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November 21, 2002

Aim For The Head

Are Balanced Lineups Better?

by Keith Woolner and Rodger A. Payne

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This week's question comes from J. M., who writes:

Thinking about how much of the Texas payroll goes to A-Rod and how bad they are I was wondering.

Based solely on offense, expected runs created - given the scenario that your total starting lineup team OPS was fixed at a certain number. Would you be better off building a team with a few superstars, balanced off with some truly horrible players or a team of mostly mediocre players?

Would a lineup of five Shawn Greens (.947 OPS) and five Cesar Izturises (.547 OPS) score more than a lineup of 10Carlos Guillens (.757 OPS)?

As a side note, can we do away with the idea that the Rangers have been forced to spend but a pittance on the rest of the team because of the Alex Rodriguez signing? Texas had an opening day payroll in excess of $105 million (3rd highest in baseball). Taking $21 million away that A-Rod was paid this year (thanks tohttp://www.bluemanc.demon.co.uk/baseball/mlbcontracts.htm for the contract detail), that still leaves $84 million Texas spent on other players, which by itself would have been the sixth highest payroll even if A-Rod had played for free. The problem wasn't that they had no money because of Rodriguez, it was how poorly they spent the other $84 million to build the rest of the roster beyond the best player in the game.

But let's now turn to the question you asked -- whether "well balanced" teams are more or less effective than "lopsided" teams of the same average production. To investigate the question, I looked at teams from 1961-2000 (strike-shortened years omitted), and looked at each team's OPS and runs scored. To calculate the "spread" (the term I'll use throughout this analysis to refer to the balance of the team's production) around the average OPS, I took the square of the difference between the team's OPS and the player's OPS, and weighted it by the number of plate appearances the player had. I then computed the team's total spread around that.

e.g.

Assume the team has an 800 OPS, and the player has a 950 OPS in 600 PA.

a. (.950-.800) = .150
b. .150^2 = .0225
c. .0225*600 = 13.5 points contributed to the team's spread

Now try it for a player with a 600 OPS in 400 PA.

a. (.600-.800) = -.200
b. (-.200)^2 = .04
c. .04*400 = 16 points contributed to the team's spread

We can see whether having the spread for each team increases the accuracy of our expected runs beyond simple OPS. To do this, I ran a linear regression on total runs, using OPS and spread as inputs. OPS, by far, dominated the regression, as by itself it explains 91% of the variance in scoring among teams. However, spread did barely clear the bar for being a significant factor in predicting scoring as well (for the statistically inclined, a t stat of -2.37, and a p-value of 0.017, or meaning that there's less than a 2% probability of seeing the results if the results were purely random with respect to spread).

To some extent higher spread seems to produce lower scoring totals for the same OPS. The magnitude of the effect at the extremes is about +/- 10 runs, so while there's some effect, you can probably gain as much or more extra accuracy by using a better model of run scoring that OPS alone.

For the curious...

The team with the lowest spread (most balanced lineup) was the 1976 Angels, which featured the following roster:

YEAR TEA LG NAME                         PA    AVG    OBP    SLG    OPS
---- --- -- -------------------- ---------- ------ ------ ------ ------
1976 CAL AL Remy,Jerry                  540   .263   .315   .303   .618
1976 CAL AL Bochte,Bruce                532   .258   .350   .311   .661
1976 CAL AL Chalk,Dave                  497   .217   .310   .253   .563
1976 CAL AL Jackson,Ron                 447   .227   .291   .344   .635
1976 CAL AL Bonds,Bobby                 422   .265   .341   .386   .727
1976 CAL AL Collins,Dave                405   .263   .336   .334   .670
1976 CAL AL Melton,Bill                 387   .208   .302   .328   .631
1976 CAL AL Torres,Rusty                300   .205   .300   .356   .656
1976 CAL AL Guerrero,Mario              278   .284   .309   .340   .649
1976 CAL AL Etchebarren,Andy            275   .227   .305   .271   .577
1976 CAL AL Briggs,Dan                  262   .214   .256   .294   .550
1976 CAL AL Stanton,Leroy               256   .190   .270   .281   .551
1976 CAL AL Solaita,Tony                249   .270   .369   .437   .807
1976 CAL AL Davis,Tommy                 235   .265   .315   .329   .644
1976 CAL AL Humphrey,Terry              214   .245   .308   .311   .620
1976 CAL AL Jones,Bob                   181   .211   .276   .355   .632
1976 CAL AL Lahoud,Joe                  116   .177   .319   .219   .538
1976 CAL AL Ramirez,Orlando              76   .200   .263   .214   .477
1976 CAL AL Easler,Mike                  56   .241   .268   .296   .564
1976 CAL AL Garrett,Adrian               53   .125   .208   .188   .395
1976 CAL AL Herrmann,Ed                  53   .174   .283   .370   .653
1976 CAL AL Alvarez,Orlando              42   .167   .167   .333   .500
1976 CAL AL Miley,Mike                   42   .184   .262   .237   .499
1976 CAL AL Dade,Paul                    12   .111   .333   .111   .444
1976 CAL AL Lopez,Carlos                 12   .000   .167   .000   .167
1976 CAL AL Nordbrook,Tim                 9   .000   .111   .000   .111
1976 CAL AL Smith,Billy                   8   .375   .375   .375   .750
1976 CAL AL Hampton,Ike                   2   .000   .000   .000   .000

Every player with 250+ PA had an OPS within 82 points of .645, and only two other players exceed that level dropping the PA threshold to 100 PA.

The widest spread was the 2000 Astros, narrowly edging out the 1961 Yankees, which both had OPS spreads about 9 times higher than the Angels.

 

YEAR TEA LG NAME                         PA    AVG    OBP    SLG    OPS
---- --- -- -------------------- ---------- ------ ------ ------ ------
2000 HOU NL Bagwell,Jeff                712   .310   .428   .615  1.044
2000 HOU NL Hidalgo,Richard             635   .314   .397   .636  1.033
2000 HOU NL Alou,Moises                 508   .355   .423   .623  1.047
2000 HOU NL Lugo,Julio                  461   .283   .347   .431   .778
2000 HOU NL Biggio,Craig                454   .268   .392   .393   .785
2000 HOU NL Berkman,Lance               410   .297   .395   .561   .956
2000 HOU NL Spiers,Bill                 405   .301   .388   .392   .779
2000 HOU NL Meluskey,Mitch              396   .300   .404   .487   .891
2000 HOU NL Bogar,Tim                   342   .207   .295   .319   .614
2000 HOU NL Cedeno,Roger                302   .282   .384   .398   .782
2000 HOU NL Ward,Daryle                 279   .258   .297   .538   .835
2000 HOU NL Truby,Chris                 273   .260   .300   .477   .777
2000 HOU NL Caminiti,Ken                251   .303   .422   .582  1.004
2000 HOU NL Eusebio,Tony                247   .280   .364   .459   .823
2000 HOU NL Mieske,Matt                  89   .173   .247   .272   .519
2000 HOU NL Barker,Glen                  75   .224   .307   .373   .680
2000 HOU NL Elarton,Scott                66   .159   .197   .190   .387
2000 HOU NL Holt,Chris                   65   .100   .169   .117   .286
2000 HOU NL Lima,Jose                    61   .167   .180   .200   .380
2000 HOU NL Johnson,Russ                 47   .178   .213   .178   .391
2000 HOU NL Chavez,Raul                  46   .256   .304   .372   .676
2000 HOU NL Reynolds,Shane               42   .225   .262   .325   .587
2000 HOU NL Miller,Wade                  40   .100   .100   .125   .225
2000 HOU NL Dotel,Octavio                33   .031   .061   .031   .092
2000 HOU NL McKnight,Tony                13   .000   .000   .000   .000
2000 HOU NL Powell,Brian                 10   .222   .300   .333   .633
2000 HOU NL Cromer,Tripp                  9   .125   .222   .125   .347
2000 HOU NL Slusarski,Joe                 9   .111   .111   .111   .222
2000 HOU NL Ginter,Keith                  9   .250   .333   .625   .958
2000 HOU NL Charles,Frank                 7   .429   .429   .571  1.000
2000 HOU NL Ensberg,Morgan                7   .286   .286   .286   .571
2000 HOU NL Zosky,Eddie                   4   .000   .000   .000   .000
2000 HOU NL Valdes,Marc                   3   .000   .000   .000   .000
2000 HOU NL Bako,Paul                     2   .000   .000   .000   .000
2000 HOU NL Wagner,Billy                  2   .000   .000   .000   .000
2000 HOU NL Franklin,Wayne                2   .000   .000   .000   .000
2000 HOU NL Maddux,Mike                   2   .000   .000   .000   .000
2000 HOU NL Cabrera,Jose                  1   .000   .000   .000   .000
2000 HOU NL Gooden,Dwight                 1   .000   .000   .000   .000
2000 HOU NL Gross,Kip                     1   .000   .000   .000   .000
2000 HOU NL Linebrink,Scott               1  1.000  1.000  1.000  2.000
2000 HOU NL Green,Jason                   1   .000   .000   .000   .000
2000 HOU NL Powell,Jay                    1   .000   .000   .000   .000
2000 HOU NL Perez,Yorkis                  1   .000   .000   .000   .000
2000 HOU NL Henry,Doug                    1   .000   .000   .000   .000

Six of the top seven players in PA cluster into two groups almost 300 points apart, and the next three after that aren't within 100 points of each other either.

 

YEAR TEA LG NAME                         PA    AVG    OBP    SLG    OPS
---- --- -- -------------------- ---------- ------ ------ ------ ------
1961 NYA AL Richardson,Bobby            694   .261   .295   .316   .611
1961 NYA AL Maris,Roger                 691   .269   .376   .620   .997
1961 NYA AL Kubek,Tony                  645   .276   .307   .395   .702
1961 NYA AL Mantle,Mickey               640   .317   .452   .687  1.138
1961 NYA AL Skowron,Bill                604   .267   .320   .472   .792
1961 NYA AL Boyer,Clete                 569   .224   .313   .347   .660
1961 NYA AL Howard,Elston               477   .348   .390   .549   .939
1961 NYA AL Berra,Yogi                  432   .271   .333   .466   .799
1961 NYA AL Blanchard,Johnny            274   .305   .383   .613   .996
1961 NYA AL Lopez,Hector                268   .222   .295   .305   .599
1961 NYA AL Cerv,Bob                    131   .271   .344   .483   .827
1961 NYA AL Ford,Whitey                 108   .177   .269   .188   .456
1961 NYA AL Gardner,Billy               108   .212   .278   .293   .571
1961 NYA AL Stafford,Bill                71   .179   .225   .239   .464
1961 NYA AL Terry,Ralph                  67   .227   .239   .258   .496
1961 NYA AL Sheldon,Rollie               58   .125   .155   .125   .280
1961 NYA AL Daley,Bud                    46   .133   .152   .156   .308
1961 NYA AL DeMaestri,Joe                41   .146   .146   .146   .293
1961 NYA AL Coates,Jim                   37   .029   .081   .029   .110
1961 NYA AL Torgeson,Earl                26   .111   .385   .111   .496
1961 NYA AL Arroyo,Luis                  25   .280   .280   .360   .640
1961 NYA AL Johnson,Deron                21   .105   .190   .105   .296
1961 NYA AL Turley,Bob                   21   .095   .095   .095   .190
1961 NYA AL Ditmar,Art                   19   .053   .053   .053   .105
1961 NYA AL Gonder,Jesse                 15   .333   .467   .417   .883
1961 NYA AL Reed,Jack                    14   .154   .214   .154   .368
1961 NYA AL Hale,Bob                     13   .154   .154   .385   .538
1961 NYA AL Tresh,Tom                     8   .250   .250   .250   .500
1961 NYA AL Reniff,Hal                    5   .000   .000   .000   .000
1961 NYA AL Clevenger,Tex                 4   .250   .250   .500   .750
1961 NYA AL McDevitt,Danny                2   .000   .500   .000   .500
1961 NYA AL Thomas,Lee                    2   .500   .500   .500  1.000
1961 NYA AL Downing,Al                    1   .000   .000   .000   .000

The 600+ PA players alone tell the story, with OPS marks of 611, 702, 792, 997, and 1138. And the next eight players have about as many PA below 600 OPS as above an 800 OPS (if we give Berra one extra point).

Click here for the exciting conclusion.

Keith Woolner is an author of Baseball Prospectus. You can contact him by clicking here.

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

Related Content:  Baseball Ops,  Ops,  Al,  Nl,  OPS+

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