Comparing Bottom-Up and Top-Down Statistical Measurement Models in Basketball

In basketball, there are two models for measuring statistics, namely the ‘Bottom Up’ model and the ‘Top Down’ model.

Bottom Up Statistical Measurement Model

The bottom up statistical measurement model is a statistical measurement built based on individual achievements. The bottom up model can be found in the box score except for plus-minus. With the bottom up method, we will measure based on the individual statistics of each player, such as points, rebounds, fouls, etc.

The weakness of measuring statistics using the bottom up model is that it only measures individual statistical achievements, without considering the contributions of teammates in generating those individual achievements. For example, if an opponent fails to make a shot and then Player A makes a defensive rebound, the bottom up model will only measure Player A’s achievement with the increase in defensive rebounds, but it will not account for the contributions of teammates who performed box-out. All teammates who contributed to Player A’s statistical achievement will be overlooked.

On October 9, 2019, local time, the New Orleans Pelicans played a preseason game against the Chicago Bulls. In that game, there was an interesting note: Zion Williamson made 12 shots out of 13 attempts. However, the plus-minus statistic showed -18.

If using the bottom up model, Zion’s individual achievement statistics are very impressive. He was the main contributor to the scoring productivity, contributing 29 points. Zion only missed 1 shot out of 13 attempts. Additionally, Zion had 4 assists and only committed 1 turnover. His offensive efficiency reached 1 point for every possession.

Top Down Statistical Measurement Model

The top down statistical measurement model is a statistical measurement built by considering the contributions of other teammates in generating the team’s statistical achievements. One example of the top down model is plus-minus. For instance, if Player A is on the court when the game score is still 0–0, and then Player A makes a two-point shot, all teammates on the court at the time Player A made the two-point shot will receive +2.

The weakness of the top down model is that it can lead to errors in measuring the statistical achievements of players with below-average abilities if those players are on a strong team. For example, if Player A, who has below-average abilities, plays alongside four teammates with above-average abilities, Player A will receive a high plus-minus value.

In a book published by Stephen M. Shea and Christopher E. Baker, it is illustrated that during the 2012–13 NBA season, Mario Chalmers outperformed Chris Paul in terms of plus-minus statistics. The reason for Mario Chalmers’ high plus-minus statistic is that he played alongside great players, such as LeBron James and Dwyane Wade. Conversely, if Player A, who has above-average abilities, plays with four teammates who have below-average abilities, then Player A will receive a low plus-minus value.

In the game between the Pelicans and the Bulls, Zion had a plus-minus of -18. This statistic was not generated solely due to Zion’s individual burden. Instead, the statistic was created because of the burden on all of Zion’s teammates when Zion was on the court.

There is No Perfect Method

From the explanations above, each method has its own weaknesses. In assessing player performance, one cannot rely solely on one model; instead, it is necessary to incorporate other methods to create an evaluation of ‘the impact of individual player performance on the success of a team.