Pythagoras's petulant persecutors

qe AG MANAGERIAL AND DECISION ECONOMICS, VOL. 18, 343-344 (1997) Pythagoras’s Petulant Persecutors Horowitz| ira University of Florida, FL. USA Ruggiero et al. (1997) argue that the ‘Pythagorean Theorem’ is an inappropriate basis for evaluating baseball managers and has an illogical arithmetic property that can result in a manager's evaluation being dependent upon the strength of his team. Their argument in the former regard is based on their failure to recognize that the existence of an ex post identity does not preclude the development of a related ex ante hypothesis; their argument in the latter regard is based on their conviction that their criterion for evaluating DHOROW.ITZ, managers is correct and any other criterion is incorrect. The present remarks clarify these issues. © 1997 by John Wiley & Sons, Ltd. > ¡E ar Manage. Decis. Econ. 18: 343-344 (1997) No. of Figures: 0 No. of Tables: 0 No. of References: 3 Over the course of a 37-year academic career, | have given by ß,(TR/OR) + B2(TR/OR)*. Continuing the published approximately 125 papers and have written analogy, this is comparable to stating the ex ante several others that never made it into print. Based on hypothesis that c, = 4% +22¥,+4,, calling this a this total, I estimate that I have received close to 300 consumption outright rejection letters from journal editors. Thus, estimate its parameters, and then asserting that the on the average of once very six weeks for the past 37 estimate of «> is the marginal propensity to consume. years I have been told that my work does not pass Most economists would judge the latter specification function, using the ex post data to muster. That’s a humbling experience. The defense for a consumption function to be simple-minded and that I have developed in the face of such an onslaught erroneous. Ruggiero et al. is a very thick skin. This reply is not being written judgement about the former specification for a team’s because Ruggiero et al. (1997) hit a tender nerve; success, and particularly about the use to which the they would have a hard time finding one. Indeed, estimates of $, and f2, bz and b2, have been put: would make the same after reading each of two earlier drafts of their namely, Comment I recommended publication, subject to They are entitled to their beliefs. There is, however, revision. I very much like what they have done and nothing inappropriate about the statistical procedure. to evaluate managers by PH = bi +b. their extension of my work. In each revision, how- Ruggiero er al. also state that the theorem ‘should ever, they chose to ignore several issues that 1 raised. not be used to model a production process...” Now, I still believe some of those issues to be of sufficient to the best of my knowledge I have never claimed import and general interest as to warrant my taking that the theorem models a production process. They advantage of the opportunity to raise them anew. have raised a strawman. I have never presented the Ruggiero et al. develop their Eqn (5) as an ex post theorem as anything other than an empirical fact of identity that links a team’s wins (1) and losses (L) to baseball life. If one knows nothing about a team the number of runs that it scores (7R) and allows except for its run ratio, then (TR/OR)” usually pro- (OR). By an analogy that is so familiar I need not vides a decent estimate of its W/L ratio. I would even bother defining the terms, C; = Y, — 1, — G; is nevertheless suggest that the approximation works for also an ex post identity. Based on the Pythagorean two reasons. Theorem, however, their Eqn (7), from which my PH argument. Second, and perhaps more to the point First, there is the authors’ identity measure of managerial performance is estimated, here, the numerator in the runs ratio does reflect states an ex ante hypothesis: notably, when a partioffensive productivity cular manager’s team has a 7R/OR ratio, the team’s reflect expected ratio of wins to losses, E[W/L], will be want to suggest that whether the theorem works or CCC 0143-6570/97/040343-02 $17.50 © 1997 by John Wiley & Sons, Ltd. and the defensive productivity. denominator does If Ruggiero et al.

1. HOROWITZ not is beside the point, and that any self-respecting ‘illogical.’ Fine. I have clearly and forthrightly stated economist should understand that the only appropriin print (Horowitz, 1994, p. 190) my belief that the ate way to evaluate managerial productivity is to seemingly greater ability to win the close games is employ a production-function approach (see e.g. precisely what distinguishes the better managers from Porter and Scully, 1982), I can understand and live the rest and that this should be the basis for ranking with their professional biases. Having a PhD in managers, which is why I like the PH approach. economics is a weighty cross that many of us have Others might argue that a criterion such as longevity, had to bear.! in point of fact, I would be delighted to which may reflect some combination of a person’s have the world debate and compare the differences ability to get along with the General Manager and the between the evaluations and rankings yielded by a players, the ability to win pennants, and the ability to classical develop talent, is the appropriate ranking statistic. and sophisticated production-function approach and my own modest Pythagorean-based Still others might want to focus solely on the number efforts. For reasons that elude me, Ruggiero ef al. of pennants won in the years when the manager’s have steadfastly dismissed my suggestion that they team was the consensus favorite to win the pennant. make the comparison themselves. This is not a matter of one view being ‘correct’ and They assert that ‘Apparently, the belief is that an the other views being ‘incorrect’. Rather, there is an effective manager will forego runs in a ballgame once honest and defendable difference in how we look at a lead is obtained, and then use these forgone runs things. Neither ‘logic’ nor ‘illogic’ has anything to do during future games in which his team is behind.’ with it. I will take Earl Weaver over Al Lopez any Although they are not entirely off-base here, the same day of the week cannot be said of their following statement to the Sunday. So would Porter and Scully (1982, p. 646). and twice on effect that managers try to win each game by as large The production-function a margin as possible. Over half a century of watching things right after all. a double-header approach does get some baseball games leaves me with the impression that when teams get ‘safely’ ahead, managers start replaAcknowledgement cing their regulars, they stop stealing bases and invoking the hit and run, and they replace their starting pitchers with lesser-quality hurlers, saving their stoppers for another day. Moreover, they do the I gratefully acknowledge Professor Ann R. Horowitz's allowing me to pick her brain over a Saturday-night dinner during which she clarified my thinking on the ex post-ex ante issue. same thing when they are far behind. A manager’s choice of a pitching rotation and who to match up NOTE against whom, when to rest players, and the like, is also critical. 1 had supposed that major-league managers were hired to win as many games as possible, 1, During my second year as a doctoral student at MIT, I interviewed for summer jobs. One interviewer kindly explained that his company was not interested in hiring given the existing talent and expectations for the PhD economists and that ‘We wouldn't hire you if you team, and taking into consideration the standings, were Paul Samuelson’. the need to develop and/or showcase players, the Professor Robert Solow to show up for his seminar, I point was regaling my classmates with this story. The punch in the season, and so forth. Until reading While we were waiting for Ruggiero et al., | was unaware of any knowledgeable line and the laughs came at the exact moment that Solow entered the room. He asked what was so funny, so I baseball figure suggesting that managers were hired repeated the story. Without batting an cye Solow asked: to win each game by as many runs as possible. “Did you tell him that you werent Paul Samuelson?” Ignorance is bliss. REFERENCES What, then, led me to encourage publication of their Comment? It is their very clever analysis that is captured in their Eqn (10) and summarized in their Table 2. I will meet my maker regretting that I had 1. Horowitz (1994). Pythagoras, Tommy Lasorda, and me: On evaluating baseball managers. Social Science Quarterly, 75, 187-94, not thought of this myself. Their analysis reveals that P. K. Porter and G. Scully (1982). Measuring managerial my approach only ranks Weaver as the best manager efficiency: the case of baseball. Southern Economic Journal, 48, 642-50. J. Ruggiero, L. Hadley, G. Ruggiero and S. Knowles (1997). A note on the Pythagorean theorem of baseball of the particular set considered, because he is the better manager when the games are close: that is, ‘as long as a team is expected to outscore their opponents production. Managerial and Decision Economics, 18, by 20%. Ruggiero er al. believe this result to be Managerial and Decision Economics, 18: 343-344 © 1997 by John Wiley & Sons, Ltd.