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whole period, 1954-83, there were on average 52.2 fouls called per game. Hence, the effect of adding the third official was substantial—a 50 percent increase in the number of enforcers was associated with a 34 percent reduction in the number of arrests. The other results in table 1 are consistent with rational behavior on the part of the participants. The time trend has been to increase the number of fouls called by about two per game per year. SCORE, as a proxy for speed and action on the court, is positively associated with more fouls per game; more action begets more fouls although the direction o f effect could be the opposite. Each 10 points scored is associated with about one more foul. The better either team shoots, as proxied by FREEPCT and FGPCT, the less it is fouled. On average a 1 percentage point increase in free throw accuracy by one team is associated with about eight fewer fouls per game by the opponent. The greater the difference between the heights of the two teams, the more fouls per game. The more disparate is the experience of the two coaches in a given game, the more fouls are called. The opposite is true for players' experience. Referees' experience has a negative and significant coefficient. Attendance is a proxy for the importance of the outcome of the game. The two rule changes, SHOOT and
DOI link for whole period, 1954-83, there were on average 52.2 fouls called per game. Hence, the effect of adding the third official was substantial—a 50 percent increase in the number of enforcers was associated with a 34 percent reduction in the number of arrests. The other results in table 1 are consistent with rational behavior on the part of the participants. The time trend has been to increase the number of fouls called by about two per game per year. SCORE, as a proxy for speed and action on the court, is positively associated with more fouls per game; more action begets more fouls although the direction o f effect could be the opposite. Each 10 points scored is associated with about one more foul. The better either team shoots, as proxied by FREEPCT and FGPCT, the less it is fouled. On average a 1 percentage point increase in free throw accuracy by one team is associated with about eight fewer fouls per game by the opponent. The greater the difference between the heights of the two teams, the more fouls per game. The more disparate is the experience of the two coaches in a given game, the more fouls are called. The opposite is true for players' experience. Referees' experience has a negative and significant coefficient. Attendance is a proxy for the importance of the outcome of the game. The two rule changes, SHOOT and
whole period, 1954-83, there were on average 52.2 fouls called per game. Hence, the effect of adding the third official was substantial—a 50 percent increase in the number of enforcers was associated with a 34 percent reduction in the number of arrests. The other results in table 1 are consistent with rational behavior on the part of the participants. The time trend has been to increase the number of fouls called by about two per game per year. SCORE, as a proxy for speed and action on the court, is positively associated with more fouls per game; more action begets more fouls although the direction o f effect could be the opposite. Each 10 points scored is associated with about one more foul. The better either team shoots, as proxied by FREEPCT and FGPCT, the less it is fouled. On average a 1 percentage point increase in free throw accuracy by one team is associated with about eight fewer fouls per game by the opponent. The greater the difference between the heights of the two teams, the more fouls per game. The more disparate is the experience of the two coaches in a given game, the more fouls are called. The opposite is true for players' experience. Referees' experience has a negative and significant coefficient. Attendance is a proxy for the importance of the outcome of the game. The two rule changes, SHOOT and
ABSTRACT
We report ordinary least squares and logistic regressions of the upset model in table 2, including O F F I C I A L . The change from two to three officials is associated with a reduced probability of upsets, and the result is statistically significant at the 10 percent level. 9 We interpret this result to mean that the quality of officiating increased with the advent o f three officials. That is, three officials reduced the variance in the outcome o f tournament games, which implies that the quality o f officiating increased with three referees. In turn this sug-