Where the savings come from
Every evaporated gallon takes three things with it: the water itself, the chemicals dissolved in it, and — the expensive part — its heat (evaporation is a cooling process; it's why the uncovered pool feels cold after a windy night). A cover blocks all three at once, which is why the savings stack faster than intuition suggests.
A worked example
A 32×16 heated (gas) pool, 6-month season: covered nights save roughly 5,000 gallons (~$30 with sewer), a third of chlorine spend (~$70), and several hundred dollars of gas that would have replaced overnight evaporative heat loss. Against a $300 cover-and-reel that's payback inside one season — and the second season is pure savings. Unheated pools pencil out slower in dollars, but gain 5–10°F of free warmth, which many owners value more.
The honest catch
Covers only save when they're on the water, and hauling a wet 300 sq ft sheet by hand gets old by July — the reel isn't a luxury, it's the difference between a cover you use and one that lives rolled up by the fence. Budget them together, as this calculator does.