COMPETITIVE BALANCE LEAGUES WANT IT Stimulates interest attendance TV ratings Cleveland Browns Home Attendance 60 000 50 000 Baseball owners particularly complain 40 000 30 000 Yankees are bad for baseball 20 000 10 000 What is competitive balance EVENNESS OF COMPETITION Use standard deviation of winning percentage Compare to ideal standard deviation all teams evenly matched as if each game decided by a flip of coin Would all win half their games in ideal league possible but unlikely wins losses winning Red Blue N is number of teams G is number of games in season wi is winning percentage of ith team is 0 500 w R w i 1 N 2 N wi w i 1 0 5 G INTERPRETING THE RATIO Many outcomes possible including three way tie or one team can go undefeated another winless Why take ratio White mean observed standard deviation ideal standard deviation ratio note use STDEVP rather than STDEV in Excel RATIO OF OBSERVED TO THEORITICAL IDEAL 3 TEAMS 4 GAMES IDEAL BALANCE 2 9 1 0 49 19 19 48 1 1 2 4 11 0 22 1 46 19 0 0 even in each game turnover among champions chance of an upset 19 47 Competitive balance ratio R Herfindal Hirschman Index HHI Intersport comparisons Policies to promote parity longer season implies smaller standard deviation comparable across leagues and years R 1 means absolute balance usually we observe R 1 higher R interpreted as imbalance but can occur by chance UNITED FOOTBALL LEAGUE 2012 3 TEAMS 4 GAMES RED TWICE AS GOOD wins losses Red Blue White w mean observed standard deviation ideal standard deviation ratio winning 1 000 0 500 0 250 0 250 Las Vegas Locomotives Omaha Nighthawks Virginia Destroyers Sacramento Mountain Lions winning 0 25 5 2 2 2 0 25 5 0 5 5 1 5 4 mean standard deviation theoretical ideal ratio i 2 R 0 500 0 306 0 250 1 225 0 500 4 w i 4 5 COMPETITIVE BALANCE RATIO SAMPLE MIDTERM 4 0 American League National League 3 5 3 0 2 5 2 0 SUMMARY OUTPUT Regression Statistics Multiple R 0 604 R Square 0 365 Adjusted R Square 0 354 Standard Error 0 509 Observations 242 ANOVA Df Regression 4 Residual 237 Total 241 1 5 intercept NL 1 time number of teams season length 1 0 0 5 Coefficients 2 327 0 064 0 013 0 017 0 003 SS 35 290 61 449 96 740 MS 8 823 0 259 F 34 027 Standard Error 0 366 0 069 0 002 0 020 0 002 t Stat 6 359 0 932 6 880 0 849 1 326 P value 0 000 0 352 0 000 0 397 0 186 0 0 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 BASEBALL IS NOT WORST BALANCE IN CHAMPIONSHIPS Downward trend Generally MLB in the middle NFL the most balanced NBA the least balanced by far 1950 Yankees beat Phillies 1951 Yankees beat Giants 1952 Yankees beat Dodgers MLB NFL NBA NHL EPL 1953 Yankees beat Dodgers historical average 1954 2 10 1 56 2 55 1 85 1 61 Giants beat Indians 1955 Dodgers beat Yankees 1956 Yankees beat Dodgers 1957 Braves beat Yankees 1958 Yankees beat Braves 1959 Dodgers beat White Sox NOSTALGIA AIN T WHAT IT USED TO BE HHI quantifies championship turnover Do a few teams dominate From 1949 through 1966 Yankees Dodgers or Giants played in every World Series 2 of them played each other in 8 of 18 Yankees in 14 of 18 Yankees in over 25 of all World Series APPLYING HHI TO BASEBALL IN 1950S 1950s American League Champions 1950s National League Champions Dodgers 5 Giants 2 Braves 2 Phillies HHI 0 34 Ideal balance when every champ is a different team 1 1 1 N c 1 HHI i 0 2 0 1 T 10 10 10 i 1 i 10 2 2 2 N c HHI i i 1 T ci number of championships by ith team N number of teams T number of years Also used to measure monopoly power APPLYING HHI TO BASEBALL IN 1990S 1990s AL Champions Yankees 3 Indians 2 Blue Jays 2 Twins Athletics HHI 0 21 Yankees 8 Indians White Sox HHI 0 66 2 THE HERFINDAHLHIRSCHMAN INDEX 2 1990s NL Champions Braves 5 Reds Phillies Marlins Padres HHI 0 32 Conclusion league championships more balanced in 1990s BASEBALL NOT UNIQUE COMPARING SPORTS In 1960s only two NBA champions MLB NFL NBA NHL EPL Celtics Champions 1960 66 1968 69 76ers 1967 HHI 0 14 0 16 0 28 0 18 0 44 Since 1999 six NBA champions R 2 10 1 56 2 55 1 85 1 61 Spurs 1999 2003 2005 2007 Lakers 2000 2002 2009 2010 Pistons 2004 Celtics 2008 Heat 2006 2012 Mavericks 2011 Leeds and von Allmen Tables 5 3 and 5 4 Recent history NFL the most balanced by either measure NBA by far the least balanced EPL seems contradictory 2 0 1 SJ 3 5 TO R 4 10 A 0 2 SL 0 4 R equality SE 0 6 E 15 MLB11 Y 5 NFL11 N 1 N 6 20 C 25 0 8 LA 0 K 0 C 5 U 10 5 0 6 O 10 D 15 0 4 H 20 15 L 20 L 25 A 25 D 30 LB 30 0 2 O Tax based on exogenous advantage hometown population 0 C 0 8 C Most promote monopsony power Several punish success An alternative idea I Salary caps and luxury tax Schedule changes V Coase invariance principle NBA lottery 1984 Hakeem Olajuwon H Promotion and relegation Reverse order draft and limits on free agency C H millions riz on a 2009 NFL SALARY DISTRIBUTIONS MILLIONS OF D ia Le m a A on gu Ba tlan dba e lti ta ck m B s Bo ore rav sto O es n rio Ch Ch Red les ic ica S ag g ox o oC W Ci h ub Cl ncin ite s ev na So Co elan ti R x lo d I ed ra n s do di D Ro ans e Fl troi ckie or t T s i H da ig K ou M ers an st ar Lo sas on A lins s A Ci s t Lo n ty ro s A ge Ro s l y M nge es A als ilw le n au s D gel M kee odg s in B er ne re s N so w N ew ta T ers ew Y w Y o in O ork rk M s a Ph kla Ya ets ila nd nk de A ee Pi lph thle s tts ia tic P Sa bur hil s Sa n gh lie n Di Pi s Fr eg ra an o tes c P Se isc adr a o e Ta St L ttle Gia s m ou M nt pa is ar s Ba C ine y ard rs D i T ev na To exa il …