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Tin content has a big effect on shrinkage, but little effect on hardness.
Antimony content has very little effect on shrinkage, but much on hardness.
COWW alloy is only about .5% tin, and so casts at virtually the same size as pure lead. Adding lead to COWW won't make a significant change in resultant diameter.
You might want to compare this with the chart in the Lyman Cast Bullet Handbook, 3rd edition, page 58.
Pure lead 45 cal bullets cast at .4515 and WW cast at .4523 and while WW have so little tin and only about 2.5% antimony, it appears that the antimony is what results in the larger casting. The tin improves the flow of the lead.
For your statement that tin has a big affect on shrinkage the same chart would have to show that Lyman #2 casts larger than linotype. It does not show this, instead it shows that the antimony content of lino results in a larger casting.