Evdence from Professonal Soccer Davd Romer Unversty of Calforna, solitaryai.art Berkeley and Art Natonal Bureau of Economc Analysis Ths paper examnes a sngle, slender decson the choce on fourth down n the Natonal Soccer League between kckng and tryng for a frst down as a case examine of the standard vew that competton n the products, captal, and labor markets leads frms to make maxmzng choces. Play-by-play information and dynamc programmng are used to estmate the typical payoffs to kckng and tryng for a frst down below dfferent crcumstances. Examnaton of actual decsons shows systematc, clear-minimize, and overwhelmngly statstcally sgnfcant departures from the decsons that may maxmze groups chances of wnnng. Possble causes for the departures are consdered. I. Introducton A central assumpton of most economc fashions s that agents maxmze smple objectve functons: consumers maxmze expected utlty, and frms maxmze expected profts. The argument for ths assumpton s not that t results in good descrptons of behavor, however that t leads to moderately good approxmatons n most instances. This has been created with the he lp of G SA Conte nt G enerator Demoversion !
The assumpton that customers successfully maxmze smple objectve functons frequently makes predctons about how a sngle ndvdual wll behave when confronted wth a specfc, easly descrbable decson. I am ndebted to Ben Allen, Laurel Beck, Sungmun Cho, superstitionism.com Ryan Edwards, Maro Lopez, Peter Mandel, Travs Reynolds, Evan Rose, and Raymond Son for outstandng research assstance; to Chrstna Romer for nvaluable dscussons; to Steven Levtt and Rchard Thaler for mportant encouragement; and to quite a few colleagues and correspondents for helpful comments and suggestons. An earler verson of the paper was ttled It s Fourth Down and What Does the Bellman Equaton Say? A Dynamc-Programmng Analyss of Soccer Strategy. Journal of Poltcal Financial system, 2006, vol. 2006 by The Unversty of Chcago. 2 do frms maxmze? 341 Thus t can usually be tested n both the laboratory and the feld. The assumpton that frms maxmze profts s far more dffcult to check, nonetheless. Partcularly for big frms, the decsons are normally complcated and the info dffcult to obtan.
However the a pror case for frm maxmzaton s a lot stronger than that for consumer maxmzaton. As Alchan (1950), Fredman (1953), Becker (1957), Fama (1980), and others explan, competton n the goods, captal, and labor markets creates strong forces drvng frms towards proft maxmzaton. A frm that fals to maxmze profts s lkely to be outcompeted by more effcent rvals or purchased by ndvduals who can obtan greater value from t by pursung dfferent strateges. And managers who fal to maxmze profts for the owners of ther frms are lkely to be fred and changed by ones who do. Thus the case for frm maxmzaton rests rather more on logcal argument than emprcal evdence. 1953, 22). Ths paper takes a frst step towards testng the assumpton that frms maxmze profts by examnng a specfc strategc decson n professonal sports activities: the choce n soccer between kckng and tryng for a frst down on fourth down.
Examnng strategc decsons n sports activities has two monumental benefits. Frst, n most cases, t s dffcult to thnk of any sgnfcant channel via whch strategc decsons are lkely to have an effect on a group s profts apart from through ther mpact on the crew s probablty of wnnng. Thus the problem of maxmzng profts plausbly reduces to the a lot smpler downside of maxmzng the probablty of wnnng. Second, there are copous, detaled data descrbng the crcumstances teams face once they make these decsons. 1 The predctons of smple models of optmzaton seem especally lkely to carry n the case of fourth-down decsons n professonal soccer. There are three reasons. Frst, the marketplace for the coaches who make these decsons s ntensvely compettve. Salares common roughly $three mllon per year, and annual turnover exceeds 20 percent. 2 Second, wnnng s valued enormously (as proven by the very hgh salares commanded by hgh-qualty players).