Parity is competitive balance among teams. In a league with greater parity, teams have more equivalent talent and outcomes are less predictable. Statistical dispersion makes parity measurable: higher spread in regular-season wins means less intra-season parity. section 18.0 section 18.4
Analyze parity from two complementary angles:
- Measure intra-season parity by grouping regular-season wins by season and comparing their dispersion before and after the 1984-85 salary-cap introduction. section 18.0 section 18.4
- Measure inter-season parity through churn: rank teams by regular-season wins, divide them into groups, and count year-over-year changes among leading teams. section 18.5 section 18.5.2
- Use several dispersion measures rather than relying on one: variance, standard deviation, range, mean absolute deviation, and median absolute deviation. section 20.7
NBA salary-cap test
Grouping NBA records by Season and calculating standard deviation shows the practical meaning of parity. In 1976-77, roughly two-thirds of teams won between 33 and 49 games; in 1996-97, the comparable interval widened to 25 through 57 wins, indicating more dispersion and less parity. Across the five measures, intra-season parity improved from 1970-71 through 1983-84 and worsened from 1984-85 through 1997-98. Churn analysis also found no salary-cap effect on inter-season parity. section 18.4.2 section 20.7 section 18.5.2
records %>% group_by(Season) %>% summarize(v_wins = var(W)) -> var_records head(var_records, n = 3) ## # A tibble: 3 × 2 ## Season v_wins ## <chr> <dbl> ## 1 1970-71 143. ## 2 1971-72 235. ## 3 1972-73 264. tail(var_records, n = 3) ## # A tibble: 3 × 2 ## Season v_wins ## <chr> <dbl> ## 1 1995-96 197. ## 2 1996-97 245. ## 3 1997-98 241.
Inspect the R pipeline that groups records by season and computes variance in regular-season wins. section 18.4.1
