## Were the Royals Better Than Their W-L Record?: Looking at Pythagorean Expectations and WAR

There has been some buzz about the Royals Pythagorean Expectation in the comments on this blog and other blogs. The Royals Pythagenpat record is easily found on Baseball Prospectus, along with 2nd and 3rd order W-L records. These standings use the amount of runs a team allowed compared to how many runs a team scored to estimate what the team's win-loss record should have been. The Royals Pythagenpat record suggests that team played better than it's 71-91 record indicates; all three formulas say the Royals "should have" won about 78 games instead of the 71 they actually won.

WAR can also be used to calculate how many wins a team "should have" one. Over at Bluebird Banter, jessef looks at the relationship between fWAR, rWAR and wins. You can find the graphs illustrating the relationship if you click the link , but the equations for the linear models are below:

The linear model describing the relationship between rWAR and wins is:

Wins = 53.8 + 0.88(rWAR)

The linear model describing the relationship between fWAR and wins is:

Wins = 45.2 + 0.93(fWAR).

While neither model is perfect, both are accurate enough to be useful in determining how many wins WAR would project a team to win. The rWAR model assumes a replacement team would win 54 games (baseball-reference claims a replacement team would win 52 games, so we will use both) while the fWAR model believes a replacement team would only win 45 games. If you add a teams total WAR and multiply it by the coefficient, you should get a reliable estimate on how many games team won. Tables breaking down how many wins each Royal was worth and analysis is located after the jump.

The first table is for the position players plus pitcher defense and hitting, the second table is for pitching.

 Position Player fWAR rWAR Catcher 2.9 1.7 Salvador Perez 1.4 1.1 Matt Treanor .9 .4 Brayan Pena .5 .3 Manuel Pina .1 -.1 First Base 1.5 1.2 Eric Hosmer 1.6 1.3 Kila Ka`aihue -.1 -.1 Second Base 1 -.3 Chris Getz 1 .5 Johnny Giavotella 0 -.5 Mike Aviles 0 -.3 Shortstop 2.2 2 Alcides Escobar 2.2 2 Third Base 1.3 1.4 Mike Moustakas .7 .5 Wilson Betemit .5 .9 Yamaico Navarro .1 0 Leftfield 7.6 6.2 Alex Gordon 6.9 5.9 Mitch Maier .7 .3 Centerfield 4.5 3.2 Melky Cabrera 4.2 2.9 Jarrod Dyson .3 .3 Right Field 3 2.8 Jeff Francoeur 2.9 2.7 Lorenzo Cain .1 .1 Designated Hitter 1.8 2.4 Billy Butler 1.8 2.4 Pitchers -.2 0 Total 25.6 20.6

• Alex Gordon accumulated 27% of the Royals position player fWAR and 29% of the Royals position player rWAR.
• Salvador Perez had an impressive 1.4 fWAR and 1.1 rWAR in only 158 PA
• The infield (and Butler to an extent) needs to produce more next season. This outfield should not be expected to put up 15.1 fWAR every season
• Chris Getz is not the answer at second, and Johnny Giavotella did not impress either. The Royals may want to take a long look at Kelly Johnson this offeason if they are serious about contending in 2012.
 Position Player fWAR rWAR Starting Pitcher 10.4 5.4 Felipe Paulino 2.6 1.9 Jeff Francis 2.6 1.4 Luke Hochevar 2.3 1.7 Bruce Chen 1.7 2.6 Kyle Davies .7 -1 Danny Duffy .6 .5 Luis Mendoza .3 .6 Vin Mazzaro -.2 -.7 Sean O`Sullivan -.5 -1.6 Relief Pitcher 3.1 9.7 Greg Holland 2 2.6 Joakim Soria .9 .8 Blake Wood .6 .9 Aaron Crow .3 2.1 Nathan Adcock .2 .2 Louis Coleman .1 1.6 Jeremy Jeffress 0 0 MITCH 0 0 Tim Collins 0 1.1 Kanekoa Texeira 0 .2 Everett Teaford -.1 .8 Kelvin Herrera -.2 -.2 Jesse Chavez -.2 -.3 Robinson Tejeda -.3 -.1 Totals 13.5 15.1

• rWAR and fWAR calculate pitching WAR very differently. I tend to think fWAR is more useful; the Royals starters were bad but they should be worth more than 36% of a team's total pitching WAR. That being said, whichever WAR you prefer, Sean O'Sullivan still is not a major-league quality pitcher.
• Greg Holland was a beast this season.
• With 2.4 fWAR being a roughly average starting pitcher, the Royals had essentially three average starters. Everyone else was either below or well below average
• Danny Duffy needs to pitch better quickly to justify a spot in the ML rotation. His walk percentage of 10.8% (4.32/9) should be halved.
Adding up the team total WAR results in 39.1 fWAR and 35.7 rWAR. Plugging these numbers into the linear models we get an expected 81.56 wins for the fWAR team and 85.22 wins for the rWAR team (or 83.22 if you go with 52 wins for a replacement level team) Either way, the WAR numbers and the Royals Pythagorean Standings support the claim that the Royals were a better team than their 71 wins indicate.

These numbers can be spun in a positive or negative light. You can claim that these numbers show that the Royals are closer to being a .500 team than their record shows. Many people expect Hosmer and Moose to perform better next season and believe Dayton Moore will improve the pitching staff. If the Royals were closer to a .500 team than their record indicated, those upgrades plus more "luck" should help the Royals reach .500 or even compete. The counter-argument is WAR is not predictive of future WAR. There are some Royals, specifically the entire outfield, that regression appears likely. That does not mean Gordon, Frenchy and Melky (or Cain) will be below-average players next season, but expecting them to play as well as they did this season based on their entire body of evidence is a bold prediction. The Royals generally stayed healthy this seasons, and at key positions, something that may not be true next year. There is also no guarantee the Royals younger players play better next season, or that Moore actually improves the team this offseason.

It seems safe to argue the Royals played better this season than their 71-91 record indicated. Why they only had 71 wins and what any of this means for next season are two questions that may dominate discussion moving forward.

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