Standardization converts raw numeric values to a common scale so comparisons reflect context rather than incompatible units, changing conditions, or one variable’s larger magnitude. It is especially useful for measurements that span seasons or for multivariable analysis such as payroll and wins. section 19.0 section 11.3
A z-score expresses how many standard deviations a value lies above or below the mean. Compute it by subtracting the mean from the raw value and dividing by the standard deviation. A positive score is above average, a negative score is below average, and zero is at the mean. section 14.2.6 section 11.3
Put payroll and wins on one scale
Team payroll and regular-season wins use very different units. Standardize both before plotting them together: the distance between each team’s salary and win z-scores then shows how closely investment aligns with return. Without this step, the comparison cannot be drawn meaningfully. section 11.4.2 section 11.3
nba_stats %>% group_by(season) %>% mutate(z_wins = (wins - mean(wins)) / sd(wins)) -> nba_stats nba_stats$z_wins <- round(nba_stats$z_wins, digits = 2) nba_stats %>% group_by(season) %>% mutate(z_pts = (PTS - mean(PTS)) / sd(PTS)) -> nba_stats nba_stats$z_pts <- round(nba_stats$z_pts, digits = 2) nba_stats %>% group_by(season) %>% mutate(z_o_pts = (O_PTS - mean(O_PTS)) / sd(O_PTS)) -> nba_stats nba_stats$z_o_pts <- round(nba_stats$z_o_pts, digits = 2)
This R workflow groups NBA records by season, creates z-scores for wins, points scored, and opponent points, then rounds the standardized values for inspection. section 14.2.6
Standardize within the comparison group when conditions change over time. For NBA seasons, calculating each season’s mean and standard deviation separately accounts for differing schedules, rules, and styles of play; a raw total can then be read relative to its own season. section 14.2.6 section 20.8
Choose a method that fits the question rather than treating standardization as one fixed recipe:
- Use z-scores: raw value minus the population mean, divided by the standard deviation. section 20.8
- Use the standard-deviation method: raw value divided by the standard deviation. section 20.8
- Use centering: raw value minus the mean. section 20.8
- Use the range method: raw value divided by the difference between the maximum and minimum values. section 20.8
Reconsider historical scoring
A 50-point scoring average can look extraordinary in raw form while still requiring era context. Comparing each annual scoring leader with that season’s league mean gives a different perspective when pace, rules, and shot opportunities vary across decades. section 19.0 section 20.8
