Stock in the wrong size is not stock
Ninety bowlers on the floor need ninety pairs only if every pair fits everybody. They do not, so each size has to be stocked against its own peak, and each size needs its own buffer. At the default distribution and a 95 percent chance of a fit, the rack needs 116 pairs on it for 90 bowlers — and 133 owned once you allow that 12 percent are being wiped, drying or behind the desk at any moment.
That is 1.48 pairs owned per bowler at the peak. Nobody budgets for that until they have counted it.
Small sizes look absurdly over-stocked and are not
Size 15 is 2 percent of the default distribution, so 1.8 bowlers are expected at a peak of 90. The rack needs 5 pairs for a 95 percent chance of a fit — nearly three times the expected demand. Size 9 is 16 percent, expects 14.4 bowlers, and needs 21, which is 1.46 times. The buffer is proportionally huge at the ends and modest in the middle, because small counts are lumpy: going from 1.8 expected to 5 actual is entirely ordinary, going from 14.4 to 40 is not.
This is why racks that look badly balanced usually are not, and why cutting the rare sizes to match their share is the mistake that produces a bowler in socks.
The last few percent are the expensive ones
Run the service target ladder and it climbs the way these things always climb. At 80 percent the rack holds 103 pairs; at 95 percent, 116; at 99 percent, 128. The step from 95 to 99 costs twelve pairs to catch four percent of peaks, and those peaks happen on the nights you are already busiest. Whether that is worth it is a service decision about what you want to say to a bowler at the counter, not an arithmetic one.
Where the model breaks
Every bowler at the peak is treated as an independent draw from your distribution. That is roughly true for walk-in open play and plainly false for groups. A birthday party of twelve nine-year-olds is one draw from a completely different distribution, and it will strip the small sizes while the model is still calculating averages. If groups are your trade, run the page with the peak set to your largest single group and read the answer as a floor rather than a target.
Questions people ask
Why does the total come to more pairs than bowlers?
Because a pair in the wrong size does not serve a bowler, so every size carries its own buffer and the buffers cannot be shared. At the defaults, 90 bowlers need 116 pairs on the rack to give each of them a 95 percent chance of a fit, and 133 owned once stock off the rack is allowed for.
Where do I get the size shares?
Count your own rental slips for a fortnight. A national shoe size table is the wrong distribution for a bowling centre, and a centre whose weekday trade is school groups has a different rack from one that runs adult leagues in the same town. The defaults in the box are placeholders to overwrite.
Does this work for house balls as well as shoes?
Yes — switch the selector and read the size column as a weight. The arithmetic is the same: each weight is stocked against its own peak. The share of stock off the rack means something different, since a house ball off the rack is on a lane rather than being cleaned, so set that figure from what you observe.
How do I find the peak bowler count?
Roughly lanes multiplied by party size when the house is full, or straight off the lane computer for the busiest hour of the busiest night. It is not the total who came through in an evening — the rack only has to serve the people bowling at the same moment.