Post #1475204 · Elektrine

2026-04-18 10:30 UTC

An excellent stat: when Joe Root was out for 50 in the Boxing day test match of 2021, his batting average dropped from 50.015873016 to 50.015789474, a change of (it says here) 0.000083542 -- the smallest-ever non-zero change from one innings to the next. Question: at that point, how many runs had he scored, and how many innings had he completed? (Spoiler your answers, please.)

Replies (3)

@icecolbeveridge@mathstodon.xyz 2026-04-18 11:42

Suppose Sir Joseph had scored \(r \) runs in \( n \) [completed] innings before this score, and call the before-and-after averages \(A_0\) and \( A_1 \). Then: * \( r = A_0 n \) * \( r + 50 = A_1 (n+1) \) So \( 50 = n(A_1 - A_0) + A_1 \) and \( n = \frac{50 - A_1}{A_0 - A_1} \) The RHS is all numbers we know, and we get \( n = \frac{0.01587\dots}{0.0000835\dots} \approx 189 \) and \( r = A_0 n \approx 9453 \).

Open ##4567968
@ajsoley@mastodon.social 2026-04-18 11:14

@icecolbeveridge@mathstodon.xyz I know nothing about this sport, but I know the numerator changed by 50 and the denominator by 100 (or some integer multiple of that). New denominator 19000.

Open ##4567969
@vpunt@mastodon.social 2026-04-18 11:27

@icecolbeveridge@mathstodon.xyz 9453 runs from 189 innings, considering 63 is the smallest integer that can multiply 0.015873016 to give an integer and with some guesswork after that based on his Cricinfo profile.

Open ##4567973