Counts, leverage and pitch sequencing

A plate appearance is a small game inside the big one, played on a board of twelve counts. Every pitch moves it one square right (a ball) or one square down (a strike), until someone reaches four balls, three strikes, or the ball is put in play.

Each square has a value — the batter's expected outcome from there — and the pitches that matter most are the ones that move between squares of very different value. A pitcher who wins those pitches wins the plate appearance; a hitter who knows which they are knows when to be aggressive.

Sequencing is where game theory enters. If the pitcher's fastball is his best pitch and he throws it every time, the hitter sits on it and it stops being his best pitch. The right mix is the one at which the hitter gains nothing by guessing — a mixed-strategy equilibrium, the same idea that tells a penalty taker to go left some fixed share of the time.

Take the lab's example: a hitter sitting fastball does .460 against fastballs and .240 against off-speed; sitting off-speed, .280 and .410. The equilibrium is 49% fastballs, and the hitter should sit fastball 37% of the time. Neither side can do better than a .347 wOBA by deviating. Throwing more fastballs than that, because the fastball is “better”, hands the hitter points.

A KBO plate appearance lasted 3.90 pitches this season. Strikeouts ended 19.5% of them and walks 9.4% — the two outcomes decided entirely by the count. The seasons the platform holds show the long drift: more pitches, more strikeouts, a strike zone that since 2024 is called by a machine.