How Elo win probability works
Arpad Elo was a Hungarian-American physics professor who built his rating system for chess in the 1960s, and its central idea is genuinely beautiful: a rating is a prediction. The gap between two ratings converts directly into an expected result, and after every match each rating moves in proportion to how surprising the outcome was. Beat a giant and you leap; scrape past a minnow and you barely tick up. Run that ledger over thousands of matches — eloratings.net runs it back to 1872 — and the numbers become self-correcting: a team keeps climbing until it stops surprising anyone.
The scale is logarithmic, tuned so that 400 points of gap means ten-to-one dominance in expected score. Here is what various gaps mean, straight from the formula below:
| Elo gap (dr) | Expected score for the stronger side |
|---|---|
| 0 | 50% |
| 100 | 64% |
| 200 | 76% |
| 400 | 91% |
The formula
EA is Team A's expected score, where a win counts as 1 and a draw as ½ — so it already includes half-credit for draws. The home bonus is 100 points added to the home side, the same convention eloratings.net uses in its own predictions; at a neutral venue nobody gets it. dr is simply the rating difference after that adjustment.
Elo alone will not tell you how often the match ends level — expected score blends wins and draws together. So we split them apart with a documented heuristic, stated plainly as a heuristic:
Roughly 25–30% of international matches end drawn, and evenly matched teams draw the most, while huge mismatches rarely do (someone scores four). From there, P(A wins) = EA − P(draw)/2, P(B wins) takes the remainder, and anything pushed negative at extreme gaps is clamped to 0.5% with the three numbers rescaled so they always total exactly 100.0%.
Worked example
Mexico at home vs Germany (ratings as of July 11, 2026): Mexico 1913 + 100 home = 2013; Germany stays at 1908, so dr = +105.
EMexico = 1 ÷ (1 + 10−105/400) = 0.647. P(draw) = 0.29 − 105/2000 = 23.75%. P(Mexico wins) = 0.647 − 0.119 = 0.528.
Result: Mexico 52.8% — Draw 23.7% — Germany 23.5%. A 105-point home-boosted edge buys you a slim favorite, not a guarantee.
FIFA runs on Elo now too
For twenty years FIFA's official ranking used an averaging formula that fans and statisticians loved to dunk on — teams could climb by strategically not playing. After the 2018 World Cup, FIFA gave up and switched: since 16 August 2018 the men's world ranking has used a formula FIFA calls "SUM", which is an Elo system — points added or subtracted per match based on the expected-versus-actual result. The remaining differences from eloratings.net: FIFA ignores margin of victory, applies no home-advantage bonus, and shields teams from losing points in the knockout stage of final tournaments, which is why the two lists agree on the neighborhood but argue about the street address.
What Elo can't see
Elo knows everything about the past and nothing about tonight. It cannot see that the starting striker felt a hamstring twinge in warmups, that the center-back is suspended, that it is 95°F at kickoff, that a goalkeeper is about to have the game of his life, or that a team which limped through qualifying has quietly become terrifying three matches into a tournament. As the old German coach Sepp Herberger put it, "the ball is round" — anything can happen, which is both the reason this calculator exists and the reason it can be wrong. Treat the output as the informed baseline that the pre-match argument should start from, not end at.
Where the ratings come from (and why they keep moving)
Team ratings are from eloratings.net (World Football Elo Ratings), snapshot as of July 11, 2026 — mid-World Cup, which matters. Tournament matches carry the system's maximum weight (K = 60 for World Cup finals matches, scaled up further by margin of victory), so a single shock result can move a team 30–40 points overnight. If the tournament has moved on since our snapshot, the true ratings have too; the Custom rating option lets you type today's numbers — or club ratings from clubelo.com — without waiting for us.
And the paragraph of lawyerly honesty: this is probability math for fun and education, not betting advice. Elo ratings are public information that every bookmaker already prices in, so this page holds no secret edge — if it could reliably beat the market, we would not be running a free calculator site; we would be unreachable, on a yacht, refusing to explain the draw heuristic to anyone.