COMPETITIVE LEAGUES WANT IT Stimulates interest BALANCE attendance Cleveland Browns Home Attendance TV ratings 60,000 50,000 Competitive balance owners particularly 40,000 ratio R complain 30,000 Herfindal-Hirschman Yankees are bad for baseball 20,000 Index HHI 10,000 What is competitive balance? Intersport comparisons 0 even in each game? Policies to promote turnover among champions?

parity chance of an upset? 1946 (12-2-0)1947 (12-1-1)1948 (14-0-0) 1949 (9-1-2)

EVENNESS OF RATIO OF OBSERVED TO COMPETITION THEORITICAL IDEAL N is number of teams Use standard deviation of winning percentage G is number of games in season th wi is winning percentage of i team Compare to “ideal” standard deviation is 0.500 w all teams evenly matched

N 2 as if each game decided by a flip of coin 1 (wi # w ) N $ " 1 Would all win half their games in ideal league? R = w = i= " 0.5 possible, but unlikely ! i G

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3 TEAMS, 4 GAMES, INTERPRETING IDEAL BALANCE THE RATIO winning wins losses % Many outcomes possible including three-way tie Red or, one team can go undefeated, another winless Blue Why take ratio? White longer season implies smaller standard deviation mean= comparable across leagues and years observed standard deviation= ideal standard deviation= R=1 means absolute balance ratio= usually we observe R > 1 higher R interpreted as imbalance note: use STDEVP rather than STDEV in Excel but can occur by chance 3 TEAMS, 4 GAMES, UNITED FOOTBALL RED TWICE AS GOOD LEAGUE 2012 winning % winning 1.000 wins losses % Omaha Nighthawks 0.500 0.250 Red Sacramento Mountain Lions 0.250 Blue

White 2 2 2 2 (0.25# .5) + (0.25# .5) + (0.5# .5) + (1# .5) " = w 4 " w mean R = mean 0.500 " i observed standard deviation standard deviation 0.306 ideal standard deviation ! theoretical ideal 0.500 0.250 ratio " i = ratio 4 1.225 !

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COMPETITIVE BALANCE RATIO SAMPLE MIDTERM 4.5 SUMMARY OUTPUT 4.0 Regression Statistics Multiple R 0.604 American League 3.5 R Square 0.365 National League Adjusted R Square 0.354 Standard Error 0.509 3.0 Observations 242 ANOVA 2.5 Df SS MS F Regression 4 35.290 8.823 34.027 2.0 Residual 237 61.449 0.259 Total 241 96.740 1.5 Coefficients Standard Error t Stat P-value intercept 2.327 0.366 6.359 0.000 1.0 NL=1 -0.064 0.069 -0.932 0.352 time -0.013 0.002 -6.880 0.000 0.5 number of teams 0.017 0.020 0.849 0.397 season length 0.003 0.002 1.326 0.186 0.0 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

BASEBALL IS BALANCE IN NOT WORST CHAMPIONSHIPS Downward trend 1950 1955 Generally MLB in the middle Yankees beat Phillies Dodgers beat Yankees NFL the most balanced 1951 1956 NBA the least balanced by far Yankees beat Giants Yankees beat Dodgers 1952 1957 Yankees beat Dodgers Braves beat Yankees MLB NFL NBA NHL EPL 1953 1958 Yankees beat Dodgers Yankees beat Braves 1954 1959 historical 2.10 1.56 2.55 1.85 1.61 Giants beat Indians Dodgers beat White Sox average