Level first or roll now

A roll is a chance per shop slot, and your level sets that chance for every cost, so the same gold buys a different roll at every level. With 50 gold and no copies held, the chance to find a 2-star of a 4-cost is 5% at level 7 and 44% at level 8. That is why a fast 8 comp levels before it rolls: for a 4-cost the level is worth more than the shops it costs.

Higher is not always better. Each level moves the odds toward pricier units, so the cheaper costs get rarer: a 3-cost fills 40% of every slot at level 7 and 32% at level 8. The same 50 gold finds a 2-star of a 3-cost 66% of the time at level 7 and 51% at level 8, before the level has cost anything. A reroll comp that levels past its cost's peak pays twice: once for the experience, and again in worse shops.

The level itself costs gold that then cannot roll. Level 8 takes 60 experience from level 7, 60 gold if you bought all of it, less what the rounds have already given you. So at a roll down the question is whether the next level raises your carry's odds by more than its experience costs you in shops. For a 4-cost at level 7, where level 8 makes it 3 times as likely per slot, it does once most of the experience is in, and the piece below shows where it flips. For a 3-cost at level 7 it never does. The level also adds a slot to your board, which no odds count, and When to level covers when that slot is worth it on its own.

One more thing the numbers leave out: they count one unit. A real roll down looks for every upgrade on your board, each pair you hold and each missing piece of the comp, and the more of them you are rolling for, the more of every shop is useful to you. Before you roll, count what you are rolling for. If the answer is one unit, the level that makes it common matters most.