Inverse xs area proportional drill bit set population

How easily they break is proportional to how strong they are.

How strong they are is proportional to the cross sectional area.

Finally, how often they break is proportional to how easily they break *and* how often you use them.

As a result, when you buy a set of general purpose wood and masonry bits, you break all of the thin useful bits and are left with a load of fat useless bits. You then buy another set and start the whole process again, accumulating yet another family of fat useless bits.

If they sold sets of bits where the number of each size of bit in the set was inversely proportional to the square of the diameter and proportional to their usefulness, then you would get through them all at a roughly similar rate.

I imagine a quick survey of "usefulness" would find 2mm wood bits for pilot holes, 6mm wood bits for screw holes and 6mm/8mm masonry bits for red and brown plugs would be the most used and therefore require perhaps three times as many.

Here is a quick calculation of how many should be in a set based on this formula:

WOOD
Size....Qty
13mm.....1
12mm.....1
11mm.....1
10mm.....2
9mm......2
8mm......3
7mm......3
6mm.....14
5mm......7
4mm.....11
3mm.....19
2mm....127
1mm....169

METAL
Size....Qty
13mm.....1
12mm.....1
11mm.....1
10mm.....2
9mm......2
8mm......8
7mm......3
6mm.....14
5mm......7
4mm.....11
3mm.....19
2mm.....42
1mm....169

This must be a sensible distribution, because the maths says so.