Centering transforms a value by subtracting a reference center, usually the mean. It adjusts for differences in context without scaling the variable's dispersion. section 19.4.3
For NBA scoring, compare each year's leading scorer with that year's scoring environment rather than comparing raw points per game across decades. Annual means account for changing rules and playing styles. section 19.0 section 20.8
A practical centering workflow is:
- Group the data by Year and calculate the annual mean of PPG. section 19.4.3
- Join the annual means to the scoring-leader records by Year. section 19.4.3
- Create c_ppg by subtracting mean from PPG: c_ppg = PPG - mean. section 19.4.3
- Plot c_ppg to inspect adjusted scoring differences across years. section 19.4.3
NBA scoring leaders
For 1950, George Mikan's 27.4 PPG minus the annual mean of 6.1 produces c_ppg = 21.3. The centered values are lower than the raw totals, but year-over-year comparisons retain the same pattern. section 19.4.3
dat2 %>% group_by(Year) %>% summarize(mean = round(mean(PPG), digits = 1)) -> dat6a head(dat6a, n = 3) ## # A tibble: 3 × 2 ## Year mean ## <fct> <dbl> ## 1 1950 6.1 ## 2 1951 6.6 ## 3 1952 7.1 tail(dat6a, n = 3) ## # A tibble: 3 × 2 ## Year mean ## <fct> <dbl> ## 1 1997 7.2 ## 2 1998 6.7 ## 3 1999 6.8
Inspect the annual means used as centering references before joining them to player records. section 19.4.3
