Points per adjusted tossups heard

PATH, or Points per Adjusted Tossups Heard, is a statistic developed by Samer Ismail to attempt to account for the shadow effect in individual PPG statistics.

Formula

1. Multiply the number of points scored by the player by 20.
2. Subtract the number of tossups correctly answered by the player's teammates and one-half the number of negs by the player's teammates from the total number of tossups heard by the player. Multiply this result by the fraction of the total questions heard by the team that the player heard.
3. Divide the result from Step 1 by the result from Step 2.

Criticism

The formula for PATH assumes that the shadow effect of Player A on Player B is of the same magnitude as the shadow effect of Player A on Player C. Because every player has a unique knowledge base, this assumption is invalid (consider the case of two physics specialists playing together, as opposed to one physics specialist and one history specialist). To counteract these problems by taking advantage of the invention of detailed stats, John Lawrence proposed category-adjusted PATH.

In addition, the correction for substitutions is mathematically unsound.