Measuring Parity at the NCAA D1 Championships

by Andrew Mering 5

March 31st, 2017 College, News

Both the Stanford women and the Texas men won their respective championships by dominating margins. In contrast, the places behind them were actually very close. The Georgia women beat Texas for 4th by 1/2 a point. The Louisville women beat NC State for 6th by 1/2 a point. The Stanford men beat USC for 5th by 5 points. So which was it? On the whole, was this year a close meet or a blowout? Both the race for first (not close) and the lower place (close) matter when answering. We need something more precise than examples to measure parity. One option is Gini coefficients (more precise definition).

The Gini coefficient is a statistic used to measure inequality. It was created to measure inequality in wealth distribution; for this article we will be using it to measure inequality in points distribution. If you want to know more about how it works check out the links I put in above with more information. For the purposes of this article you need to know two things:

1)  For Gini coefficients, 0 is total equality (i.e. all teams score the same number of points), 1 is total inequality (i.e. the top team scores all the points), and values in between mean different degrees of unequal distribution of points.

2) The Gini coefficient measures inequality over the whole population, so a meet with more teams scoring (aka more parity) might actually increase inequality if there are too many teams with just a couple points**. More teams scoring would actually indicate more parity, so I calculated the Gini’s for the top N teams instead of the whole field of scoring teams (i.e. Gini of the top 10, top 20 ect.). This fixes the problem of more scoring teams= less equality, but what we want is more scoring teams = more equality. Therefore, I also calculated the percent of the total points scored by the top N teams. Fewer points scored by the top teams would indicate more parity.

Measuring Parity

This year didn’t stand out in any meaningful way in terms of equality among teams, but there are some interesting long term trends. Inequality among the top 20 men’s teams was steadily decreasing from the start of NCAA competition in the 30’s until about 2000. Then it jumped and has been slow decreasing again since. This year was in line with the recent trend.

The long term trend among top 5 men’s teams has also been towards increasing parity, but the short term trend has been towards less parity. This makes sense as Texas has been winning by large margins recently. The Gini for top 5 men’s teams was at .11 in 2014 and .07 in 2010, but has been above .14 the last 3 years.

Among top 20 teams, the women tied an all time high in parity this year with a Gini of .34 (tied with 1997). The next all time most equal years wer last year and 2011 with .35.

The top 5 women were less equal this year than in the near past with a Gini of .19 vs .09 last year. This year did set an all time low percentage of points accounted for by the top 5 teams with 42%. The all time low for inequality among top 5 teams was in 2010 with a Gini of .02. That year the 5th place team was within 40 points of 1st.

Gini coefficients don’t tell the whole story. They only measure the inequality among the group they’ve been applied to. The complementary percentage of total points accounted for by that group stat is necessary to get a fuller picture (Complete Gini and percent data for top 5, 10, and 20 teams is in the tables at the bottom of this post). Among top 10 teams the lowest Gini was .14 in 1987, but that doesn’t mean that was the most equal year. In 1987, the top 10 accounted for 72% of all points. In 1997, the top 10 accounted for only 66% of points and the Gini was .19. Here’s a comparison of Gini coefficients vs 10 points share. Down and left is more equal. Up and right is less equal:

And for the women:

 

Women’s Equality over Time

5 Places 10 Places 20 Places
Gini % of Points in top 5 Gini % of Points in top 10 Gini % of Points in top 20
2017 0.16 42% 0.20 65% 0.34 90%
2016 0.09 43% 0.18 68% 0.35 90%
2015 0.18 44% 0.27 64% 0.36 86%
2014 0.13 48% 0.24 70% 0.43 86%
2013 0.09 45% 0.17 74% 0.40 91%
2012 0.06 43% 0.14 71% 0.36 91%
2011 0.10 43% 0.16 68% 0.35 90%
2010 0.02 46% 0.19 71% 0.39 89%
2009 0.07 45% 0.19 71% 0.39 90%
2008 0.09 44% 0.22 67% 0.38 87%
2007 0.13 51% 0.24 74% 0.42 91%
2006 0.17 50% 0.28 70% 0.39 91%
2005 0.13 55% 0.31 74% 0.44 92%
2004 0.18 46% 0.25 69% 0.36 92%
2003 0.14 44% 0.19 70% 0.36 91%
2002 0.10 44% 0.12 74% 0.36 91%
2001 0.05 43% 0.16 69% 0.36 88%
2000 0.15 47% 0.25 68% 0.36 90%
1999 0.10 49% 0.25 70% 0.38 92%
1998 0.07 45% 0.16 73% 0.36 94%
1997 0.05 45% 0.19 70% 0.34 93%
1996 0.10 47% 0.19 72% 0.37 94%
1995 0.14 47% 0.23 71% 0.40 90%
1994 0.15 46% 0.23 68% 0.38 89%
1993 0.19 50% 0.27 73% 0.41 93%
1992 0.23 56% 0.34 76% 0.49 92%
1991 0.27 56% 0.36 75% 0.49 91%
1990 0.21 55% 0.36 72% 0.47 89%
1989 0.19 55% 0.32 74% 0.46 91%
1988 0.23 54% 0.31 75% 0.47 92%
1987 0.22 55% 0.34 74% 0.45 93%
1986 0.24 56% 0.34 74% 0.47 89%
1985 0.20 50% 0.30 70% 0.40 90%
1984 0.13 63% 0.34 82% 0.51 96%
1983 0.17 57% 0.27 82% 0.48 96%
1982 0.18 61% 0.29 86% 0.51 99%

Men’s Equality over Time

5 Places 10 Places 20 Places
Gini % of Points in top 5 Gini % of Points in top 10 Gini % of Points in top 20
2017 0.16 42% 0.20 67% 0.34 90%
2016 0.14 46% 0.21 70% 0.35 94%
2015 0.15 44% 0.20 69% 0.35 92%
2014 0.11 46% 0.22 69% 0.37 91%
2013 0.11 44% 0.16 73% 0.37 92%
2012 0.12 53% 0.26 75% 0.43 92%
2011 0.12 49% 0.23 73% 0.38 94%
2010 0.07 52% 0.25 74% 0.42 93%
2009 0.10 53% 0.25 77% 0.46 92%
2008 0.09 47% 0.19 73% 0.40 91%
2007 0.13 50% 0.25 73% 0.39 93%
2006 0.12 46% 0.19 73% 0.41 91%
2005 0.09 49% 0.20 74% 0.37 96%
2004 0.16 50% 0.27 73% 0.39 94%
2003 0.15 50% 0.24 73% 0.40 94%
2002 0.15 49% 0.21 76% 0.41 95%
2001 0.17 50% 0.23 75% 0.42 94%
2000 0.14 46% 0.20 72% 0.37 94%
1999 0.10 46% 0.22 69% 0.36 93%
1998 0.20 45% 0.26 66% 0.34 91%
1997 0.14 42% 0.19 66% 0.31 89%
1996 0.10 47% 0.24 68% 0.38 89%
1995 0.16 50% 0.21 77% 0.43 94%
1994 0.16 48% 0.19 74% 0.38 91%
1993 0.15 44% 0.23 66% 0.34 90%
1992 0.20 45% 0.21 70% 0.37 92%
1991 0.13 45% 0.20 69% 0.35 91%
1990 0.10 48% 0.21 72% 0.40 92%
1989 0.09 46% 0.21 69% 0.36 90%
1988 0.15 48% 0.24 70% 0.38 90%
1987 0.07 46% 0.14 72% 0.36 90%
1986 0.06 52% 0.24 73% 0.41 91%
1985 0.10 48% 0.19 75% 0.41 93%
1984 0.13 58% 0.26 82% 0.48 97%
1983 0.09 52% 0.22 79% 0.44 95%
1982 0.10 47% 0.18 74% 0.38 95%
1981 0.11 48% 0.19 76% 0.38 98%
1980 0.06 52% 0.21 79% 0.43 96%
1979 0.06 59% 0.25 84% 0.50 97%
1978 0.14 51% 0.19 81% 0.43 98%
1977 0.18 56% 0.28 80% 0.47 96%
1976 0.19 61% 0.32 81% 0.49 97%
1975 0.16 58% 0.30 82% 0.49 97%
1974 0.13 68% 0.32 88% 0.55 98%
1973 0.18 64% 0.33 86% 0.53 98%
1972 0.24 62% 0.34 85% 0.53 98%
1971 0.19 57% 0.28 82% 0.48 96%
1970 0.17 56% 0.29 78% 0.44 97%
1969 0.22 65% 0.39 82% 0.53 96%
1968 0.20 58% 0.34 77% 0.48 94%
1967 0.12 58% 0.28 82% 0.49 96%
1966 0.15 59% 0.31 81% 0.50 94%
1965 0.22 62% 0.33 84% 0.53 95%
1964 0.26 78% 0.44 93% 0.60 100%
1963 0.16 70% 0.36 90% 0.57 99%
1962 0.23 61% 0.35 82% 0.50 97%
1961 0.25 65% 0.39 83% 0.53 97%
1960 0.22 73% 0.39 93% 0.57 100%
1959 0.29 74% 0.42 94% 0.60 100%
1958 0.15 69% 0.37 85% 0.53 99%
1957 0.16 69% 0.37 88% 0.56 99%
1956 0.22 60% 0.30 85% 0.45 100%
1955 0.31 66% 0.40 86% 0.55 99%
1954 0.32 69% 0.46 84% 0.57 99%
1953 0.27 76% 0.47 87% 0.58 99%
1952 0.31 78% 0.46 94% 0.61 100%
1951 0.28 70% 0.42 87% 0.52 100%
1950 0.26 67% 0.36 90% 0.53 100%
1949 0.25 66% 0.33 89% 0.49 100%
1948 0.22 70% 0.35 94% 0.57 100%
1947 0.31 79% 0.47 96% 0.64 100%
1946 0.33 71% 0.41 92% 0.58 100%
1945 0.32 77% 0.43 97% 0.64 100%
1944 0.13 73% 0.37 92% 0.56 100%
1943 0.46 79% 0.50 96% 0.66 100%
1942 0.39 79% 0.49 96% 0.64 100%
1941 0.25 87% 0.52 95% 0.66 100%
1940 0.16 83% 0.30 100% 0.65 100%
1939 0.22 90% 0.52 96% 0.67 100%
1938 0.19 82% 0.46 94% 0.62 100%
1937 0.35 87% 0.53 100% 0.71 100%

**The way to avoid this issue would be to include every team in the NCAA. This stat is designed to include the whole population and that’s the whole population. Using every team would introduce new problems. The number of teams in the NCAA changes over time. That would heavily influence this stat. In years where the division was small but had a only a couple teams dominating the meet (like in the 80’s for the women)  we might see more equality, when, at nationals there was actually less. If we used a fixed number of teams such as 100, it’s back to a different version of the cut off solution I actually used above, but with less ability to examine difference in smaller subsets. This article is about nationals not the whole division. If we wanted whole division inequality, I think a better solution would be to calculate Ginis for a “true team nationals” (similar to the super nationals in this article, but with teams instead of whole conferences).

Leave a Reply

5 Comments on "Measuring Parity at the NCAA D1 Championships"

Sort by:   newest | oldest | most voted

Great diagnostic but it might help if the standard deviation were calculated with zero random parameter. Also would be interesting to compare this to Q-value matrix formula.

I always love these data posts. The first thing I thought of is whether we would see a trend for the years before Olympics – you would expect that there would be more parity as top teams lose a few studs to redshirt, while less schools may do even better due to increased interest/energy in the sport.

Can you please provide a link to where you found the placing and respective points scored amongst the teams for each championship?

Andrew Mering

Men: http://fs.ncaa.org/Docs/stats/swimming_champs_records/2016-17/D1men.pdf
Women: http://fs.ncaa.org/Docs/stats/swimming_champs_records/2016-17/D1women.pdf
The point are at the bottom in the section called all time team results. This year isn’t in those yet, so I had to add it separately.

wpDiscuz