liveBook · Manning

37% rule

As explained in Statistics Slam Dunk

Optimal stopping is the problem of choosing when to stop observing sequential opportunities to maximize an objective under uncertainty.

The 37% rule, also called optimal stopping or the look-then-leap rule, guides a one-time choice among sequential opportunities. Reject the first 37% as a comparison set, then choose the first later option that is at least as good as every option seen so far. Its aim is the highest probability of the best available outcome while avoiding endless, valueless searching—not a guarantee of the best result. section 8.0 section 8.5.1

The rule requires a fixed pool or deadline and no second chances. With 20 candidates or 20 seconds, 37% is seven when rounded down: observe the first seven, then act on the first option that clears the earlier benchmark. section 8.5.1 section 8.6

A 24-second NBA possession

Passing and dribbling can be treated as observing candidates; shooting is the irreversible choice. A literal 37% strategy would delay a shot during the opening portion of the possession, then take the first shot opportunity that compares favorably with prior ones. League-wide 2019–20 results instead showed points and field-goal percentage falling as possessions lasted longer, favoring earlier shots. section 8.0 section 8.5.4

pbp %>% 
 filter(team == "MIL",
        play_length2 >= 5 & play_length2 <= 24,
        event_type == "shot" | event_type == "miss") -> MIL
dim(MIL)
## [1] 5436   45

This R pipeline isolates Milwaukee shot and miss events from five through 24 seconds of possession, creating the data used to test scoring patterns by timing. section 8.5.1

Team-level results show why the rule must be tested rather than assumed:

  • Atlanta’s best points and field-goal percentage occurred at seven seconds, with no equal-or-better result after the 37% mark; this did not support the rule. section 8.5.2
  • Charlotte’s strongest early result came at six seconds, but an 18-second result exceeded it on both measures, matching the rule more closely. section 8.5.3
  • Across the league, apparent optimal-stopping patterns may instead reflect regression to the mean, especially where late-second observations are sparse. section 8.5.4 section 8.6

Outside basketball, the same decision pattern fits a home search with a 60-day deadline, speed dating, or selecting legal precedent—provided choices cannot be revisited. For a 60-day home search, inspect without committing for the first 22 days, then offer on the first house that favorably compares with the early set. section 8.6

How Statistics Slam Dunk covers it

How deep it goes
Defines the decision rule, computes its threshold, and evaluates it with team and league scoring visualizations without formal proof.
Examples
Uses hiring, home buying, speed dating, legal research, and 2019–20 Bucks, Hawks, Hornets, and NBA possessions.
What it assumes
Introduces the rule through everyday decisions while applying R-based data wrangling and visualization to play-by-play data.
What you can do after
Evaluate/understand whether a sequential NBA shooting decision fits the 37% rule using points and field-goal percentage by possession second.
How it connects
Connects optimal stopping with regression to the mean, field-goal percentage, frequency tables, and ggplot2 trendlines.

Related concepts

This explainer was generated by Manning's knowledge graph from the text of Statistics Slam Dunk. The section links point to the parts of the book it draws on.