Bowling Handicaps and Darts Checkouts: The League Maths

Two league games, two small pieces of arithmetic that decide who wins. One is designed to make unequal players competitive; the other is a search problem with seven dead ends in it.

The bowling handicap formula

The basis score is meant to sit above every bowler in the league, which is why 220 and above are common choices. A bowler who averages over the basis simply gets nothing — the handicap floors at zero rather than penalising them.

Forty-six pins of difference for the same bowler, purely from the rule sheet. If you are comparing your handicap with someone from another league, you are comparing two different things.

Why 80% and not 100%

Take a 147 average against a 205 average in a 220 basis, 80% league. Both bowl exactly their average.

The stronger bowler wins by 12. That is not a flaw — it is exactly 20% of the 58-pin gap between their averages, which is what choosing 80% means. To beat them, the 147 bowler has to shoot 13 pins above their own average, which is an achievable night rather than a miracle.

The average matters more than the formula

The formula is trivial; the average going into it is where leagues actually argue. United States Bowling Congress rules define an average as total pins divided by games bowled with fractions disregarded, and Rule 319 governs which average a handicap event must use.

• The entering average is normally the highest from the previous season in a single USBC league of at least 21 games, or a composite across leagues.
• If your current average over 21 or more games is 10 or more pins higher than that prior-season figure, you must use the current one.
• Submitting an average that is too low, and so collecting extra handicap, can get a score disqualified.
• Leagues add rules on top — how many games a new bowler needs, what average they are assigned meanwhile, and whether handicaps update weekly or are fixed for a period.

Darts: the checkout

In 501 you must finish on a double. That single rule turns the endgame into a search problem: from your remaining score, is there a sequence of at most three darts, ending on a double or the bullseye, that lands on exactly zero?

The board offers trebles up to T20 at 60, doubles up to D20 at 40, singles, the outer bull at 25 and the inner bullseye at 50. The bullseye counts as double 25, so it is a legal finishing dart; the outer 25 is not and can never finish a leg.

170 is the ceiling because the three highest-scoring darts available that end on a legal double are T20, T20 and the bull. Anything above 170 cannot be finished in three darts, which is why commentators call 170 the maximum checkout.

The seven bogey numbers

Below 170 you would expect everything to be reachable. It is not. Seven scores have no three-dart finish at all, and they are not arbitrary — they fall out of the arithmetic of what the board can score.

If you find yourself on one, the goal is no longer to finish — it is to leave yourself something you can finish next visit. Score a dart or two, get down to a number with a clean route, and take the three darts you have left on the next turn. Players talk about "setting up" for this reason.

The same logic explains why experienced players like leaving 32. It finishes on D16, and if you miss D16 with a single 16, you are left on 16, which is D8. Miss that with a single and you are on 8, which is D4. The number keeps halving into another double, so a miss does not strand you on an odd number needing a setup dart. That is a better position than 36, where one thin miss leaves 18, then 9, which is odd and needs a dart spent fixing it.

How a bowling score is counted in the first place

A handicap is added to a score, so it helps to be clear about how the score itself is built. In standard ten-pin scoring, a game has ten frames. A strike scores 10 plus the pins from your next two balls; a spare scores 10 plus the pins from your next ball; an open frame scores just the pins knocked down. The tenth frame gives bonus balls after a strike or spare so those bonuses can be completed.

Two reference points are worth knowing. Twelve strikes in a row is a perfect game of 300. And a bowler who gets a spare in every frame, knocking down nine with the first ball each time and nine with the final bonus ball, scores 190. That is why converting spares matters so much for improving an average: a spare in every frame is already a very respectable game without a single strike.

Working out an average, the USBC way

United States Bowling Congress rules define an average as total pins divided by games bowled, with fractions disregarded. Dropping the fraction rather than rounding is small but it matters, because it feeds straight into the handicap.

Handicap across a range of averages and league rules

Two patterns show up in the table. Every ten pins of average improvement costs you eight pins of handicap at 80%, nine at 90% and ten at 100%, which is just the percentage factor at work. And a higher percentage is not automatically more generous: at a 200 basis and 100%, a 180 bowler gets only 20 pins, less than at the other two settings. The basis and the percentage have to be read together.

Series and team handicaps

League results are usually decided over a series of games and between teams, and the handicap follows the same simple rule at every level: it is added to every game.

In most leagues a team's handicap is the sum of its bowlers' individual handicaps, applied to each game. A team of four bowlers averaging 147, 170, 205 and 128, at a 220 basis and 80%, carries handicaps of 58, 40, 12 and 73, a team handicap of 183 pins per game. Some leagues calculate team handicaps differently, for example from the team's combined average, which is exactly why the league rule sheet is the final word.

How many finishes are possible from each score

Running the checkout search across every score from 2 to 170 gives a complete picture of the endgame, and it is more lopsided than most players expect.

Odd numbers can never be finished with one dart, because every double is even and the bullseye counts as 50. The highest odd number you can finish in two darts is 107, as T19 and the bull, and the highest two-dart finish of all is 110, as T20 and the bull. Not every score below 110 is a two-dart finish, though: 99, 102, 103, 105, 106, 108 and 109 all need three darts, a second, less famous set of awkward numbers that sit just below the two-dart zone.

Why some leaves are better than others

The body of this guide explained why players like to leave 32. The same logic can be applied to every even leave from 2 to 40: count how many times the number can be halved while still leaving a double. Each halving is a second chance if the dart lands in the single of the same number.

32 is the best leave on the board by this measure, with five doubles in a row available if every dart lands in the single instead. 40 is the most popular leave for a different reason: double 20 is at the top of the board, where most players spend their time aiming anyway. Numbers like 38 or 22 leave you on an odd number after a single miss, which costs a dart to fix. The calculator shows the route for any score; this table explains why experienced players steer towards some leaves and away from others.

The three-dart average and the nine-dart finish

The standard measure of darts scoring is the three-dart average: points scored per dart, multiplied by three. It lets you compare players regardless of how many legs they played.

The minimum possible is nine darts, which requires 501 in three visits: the classic route is two maximums of 180 and then a 141 checkout, T20, T19, D12. That leg averages 167, the highest possible three-dart average for a completed 501 leg. A nine-dart finish is to darts what a perfect 300 is to bowling: the ceiling of the game's own arithmetic.

Common mistakes with league arithmetic

• **Rounding an average up.** USBC averages drop the fraction; a 147.67 average is 147.
• **Comparing handicaps between leagues.** Different basis and percentage settings give different handicaps for the same average.
• **Forgetting the handicap applies per game.** Across a three-game series it is added three times.
• **Going for an odd leave in darts.** An odd number can never be finished in one dart; set up an even number first.
• **Aiming at a bogey number.** From 159, 162, 163, 165, 166, 168 or 169 there is no three-dart finish; use the visit to set up a finish instead.
• **Judging form from one leg.** A three-dart average over many legs says far more than any single leg.

How much of the gap a handicap leaves

The body of this guide showed that at 80% the better bowler keeps 20% of the average gap. That generalises neatly: when both bowlers shoot exactly their average, the stronger one wins by the average gap multiplied by one minus the percentage factor. Fractions dropped in the handicap can shift this by a pin, but the pattern holds.

This table is the clearest way to explain a league's percentage choice to its members. At 100%, the average gap disappears entirely and every match between two players bowling to form is a tie. At 90%, a much stronger bowler keeps a small edge. At 80%, the edge is larger but still modest compared with the normal game-to-game variation in anyone's score, which is why weaker bowlers in an 80% league still win plenty of individual games.

How many ways there are to check out

The calculator returns one route for each score. Counting every possible route shows how much choice a player actually has. The counts below treat each segment of the board as distinct, so a single 20 and a double 10 are different darts, and count the order of the first two darts separately.

The pattern explains why high checkouts are so hard. From 40 there are dozens of ways home in two darts and hundreds in three; from 141 there are only 20 three-dart routes; from 160 just three; and from 170 exactly one, T20, T20, bull. A player on a big finish has almost no room for a dart that lands in the wrong segment, while a player on 40 can miss and still have many ways to finish. It is the arithmetic behind the advice to leave a small, flexible number rather than chase a big checkout.

What a spare is worth in pins

The scoring rules make a striking point about where averages come from. A bowler who knocks down nine pins with the first ball of every frame and misses every spare scores 90. The same bowler converting every one of those spares, with nine on the final bonus ball, scores 190. Same first balls, a hundred pins difference, entirely from spares.

The jump from 90 to 190 is far larger than most bowlers would guess, and it is why coaches so often say averages are built on spare conversion rather than on strikes. It also puts handicaps in context: a 58-pin handicap is less than the value of converting six more spares over a game.

Sources

• United States Bowling Congress Playing Rules, including Rule 319 on averages for handicap and classified tournaments: https://bowl.com/rules/usbc-playing-rules — note that the basis score and percentage factor are set by each league rather than by USBC.
• The darts checkouts and the list of bogey numbers in this guide were not copied from a chart. They were generated by exhaustive search over every scoring segment on a standard board, under standard double-out rules, and the seven bogey numbers are the complete result of that search across 2 to 170.

Where to go next

A handicap and a rating are two answers to the same question. How Elo ratings work covers the other one, where instead of adding pins to a weaker player you move both players’ numbers by how far the result differed from the prediction.

Common questions