Do Firms Maximize? Evidence from Professional Football David Romer Do Firms Maximize? Evidence from Professional Football David Romer University of California, Berkeley and National Bureau of Economic Research John M. Vignoe BFIN 7220 March 20, 2014

Do NFL teams make maximize their chance on winning on 4 th down? AUTHORS PREMISE  Standard view that competition in the goods, capital, and labor markets leads firms to make maximizing choices.  The choice on 4 th down in the NFL between kicking and trying for a first down should maximize the chance of “winning”.  Maximizing Profit in the NFL can be simplified to Maximizing the chance of winning.  Failure to Maximize in this setting would be very striking!!!!

INTRODUCTION / BACKGROUND  Maximize profits in NFL = Maximize the chance of “Winning”.  Examine one strategic decision in the NFL - Kick or “Go For it” on 4 th down  Strategic Decisions in Sports has two Distinct advantage:  1. DETAILED REPETITIVE DATA SHOWING THE RESULTS FROM DECISIONS TEAMS MAKE.  2. DIFFICULT TO SUMMIZE THAT STRATEGIC DECISIONS WILL IMPACT PROFITS MORE THAN INCREASING THE PROBABILITY OF WINNING.  Simple models of Optimization in the NFL should hold:  Competitive market for coaches who make the decisions (Average annual salary of $3 million)  Winning is very highly valued as evidenced by high player salaries  Information about other decisions are readily available and easily Imitateable.

DATA  TEAMS CHOICES DEPART FROM THE CHOICES THAT WOULD MAXIMIZE WINNING.  DATA IS STATISTICALLY SIGNIFICANT  PLAY BY PLAY ACCOUNTS OF ALL NFL GAMES DOWNLOADED BETWEEN  DYNAMIC PROGRAMMING ANALYSIS  METHOD OF BREAKING LARGE PROBLEM INTO A SERIES OF SMALLER PROBLEMS IN ORDER TO PRODUCE RESULTS.  101 SITUATIONS – o 1 ST DOWN AND 10 ON EACH YARD LINE FROM OWN 1 TO OPPONENTS 10. o FIRST AND GOAL ON EACH YARD LINE FROM OPPONENTS 9 TO 1 o KICKOFF FROM OWN 30 (AFTER TD, FIELD GOAL, & BEGINNING OF GAME) o KICKOFF FROM 20 AFTER A SAFETY

EQUATIONS  D i gt V i = E [ P gt +B gt  D gt +1 V i ]  V i  V i value of situation i  g  g games  t  t situations  D i gt  D i gtdummy situation  P gt  P gtnet points scored - ball in situation gt.  B gt  B gtdummy situation

 e gt  e gtdifference between realized value of situation g,t one situation later and the expectation of the realized value conditional on being in situation g,t. e gt =[Pgt +Bgt  DigtVi] – E[Pgt +Bgt  Dgt +1Vi ]

RESULTS figure 1

Figure 1 – estimated value for 1 st and 10 or 1 st and goal as a function of teams field position The estimated value of situations (solid line) and two-standard-error bands (dotted lines). The estimated value of a kickoff is 0.62 (standard error 0.04) The estimated value of a free kick is –1.21 (standard error 0.51).

KICKING vs. GOING FOR IT  USES RESULTS FROM FIGURE 1.  FOUR STEPS 1. VALUE OF KICKING IN DIFFERENT CIRCUMSTANCES 2. VALUE OF GOING FOR IT IN DIFFERENT CIRCUMSTANCES 3. COMPARES 1&2 TO DETERMING WHICH IS BETTER AS A FUNCTION OF TEAMS FIELD POSITION AND DISTANCE TO 1 ST DOWN. 4. EXAMINE TEAMS ACTUAL DECISIONS 5. SIMILAR ANALYSIS FOR BOTH o o 3 RD DOWN PLAYS USED SINCE TEAMS RARELY GO FOR ITON 4 TH DOWN o o VALUE OF GOING FOR IT DEPENDS ON TEAMS FIELD POSITION AND # OF YARD TO FIRST DOWN OR TOUCHDOWN.

Figure 2 (dotted lines show 2 standard errors) (a) estimated value for kicks as a function of teams position on field..Teams choice to kick field goal vs punt changes rapidly at 35 yard line. (b) estimated value of the difference between the values of the kicks and of turning the ball over. (opposing team w 1 st down on same spot) Own 10 to midfield is steady points/38 yd field goalOwn 10 to midfield is steady points/38 yd field goal Dips at opponents 35 – very difficult field goal and put yields few points.Dips at opponents 35 – very difficult field goal and put yields few points. Closer to goal (field goal range) probability rises slightly but value of leaving opponent with ball rises considerably.Closer to goal (field goal range) probability rises slightly but value of leaving opponent with ball rises considerably.

“ “Going for it”   Smooth the estimates   Focus on values of going for it and turning it over on a particular spot as opposed to just going for it directly   Closer to opponents goal line less room to work – chances of success and avg. number of yards gained are likely to be lower.  G i  G i y - value of going for it on yard line i with y yards to go.  i i –  i i – yard line opposite yard line i.

VALUE OF GOING FOR IT BEFORE OPPONENTS 17 G iy + V ii = a 0 +a 1 y + ay ( SQUARED ) VALUE OF GOING FROM OPPONENTS 17 TO THE GOAL LINE Giy + Vii = b0+b1y+b2i+b3y (SQUARED)+ b4yi+b5i (SQUARED) +b6y (SQUARED) i+b7yi (SQUARED)+ b8y (SQUARED) i (SQUARED)

Figure 3 The estimated difference between the values of going for it and of the other team having the ball on the spot at a generic yard line outside the opponent’s 17 (solid line) and at the opponent’s 5 (dashed line). The dotted lines show the two-standard-error bands.

CONCLUSIONS  Teams choices are dramatically more conservative than those recommended by the dynamic programming analysis  Behavior of NFL on 4 th down departs from the behavior that would maximize their chances of winning.  Even though decisions are simple and systematic, coaches are high paid, and market for their services is very competitive – Agents in NFL do not maximize  Experience and Intuition seems to prevail in decision making even though statistically significant data exists to the contrarty.  Little evidence about whether conservative behavior exists because decision makers have non standard objectives or because they are imperfect maximizers.

QUESTIONS?