Exercise 3: Twenty PRs Instead of Eight — Possible Solution
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RESULTS
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    20 PRs per author:
    GATE-ONLY: average 11.99 mistakes across 20 PRs
    TEACHING: average 4.09 mistakes across 20 PRs
    Reduction: 66%

    (chapter's own 8-PR result: gate=4.80, teaching=2.64, reduction=45%)

    Per-PR mistake rate:
      Gate-only: 0.60/PR at both 8 and 20 PRs (unchanged - flat, as expected)
      Teaching: 0.33/PR at 8 PRs, dropping to 0.20/PR at 20 PRs

DOES THE GAP GROW, SHRINK, OR STAY PROPORTIONAL?
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It grows - both in absolute terms (7.90 fewer mistakes at 20 PRs vs.
2.16 fewer at 8) and in relative terms (66% reduction vs. 45%). The
gate-only rate stays perfectly flat at 0.60 per PR regardless of how
many PRs are observed, since nothing about that policy ever changes
the underlying mistake probability. The teaching rate keeps compounding
downward with every additional PR, since each teaching moment further
reduces the rate for every PR that follows it - more PRs means more
opportunities for that compounding effect to keep paying off.

WHY THIS WORKS AS AN ANSWER
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This is an important, realistic correction to reading the chapter's
own 8-PR number as "the" improvement teaching reviews provide - the
real payoff compounds over an author's own career, not just their
first handful of PRs. A team evaluating whether teaching-style reviews
are "worth the extra time" by looking only at a new hire's first
sprint or two would systematically undervalue the practice, since the
gap between the two review styles is still actively widening at that
point, not yet near its long-run difference.