Rating managerial effectiveness

Ed Szczepanski

The Bill James creation of Pythagorean Wins works well in determining team success. Can it be applied to managers as well?

Pythagorean Wins (PW) is a concept invented by Bill James which numerically states the obvious--teams that score more runs than their opponents typically win more games. This is the formula:

Runs Scored ^ 2 / ((Runs Scored ^ 2) + (Runs Allowed ^ 2))

It's a retrospective formula in that it can only describe what already occurred, but it still has value. It's common to relegate major differences between the formula and actual records to "luck." For example, if a team wins nine games by one run and loses the tenth 10-1, the PW formula would suggest a .500 record instead of the actual 9-1 performance. This is an extreme example but describes some of the variability involved.

Can PW be used to evaluate managerial effectiveness? I'll use the manager with the most wins (regular season only) in baseball history, Connie Mack, as an example:

From To Wins Losses Win% Runs RA PW% PW
Connie Mack 1894 1950 3731 3948 .486 35147 36377 .483 23.0

Mack had an actual career winning percent of .486, whereas the PW formula suggests his teams should only have won at a .483 rate, suggesting his teams outperformed expectations by 23 wins. In 53 years as a manager that worked out to around one-half a win per year.

The chart below shows managers of more recent vintage:

Manager From To W L W% R RA PW% PW
Tony LaRussa 1979 2011 2683 2331 .535 23747 22229 .533 10.6
Bobby Cox 1978 2010 2504 2001 .556 20890 18577 .558 -11.6
Joe Torre 1977 2010 2326 1997 .538 20608 19000 .541 -10.7
Sparky Anderson 1970 1995 2193 1834 .545 19201 17654 .542 10.8
Gene Mauch 1960 1987 1902 2037 .483 16566 17071 .485 -8.4
Lou Piniella 1986 2010 1835 1713 .517 17441 16798 .519 -5.6
Jim Leyland 1986 2013 1769 1728 .506 16092 15983 .503 8.6
Dusty Baker 1993 2013 1671 1504 .526 14925 14249 .523 10.0
Tom Lasorda 1976 1996 1599 1439 .526 12498 11600 .537 -33.1
Dick Williams 1967 1988 1571 1452 .520 12664 12200 .519 3.1
Bruce Bochy 1995 2013 1530 1530 .500 13351 13635 .489 32.2
Earl Weaver 1968 1986 1480 1060 .583 11232 9536 .581 3.9
Davey Johnson 1984 2013 1372 1071 .562 11475 10181 .560 5.0
Chuck Tanner 1970 1988 1352 1381 .495 11241 11342 .496 -2.3
Billy Martin 1969 1988 1252 1013 .553 10204 9213 .551 4.2
Whitey Herzog 1973 1990 1243 1090 .533 10085 9557 .527 13.8

PWs dropped dramatically as these managers managed far fewer games than Mack. But this is only half the story--let's look at Tony LaRussa season-by-season to see how PWs move (playoff years in bold):

Team Year W L W% R RA PW% PW
Chicago White Sox 1979 27 27 .500 249 230 .540 -2.1
Chicago White Sox 1980 70 90 .438 587 722 .398 6.3
Chicago White Sox 1981 54 52 .509 476 423 .559 -5.2
Chicago White Sox 1982 87 75 .537 786 710 .551 -2.2
Chicago White Sox 1983 99 63 .611 800 650 .602 1.4
Chicago White Sox 1984 74 88 .457 679 736 .460 -0.5
Chicago White Sox 1985 85 77 .525 736 720 .511 2.2
Chicago White Sox 1986 26 38 .406 280 324 .428 -1.4
Oakland 1987 81 81 .500 806 789 .511 -1.7
Oakland 1988 104 58 .642 800 620 .625 2.8
Oakland 1989 99 63 .611 712 576 .604 1.1
Oakland 1990 103 59 .636 733 570 .623 2.0
Oakland 1991 84 78 .519 760 776 .490 4.7
Oakland 1992 96 66 .593 745 672 .551 6.7
Oakland 1993 68 94 .420 715 846 .417 0.5
Oakland 1994 51 63 .447 549 589 .465 -2.0
Oakland 1995 67 77 .465 730 761 .479 -2.0
St. Louis 1996 88 74 .543 759 706 .536 1.1
St. Louis 1997 73 89 .451 689 708 .486 -5.8
St. Louis 1998 83 79 .512 810 782 .518 -0.8
St. Louis 1999 75 86 .466 809 838 .482 -2.7
St. Louis 2000 95 67 .586 887 771 .570 2.7
St. Louis 2001 93 69 .574 814 684 .586 -2.0
St. Louis 2002 97 65 .599 787 648 .596 0.5
St. Louis 2003 85 77 .525 876 796 .548 -3.7
St. Louis 2004 105 57 .648 855 659 .627 3.4
St. Louis 2005 100 62 .617 805 634 .617 0.0
St. Louis 2006 83 78 .516 781 762 .512 0.5
St. Louis 2007 78 84 .481 725 829 .433 7.8
St. Louis 2008 86 76 .531 779 725 .536 -0.8
St. Louis 2009 91 71 .562 730 640 .565 -0.6
St. Louis 2010 86 76 .531 736 641 .569 -6.1
St. Louis 2011 90 72 .556 762 692 .548 1.2

This is the real story--what luck gave in one year was taken away in another, as PWs fluctuated from as many as 7.8 in 2007 to as few as -6.1 in 2010. There's a randomness that had a tendency to regress to the mean, suggesting it really is luck, the kind of luck seen in having a better record in one-run games or having fewer blowout games, but it's difficult to credit this to the manager.

If PWs fall short, what can be used to measure manager effectiveness? I'll throw out a couple of ideas, neither of which is perfect. The first is record in one-run games (1RGw and 1RGl) and the second the number of games in first (G1st). Here are these values for the recent managers:

Manager From To W L W% 1RGw 1RGl 1RW% G1st G1%
Tony LaRussa 1979 2011 2683 2331 .535 714 706 .503 1838 36.7%
Bobby Cox 1978 2010 2504 2001 .556 692 620 .527 1842 40.9%
Joe Torre 1977 2010 2326 1997 .538 665 564 .541 1555 36.0%
Sparky Anderson 1970 1995 2193 1834 .545 607 520 .539 983 24.4%
Gene Mauch 1960 1987 1902 2037 .483 612 599 .505 621 15.8%
Lou Piniella 1986 2010 1835 1713 .517 483 469 .507 1118 31.5%
Jim Leyland 1986 2013 1769 1728 .506 522 500 .511 1090 31.2%
Dusty Baker 1993 2013 1671 1504 .526 488 422 .536 833 26.2%
Tom Lasorda 1976 1996 1599 1439 .526 519 534 .493 1028 33.8%
Dick Williams 1967 1988 1571 1452 .520 495 474 .511 789 26.1%
Bruce Bochy 1995 2013 1530 1530 .500 499 394 .559 727 23.8%
Earl Weaver 1968 1986 1480 1060 .583 451 335 .574 789 31.1%
Davey Johnson 1984 2013 1372 1071 .562 397 350 .531 1013 41.5%
Chuck Tanner 1970 1988 1352 1381 .495 447 479 .483 295 10.8%
Billy Martin 1969 1988 1252 1013 .553 364 332 .523 703 31.0%
Whitey Herzog 1973 1990 1243 1090 .533 400 340 .541 807 34.6%

I suspect one of the best predictors of a good manager is having good players. Tony LaRussa was considered a bright young manager but it took the Oakland Athletics of the late 1980s to propel him to among the best in the game (along with George Will's book "Men at Work"). When the Athletics regressed in the early 1990s, LaRussa's genius could do nothing except perhaps soften the slide. Joe Torre was average, at best, in his three stops prior to joining the Yankees, and Bobby Cox had been underwhelming in stints with Atlanta and Toronto prior to installing himself as Braves manager in 1990.

None of this is to diminish the role of a manager--it's one thing to look back retrospectively and entirely another to make in-game decisions, especially with the game on the line. But it's too much to take PWs and use them as a proxy measure of managerial skill. I've introduced the Mistake Index before (in this Beyond the Box Score post and more completely here), which suggests the number of mistakes correlates well with a team's record. If a manager can decrease mistakes, he certainly can play a role, but that's not luck--that's skill and the ability to teach, two highly desired and valuable qualities.

There's a reason Pythagorean Wins aren't listed on Baseball-Reference manager pages--it's not an accurate measure of managerial effectiveness. Like many other numbers, it's fun to look at to see if it increases our understanding, but in this case it appears to add little value. The next big thing in measuring managerial effectiveness is right around the corner as MLB Advanced Media (MLBAM) installs cameras that can track each play. When that is fully implemented the things a manager can really control, like fielder positioning can be measured and evaluated. Until then, we do the best we can with the tools at hand, and Pythagorean Wins for managers doesn't appear to be the best suited metric.

All data from Baseball-Reference.com

Scott Lindholm is a web columnist for 670 The Score in Chicago. Follow him on Twitter @ScottLindholm.

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