Two Methods, One Shared Mechanic
Both the snowball and avalanche methods work the same way structurally: pay the minimum on every debt, then direct every spare dollar at one specific target debt until it's gone, then roll that debt's entire payment — minimum plus whatever extra was going to it — onto the next target. The only difference between the two methods is how the target debt gets chosen. Snowball picks the smallest remaining balance. Avalanche picks the highest interest rate. That single decision is the entire difference between them.
Why Avalanche Wins on Paper
Interest accrues on whatever balance is outstanding, so leaving a high-rate debt outstanding longer while a low-rate debt gets paid off first means paying more total interest than necessary — money spent on interest that a different order could have avoided. Avalanche, by always attacking the highest rate first, minimizes the total interest paid across the entire payoff process. This is provably true in the math, not a rule of thumb: for the same total payment capacity, avalanche's total interest paid is always less than or equal to snowball's.
Why Snowball Still Wins for a Lot of People
The optimal method on paper isn't automatically the optimal method in practice, because paying off debt is a multi-month or multi-year behavioral commitment, not a one-time calculation. Snowball's smallest-balance-first order produces the first fully-paid-off debt sooner, which is a concrete, motivating milestone early in the process — a real factor in whether someone stays consistent with extra payments for years versus losing momentum a few months in. A mathematically optimal plan that gets abandoned in month four saves nothing; a slightly less optimal plan that gets finished saves everything the plan promised.
How to Actually Decide
If the interest-rate spread between debts is large (a 24% credit card next to a 4% student loan) and the dollar savings from avalanche are substantial, the math case for avalanche is strong. If the debts have similar rates, or if past experience suggests a need for early, visible progress to stay motivated, snowball's psychological structure may be worth more than the marginal interest savings. The honest answer is that the "right" method is whichever one gets fully executed — running both scenarios with real numbers, rather than picking based on which is generically recommended, is what actually informs that decision.