I'm doing some research for an article that I'm writing about competitive balance in sports, specifically professional football and baseball. My goal is to examine the many possible meanings of "competitive balance" and compare the competitiveness of the two leagues, given a certain definition. The first kind of competitive balance that I'm examining is the standard deviation of wins per year. In other words, I want to know how far apart the average team is from the average number of wins (8 in the NFL and 81 in MLB). A larger standard deviation would means more extreme values, with very high and very low win totals, suggesting very good teams and very bad teams. Alternatively, a small standard deviation means non-extreme values, with win totals concentrated around the mean, suggesting greater balance through out the league.
It is commonly stated that the NFL has greater competitive balance than MLB. Supposedly, the NFL's salary cap prevents high revenue teams from dominating the sport. The Yankees are criticized as the poster child for the unfairness of MLB's economic system. However, the truth about relative competitive balance depends on how we define competitive balance.
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MLB Win Total |
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|
| Variable |
OBV |
Mean |
Std. Dev. |
Min |
Max |
| Year2011 |
30 |
80.96667 |
11.41531 |
56 |
102 |
| Year2010 |
30 |
81 |
11.0047 |
57 |
97 |
| Year2009 |
30 |
81 |
11.43497 |
59 |
103 |
| Year2008 |
30 |
80.93333 |
11.08566 |
59 |
100 |
| Year2007 |
30 |
81.03333 |
9.293985 |
66 |
96 |
| Year2006 |
30 |
80.96667 |
10.08407 |
61 |
97 |
| Year2005 |
30 |
81 |
10.83417 |
56 |
100 |
| Year2004 |
30 |
80.93333 |
13.54668 |
51 |
105 |
| Year2003 |
30 |
80.96667 |
13.36615 |
43 |
101 |
| Year2002 |
30 |
80.83333 |
14.75334 |
55 |
103 |
| Year2001 |
30 |
80.93333 |
13.00645 |
62 |
116 |
| Year2000 |
30 |
80.93333 |
9.985967 |
65 |
97 |
| Year1999 |
30 |
80.9 |
12.51578 |
63 |
103 |
| Year1998 |
30 |
81 |
13.52902 |
54 |
114 |
The table above shows the range and STD DEV of win totals in MLB since 1998. This past season, around 2/3* of the teams were within 11.4 wins of the mean on either side (81).
*Under the normal distribution, around 2/3 of the sample falls within 1 STD DEV of the mean.*
NFL Win Totals
| Variable |
Obs |
Mean |
Std. Dev. |
Min |
Max |
| year2011 |
32 |
8 |
3.272564 |
2 |
15 |
| year2010 |
32 |
8 |
2.994619 |
2 |
14 |
| year2009 |
32 |
8 |
3.222902 |
1 |
14 |
| year2008 |
32 |
7.96875 |
3.326185 |
0 |
13 |
| year2007 |
32 |
8 |
3.321484 |
1 |
16 |
| year2006 |
32 |
8 |
2.896048 |
2 |
14 |
| year2005 |
32 |
8 |
3.388786 |
2 |
14 |
| year2004 |
32 |
8 |
3.079589 |
2 |
15 |
| year2003 |
32 |
8 |
3.069097 |
4 |
14 |
| year2002 |
32 |
7.96875 |
2.621061 |
2 |
12 |
| year2001 |
31 |
8 |
3.255764 |
1 |
14 |
| year2000 |
31 |
8 |
3.151719 |
1 |
13 |
| year1999 |
31 |
8 |
2.988868 |
2 |
14 |
| year1998 |
31 |
7.903226 |
3.409348 |
3 |
15 |
| year1997 |
31 |
8.032258 |
2.915292 |
3 |
13 |
The table above shows the range and STD DEV of win totals in NFL since
1998. This past season, around 2/3* of the teams were within 3.3 wins
of the mean on either side (8).
In order to compare the STD DEV's of wins in the two leagues, one of the leagues has to be rescaled to account for the different number of games (162 vs. 16). In the table below, the NFL has been rescaled.
| Variable |
Obs |
Mean |
Std. Dev. |
Min |
Max |
| xyear2011 |
32 |
81 |
33.13471 |
20.25 |
151.875 |
| xyear2010 |
32 |
81 |
30.32052 |
20.25 |
141.75 |
| xyear2009 |
32 |
81 |
32.63188 |
10.125 |
141.75 |
| xyear2008 |
32 |
80.68359 |
33.67763 |
0 |
131.625 |
| xyear2007 |
32 |
81 |
33.63003 |
10.125 |
162 |
| xyear2006 |
32 |
81 |
29.32249 |
20.25 |
141.75 |
| xyear2005 |
32 |
81 |
34.31146 |
20.25 |
141.75 |
| xyear2004 |
32 |
81 |
31.18084 |
20.25 |
151.875 |
| xyear2003 |
32 |
81 |
31.0746 |
40.5 |
141.75 |
| xyear2002 |
32 |
80.68359 |
26.53824 |
20.25 |
121.5 |
| xyear2001 |
31 |
81 |
32.96461 |
10.125 |
141.75 |
| xyear2000 |
31 |
81 |
31.91116 |
10.125 |
131.625 |
| xyear1999 |
31 |
81 |
30.26229 |
20.25 |
141.75 |
| xyear1998 |
31 |
80.02016 |
34.51965 |
30.375 |
151.875 |
After rescaling the NFL, we see that this league has a much higher STD DEV in every year going back to 1998. That 2/3 range mentioned above is much bigger in the NFL than in MLB, meaning that in the the NFL, the average team is further away from the mean than in MLB.
By this definition of competitive balance, the NFL could be considered to have less competitive balance than MLB in the sense that the NFL is more likely than MLB to have a large discrepancy between the best and worst team. Alternatively, MLB is likely to have final win totals concentrated relatively tightly around 81.
The data does not prove either way whether the NFL has more competitive balance than MLB; however, this first definition of competitive balance does not support the notion that the NFL is more competitive. Keep in mind that the differences in distribution of the win totals could be explained by other factors: the functional design of the game, injury rate, preparation time, etc. This one piece of analysis should not be taken overly seriously. This was merely one peek at a much larger question.
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