainable.

The bottom six names on this list were even surprising to me. Miley started the season in Arizona's bullpen, but has posted a 2.27 ERA and 2.89 FIP since becoming a starter. Miley's HR/9 (0.21), as a starter, is a candidate for regression, especially because he'll be starting the majority of games in home run-friendly Chase Field. Doubront was not supposed to be the Red Sox best pitcher this season, but he's been just that, posting an xFIP of 3.53 thus far.

The Rockies have been awful through the first two months, and Nicasio's ERA (5.11) is almost just as bad. Nicasio's peripherals paint a different story; however, as his K/9 (8.47) is good and SIERA (3.77) has been serviceable. The Orioles' Arrieta sports a bad ERA (5.37) that also isn't a great reflection of his performance based on peripherals. Arrieta looks like the Orioles' worst starter based on traditional statistics, but his xFIP- (85) and SIERA (3.57) grade him as an above average pitcher.

Much the opposite of Arrieta and Nicasio, the Astros' Norris saw results that reflected his "true" performance. Norris' ERA (3.34) and SIERA (3.52) are very similar which bodes well for the righty moving forward in 2012. Bumgarner probably is the most talented pitcher on this list. The lefty has been getting better results than his peripherals as his K-rate (6.41) is down from last season, but so is his BABIP (.257) and ERA (3.14). His FIP (3.66) is up by a full point from 2011.

There's an obvious commonality with all twenty players on these leaderboards; they are all pre-arbitration players. Players with less than three years of Major League service are eligible for the league minimum salary; thus, the denominator of their WAR/$'s are significantly lower than free-agent eligible players, and even those eligible for arbitration. So it's to be expected that any WAR coming from players who make replacment-level salaries would result in an excessively high WAR/$.

Last season one WAR was worth 4.5 million on the open market, according to Fangraphs. Based on what I've seen on their value leaderboards, they're using the same figure for 2012. Based on that calculation a WAR/$ of 0.22 is the market standard; players with a WAR/$ above that would be considered valuable, while those below that figure would be costing their teams money.

The players on these leaderboards have WAR/$'s well above the market standard. It's tough to measure them against the market-rate though, because they aren't market eligible players yet. It could be argued that the value of players who are eligible for league minimum salaries should be evaluated differently than the value of players who have enough experience to not be eligible. A set of three different leaderboards based on the three salary eligibility ranges, could make some sense, but I think that's taking something a way from the extremely valuable pre-arb players.

Pre-arb players shouldn't be faulted for achieving the same amount of on-field value that a FA-eligible player can produce, just because their salaries are so low. It's hard to argue that AJ Ellis' 2.5 WAR isn't more valuable to the Dodgers than the 2.6 WAR that Carlos Ruiz has put up for the Phillies, at least financially, because Ruiz makes over $3 million more.

Their salaries are low for a few reasons.

It's part of of baseball's system for teams to make money off of strong young talent, before those players make money off of their teams as they pay for their decline during FA-eligible years. Players with less than three years of MLB experience are just that, inexperienced. Proven players get paid over unproven ones, almost every single time, no matter how much potential the unproven player may have. And finally, rules are rules. Stanton would make a ridiculous sum of money on the open market at the moment, but the Marlins are well within their right to pay him less than $500k for his powerful and productive services.

Another thing to keep in mind is that MLB franchises are businesses. Even teams like Boston, New York and Philadelphia can't acquire all of their wins through the free agent market. Young and extra-valuable players like those listed on these leaderboards are crucial to any winning team, because they allow for investment into proven (more-costly) players who can further help the team.

Laggards:

Talking about high-value/low-cost is an interesting topic, but talking about low-value/high-cost players can be just as much fun, if not more. Unfortunately, using a WAR/$ analysis to find the least valuable players in baseball is problematic. It works really well for low positive WAR players (Barry Zito has an awful 0.01 WAR/$), but many of baseballs low-value players are below-replacement level, with negative WAR's. For example:

Player X: -0.5 WAR with $5 million salary; -0.1 WAR/$

Player Y: -0.5 WAR with $10 million salary; -0.05 WAR/$

Player X has a lower WAR/$ than Player Y, so you would assume he was less valuable (or more costly), but in fact Player Y is clearly less valuable. A $/WAR analysis with players who cost their team more than $4.5 million per WAR, also would be usual but again negative WAR's complicate things. Thus, creating complimentary value "laggard"-boards is difficult.

I then thought to convert the low-value lists into a "most costly" leaderboard. For example, Vernon Wells currently has a WAR of 0.0, but gets paid a salary of $21 million by the Angels. We are now just over 30% of the way into the 2012 season (I used 31%), Wells' services have cost the Angels $6.5 million thus far for zero value (net cost of $6.5 million). But that nasty negative WAR complicates matters even in this case, but not as strongly. For instance Seattle's Chone Figgins has been worth -1.0 WAR for $9.5 million annual salary ($2.945 million thus far). If we assume that a every win below replacement costs a team $4.5 million then Figgins has cost the Mariners $7.45 million. Under this assumption despite Wells making over $10 million more than Figgins, his ability (ha!) to stay at replacment level rendered him less costly than Figgins, a player well below that level.

However the assumption that a win below replacement costs as much as a win above replacement is worth is kind of ridiculous. My guess is that a -1.0 WAR hurts a team much more than 1.0 WAR helps it, because replacement level play is cheap and easy to come by, making negative WAR players very costly; especially if, like Figgins, they're making well above the league minimum salary. I honestly don't know how much more a win below replacement costs a team in value above the current $4.5 million market value, making this analysis nearly impossible.

Also players such as Ryan Howard, Chase Utley and Carl Crawford who will make anywhere between $15-$21 million this season but did not play a game during April or May. They were not able to contribute any value to their teams, but came at a very high cost. Should these players be included in a list of low-value/high-cost players through the first two months? Probably not, but that doesn't mean they shouldn't be considered. Utley and Howard make up roughly 1/5 of the Philadelphia's payroll, but they have been of no use to the team.

Despite the fact that the $4.5 million assumption probably doesn't work for negative WAR, my best shot at the laggardboards used this "net cost" as a way to list the ten hitters and pitchers laggards in April and May, who actually appeared in games (the Crawfords of the worlds were excluded)>

Batting Laggards:

Hitter	WAR	Salary ($Mill)	Net Cost
1. Chone Figgins	-1.0	$9.50	$7.45
2. Marlon Byrd	-1.0	$6.50	$6.52
3. Vernon Wells	0.0	$21	$6.51
4. Jason Bay	-0.1	$18.13	$6.07
5. Michael Young	-0.2	$16	$5.86
6. Rickie Weeks	-0.4	$10	$4.90
7. Adam Lind	-0.7	$5.15	$4.75
8. Erick Aybar	-0.6	$5.08	$4.27
9. Mark Reynolds	-0.4	$8	$4.13
10.Aubrey Huff	-0.2	$10	$4.00

I'm sure the inclusion of Figgins, Wells and Bay on this list surprises no one. Lind and Byrd have either been cut or essentially dumped from their teams after their awful starts. But Weeks and Young would be considered stars by most people's standards; yet, have been among the least valuable position players thus far in 2012. Aybar's start has to make the Angels' concerned about the extension they gave him before the start of the season.

Pitching Laggards:

Pitchers	WAR	Salary ($Mill)	Net Cost
1. Barry Zito	0.2	$19	$4.99
2. Ervin Santana	-0.3	$11.20	$4.82
3. Jason Marquis	-0.7	$3	$4.08
4. Jeremy Guthrie	-0.3	$8.20	$3.89
5. Ubaldo Jimenez	-0.5	$4.20	$3.55
6. Carlos Marmol	-0.3	$7	$3.52
7. Chad Qualls	-0.7	$1.15	$3.51
8 .Brett Myers	0.2	$12	$2.82
9. Heath Bell	-0.1	$7	$2.62
10.Clay Bucholz	-0.3	$4	$2.43

Unsurprisingly, Zito leads this list as his contract, like the one of Wells, has been the butt of jokes for years now, and 2012 should be no different. Santana was supposed to be the Angels' fourth ace, but has instead fallen in love with the home run ball.

The fall from grace of Jimenez is troubling, especially because the competitive Indians need Ubaldo to be Ubaldo if they're going to continue to contention in the AL Central. High-priced relievers (Bell, Myers, and Marmol) and completely awful ones (Qualls) also find themselves amongst the most costly players thus far. Colorado was expecting Guthrie to be an ace when he was brought in this off-season, he's been just the opposite of that.

Bucholz was not supposed to be out-pitched by the likes of Doubront this season, but he was out-pitched by everyone on the Red Sox staff during April and May.

If anyone has ideas for a way to discover who cost their team the most money this season outside of just negative WAR/high cost players, I'm open to suggestions

Many thanks to Cot's Contracts and Fangraphs for making this post possible

You can follow Glenn on twitter @Baseballs_econ