A personal foul call records a personal foul committed by a team in a game. In a game-level data set, it can be treated as a numeric count for each road and home team, then compared to ask whether officiating patterns may contribute to home-court advantage. Free throw attempts are a related outcome because they are usually awarded after an opponent commits a personal foul, though not every foul produces free throws. section 7.0 section 7.3
Start by separating regular-season games from other games, then calculate total and mean personal fouls for road and home teams. Raw differences describe the pattern, but they do not by themselves establish whether the group means differ beyond chance. A two-group t-test supplies that check: at a 0.05 threshold, a p-value at or below 0.05 leads to rejecting the null hypothesis that the means are equal. section 7.4.1 section 7.0
fouls1819 %>% filter(dataset == "NBA 2018-2019 Regular Season") -> fouls1819reg sum(fouls1819reg$pfR) - sum(fouls1819reg$pfH) ## [1] 470 mean(fouls1819reg$pfR) - mean(fouls1819reg$pfH) ## [1] 0.3821138 mean(fouls1819reg$ftaR) - mean(fouls1819reg$ftaH) ## [1] -0.6504065 sum(fouls1819reg$ftR) / sum(fouls1819reg$ftaR) ## [1] 0.7655742 sum(fouls1819reg$ftH) / sum(fouls1819reg$ftaH) ## [1] 0.7670176
This calculation filters 2018–19 regular-season games and compares road and home foul totals and per-game averages. Road teams were called for 470 more personal fouls overall, or about 0.38 more per game; home teams attempted about 0.65 more free throws per game. section 7.4.1
Home versus road calls in 2018–19
Road teams averaged 21.10 personal fouls per game, compared with 20.71 for home teams. The Welch two-sample t-test returned p = 0.027, so the difference was statistically significant using the 0.05 cutoff. The result indicates a detectable difference in this data set, not its cause or its effect on game outcomes. section 7.4.1 section 7.6
Repeat the comparison across contexts before drawing a broad conclusion. Before COVID-19 suspended the 2019–20 season, road teams averaged about 0.39 more fouls per game and the t-test was barely significant (p = 0.049). In the 89-game Orlando segment without fans, the road-team difference was larger at about 0.61 per game but not statistically significant (p = 0.35), illustrating how record count affects significance. section 7.5.1 section 7.5.2
Statistical significance and practical size answer different questions. Pair t-tests with Cohen’s d: significance depends on means, variance, and record count, whereas Cohen’s d assesses the size of the difference using means and standard deviations. Across the analyzed seasons and splits, differences directionally favored home teams but Cohen’s d rated them negligible; the evidence supports a slight pattern, not an explanation of why it occurs. section 7.0 section 7.6
