First is the worst, second is the best? A Markov chain analysis of the basketball game knockout

TL;DR

This paper models the playground basketball game Knockout using Markov chains to analyze winning probabilities, game duration, and strategies, providing insights into whether the common wisdom about player order holds true.

Contribution

It introduces a Markov process framework to analyze Knockout, solving for two players and numerically for multiple players, and explores strategic implications.

Findings

First player is often at a disadvantage in winning probability.

Average game length depends on players' shooting percentages.

Strategic tips vary with skill levels and player order.

Abstract

The game of Knockout is a classic playground game played with two basketballs. This paper uses a Markov process to analyze each player's probability of winning the game given their starting position in line and shooting percentages, assuming all players are equally skilled. The two-player case is solved in general for any probability of a long shot and short shot shooting percentage and the n-player case with n > 2 is solved numerically. In doing so, this paper answers the question of whether or not the playground wisdom of ``first is the worst, second is best'' is true. We also examine the average number of rounds it takes before the game ends, analyze trends in the data to recommend tips to win at Knockout, and provide questions in the case of players not being equally skilled.