A basketball team trailing late in a game will often commit deliberate fouls. The tactic looks self-defeating, since it gives the opponent free throws, but the arithmetic supports it under specific conditions.
The clock is the scarce resource
A trailing team needs both points and possessions, and a leading team can consume most of the shot clock before attempting anything.
Left alone, the leading side can burn a large share of the remaining time across very few possessions, leaving the trailing team no opportunity to score.
Fouling stops the clock immediately, converting a long possession into a brief one and preserving time the trailing team needs.
Free throws are cheaper than a full possession
Two free throws yield fewer points on average than a leading team would generate from an uncontested possession followed by an offensive rebound.
More importantly, the ball returns to the trailing team afterwards, which a normal possession does not guarantee.
The trade is a small expected points concession in exchange for a guaranteed possession and a stopped clock.
The target is chosen deliberately
Teams foul the opponent least likely to convert from the line, since the expected cost of the tactic depends almost entirely on that player's accuracy.
This produced the practice of fouling a specific weak shooter repeatedly and away from the ball, which slowed games considerably.
Rule changes penalising off-ball fouls in the closing period curtailed the extreme version while leaving the ordinary tactic intact.
Foul counts constrain the tactic
Once a team passes a threshold of team fouls in a period, every subsequent foul awards free throws regardless of where it occurs.
Committing fouls earlier therefore raises the cost of fouling later, so teams manage their foul count with the endgame in mind.
Individual foul limits add a second constraint, since a player who fouls out is unavailable for the remainder of the game.
The margin decides whether it is worth it
The tactic works when the deficit is small enough to be erased in the possessions remaining, and it fails when the gap is too large.
Coaches calculate a rough threshold before the situation arises, based on the score difference, the time left and who is on the floor.
Beyond that threshold, fouling simply extends a decided game, which is why teams sometimes accept a loss rather than prolong it.
