Upgrade or buy?
Is it cheaper to upgrade the item you have to the next plus, or to buy it ready-made? From current listing prices we find the break-even chance for every step. If your real chance is above it, upgrade; if it's below, buy.
Search for an item above. All of that item's pluses and the break-even chance between them show up.
If the upgrade fails the item is gone. So to get one +N+1 you burn on average 1 ÷ chance +N items.
That gives the math: if +N costs A and +N+1 costs B, upgrading costs A ÷ chance. The chance where that equals B is A ÷ B. That's the number in the table.
Easy to read: if break-even says 40%, upgrading pays off when you land that step more than forty times in a hundred. If you can't, buying is cheaper.
Scroll, Trina, anvil and repair costs are not in this math. Count them and upgrading gets a bit pricier; the real threshold is slightly above the table.
Some methods don't lose the item completely on failure (Reverse, for one). If you use one of those, upgrading is more profitable than the table says.
Try your upgrade chance in the Anvil simulator: pick your method, see your own chance, then compare it with the threshold here.