How every number is worked out

A bowler's league average is their pins divided by their games, with the fraction dropped (a league can choose rounding instead). Only games actually rolled count: absentee scores, vacancies and the credit for an unfinished game never do.

Until a bowler has bowled the league's establishing games (3 unless the league sets another number), the entering average is used: the book average the secretary typed, usually last season's. A bowler with no average at all establishes one in their first session, and that night's handicap comes from the games they roll that night (USBC Rule 108c).

Beside each average the sheet prints the series that raises it by one pin next week and the series that drops it by one.

Handicap = (basis − average) × percentage, fraction dropped, with an optional cap. Averages above the basis get 0, or a negative handicap if the league adopted that option (USBC Rule 100d-2; 100% when the rules are silent).

A night is always bowled with the handicaps from the averages before it. Publishing the week moves the averages, and next week's handicaps follow.

• —Absentee (USBC Rule 112): the absent bowler's average minus 10 pins, or the league's number, with their own handicap.
• —Vacancy (Rule 112): a team without a full lineup gets the league's vacancy score (USBC's adult default is 120), and, if the league says so, the handicap of an average equal to that score.
• —Incomplete game (Rule 111c): the pins rolled plus a tenth of the absentee score for each missed frame, typed by the secretary as i and the score.

• —Team points for each game and for the series, comparing the teams' totals with handicap (scratch in a scratch league). Ties split the points.
• —Individual points, if the league uses them: each lineup place against the same place on the other team, game by game and for the series.
• —A team bowling the bye wins every point, a set number of points, or what it wins against a lineup of vacancies: the league's choice.
• —Standings rank teams by points won. Equal points share a place: pins never break a position tie (Rule 118); a roll-off does.

Before opening, we took real standing sheets that league secretaries had published to USBC's League Standing Sheets: a handicap league (90% of 220), a league with vacancies and byes, and a scratch league with individual points. From one week's sheet and the next week's games, the engine rebuilt the next week's sheet: every bowler's pins, games, average and handicap, every absentee and vacancy score, every team's game totals and every match's points matched to the pin. The check runs as a test on every change we make.