Bowling Spare Conversion Chart

Click the pins that are still standing. Everything below is computed from the deck, so any of the 1,024 possible leaves gets an answer — not just the dozen or so that have nicknames.

The 3-6-9 system is one multiplication

Taught as a list to memorise — three boards left for the 3 pin, six for the 6, nine for the 10 — it is not a list at all. Every one of those numbers is the pin's distance from the middle of the lane, in inches, halved. The 3 pin stands 6 inches right of centre and gets 3 boards; the 6 stands 12 and gets 6; the 10 stands 18 and gets 9. Written that way it covers pins the rhyme never mentioned, and it mirrors for a left-hander without a second table.

It does not point the ball at the pin, though, and the arithmetic says so plainly. Your eyes stay on one arrow, so the arrow is a pivot: the arrows are 15 feet out and the head pin 60 feet, which multiplies any move of your feet by 3× by the time the ball arrives. Nine boards of feet is 28.7 inches across the deck — but the 10 pin sits only 18 inches from the head pin. The system deliberately sends you 10.7 inches, about 10 boards, past it. That surplus is the hook you are giving up: a spare ball is thrown flat and a strike ball is not, so the extra movement pays for the curve that is no longer there. The multiplication is exact; the hook reading is the explanation for it.

How many leaves are splits

The head pin has to be down for a split to be possible at all, which leaves 512 arrangements out of 1,024. Classifying every one of them by the published rule gives 196 splits, or 38.3% of the ones that were eligible.

Ask which leave size is the split size and you get two answers that disagree, which is the part worth knowing. By share it is the smallest: of the 36 two-pin leaves that could be splits, exactly 24 are — 66.7%, two thirds on the nose — and the share then falls away without a bump the more pins you leave, because more pins means more chance they are joined up. 8 standing or more is never a split at all.

By count it is not the smallest at all. Four-pin leaves are only 49.2% splits, but there are so many more of them that they supply 62 of the 196 — 32% of every split there is. The two-pin leaves everybody pictures when they hear the word account for 12%. Most splits are four pins standing, and most of them have no name.

Share of leaves that are splits, by number of pins standing (head pin down). It falls at every step, peaking at 2 pins.

The deck, in boards

Boards are counted from your own side — the right gutter for a right-hander, the left for a left-hander. The lane is 41.5 inches across and divided into 39 of them, so a board is 1.0641 inches. The nominal figure quoted in pro shops is 1 1/16 inch, and 39 of those come to 41.4375 — a 0.0625-inch shortfall across the lane, which is why board numbers and inch measurements never quite line up.

The rack is an equilateral triangle with 12-inch sides, so every one of the 18 touching pin pairs on the deck is exactly 12.000 inches — side by side and diagonally alike, with no second distance to remember. The rows are therefore 10.39 inches apart rather than 12, and side-by-side pins stand 11.28 boards apart, not the five that gets quoted.

Named leaves

⚠ marks the ones the rule scores as splits. Click any of them to load it onto the deck. Left-handers get the mirror image of every line below without changing a number, because the boards are counted from your own side.

One caveat stated plainly: the published split rule has a clause about a downed pin standing immediately ahead of two or more standing ones, and read at its widest that clause calls 89.6% of eligible leaves splits — including the 8-9-10. Its published example is the 5-6, a touching pair screened by the pin in front, so that is the shape it is applied to here. Every leave a bowler would recognise as a split comes out the same either way. Track how you actually do with the Score Keeper.