DOTA 2 GROUPS

Win Probability by MMR Difference — Dota 2 Fair Games

Updated 2026-07-13

What is the win probability for a given MMR difference in Dota 2?

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The win probability for a given MMR difference can be estimated using the standard Elo expected-score formula: E_A = 1 / (1 + 10^((R_B - R_A) / 400)), where R_A and R_B are the two sides' ratings and E_A is Team A's expected score, treated as a win probability. Dota 2's matchmaking rating behaves like an Elo-style rating in that it rises after wins and falls after losses relative to an opponent's rating, but Valve has never published the exact formula, K-factor, or adjustments behind Dota's MMR system, so this is a well-documented approximation of how a rating-gap-to-win-probability relationship works, not a claim about Valve's exact internal math.

The formula is symmetric: whatever probability it assigns to the stronger side, the weaker side gets one minus that number. A 300-point gap that gives the favorite an 85% expected win probability leaves the underdog at 15% — long odds, but not zero, which is consistent with how any single Dota 2 game still has one team's draft, item timings, and mistakes to decide the outcome regardless of the average rating gap on paper.

How much does a 100, 300, or 500 MMR gap actually skew a match?

Plugging round numbers into the formula shows how fast the curve moves. A 100-point gap gives the higher-rated side roughly a 64% win probability — noticeable, but still a game either team can win. A 300-point gap pushes that to roughly 85%, where the stronger side is a clear favorite but upsets remain realistic. A 500-point gap reaches roughly 95%, which still leaves the underdog a real, if slim, chance in any single game.

Does Dota 2's actual matchmaker use Elo?

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Dota's MMR is Elo-like, not plain Elo. It shares Elo's core property — win against a higher-rated opponent and gain more, lose to a lower-rated one and lose more — but with the 7.33 update in 2023 Valve said ranked matchmaking runs on a Glicko-style system, which tracks a confidence value alongside each player's rating and can produce meaningfully different numbers than plain Elo for the same two ratings. The exact formula and parameters remain unpublished. Treat the Elo formula in this article as the standard, well-documented approximation used to reason about rating gaps in general, not as a description of Valve's internal system.

This same formula works for comparing two five-player teams, not just two individual players — treat each team's average MMR, or total strength score, as a single rating and plug the two team numbers in as R_A and R_B. A 300-point gap between two teams' average MMR carries the same roughly-85%-favorite math as a 300-point gap between two individual players, which is why total team strength, not any one player's rank, is the number worth tracking when judging whether a 10-stack split is fair.

Where does the fair-game threshold sit on this curve?

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A useful way to read this curve for team-balancing purposes is that gaps of roughly 100 points or less — a favorite at about 64% or under — sit in the range most groups would call a fair game, while gaps past 400-500 points put a single side so far ahead that the outcome feels decided before the draft finishes. This is also the logic behind treating total team strength, not raw average MMR, as the number that matters: Dota 2 Groups' Auto Balance targets a balance score of 85% or higher, which keeps the effective strength gap between two five-stacks in the range where the Elo curve still predicts a competitive, winnable game for both sides.

Frequently asked questions

What formula estimates win probability from an MMR gap?

The standard Elo expected-score formula: E_A = 1 / (1 + 10^((R_B - R_A) / 400)). Plugging in two ratings gives the higher-rated side's expected win probability. It's a well-documented approximation from rating systems generally, not a description of Valve's unpublished exact Dota 2 matchmaking formula.

What's the win probability for a 500 MMR gap?

Using the standard Elo expected-score formula, a 500-point average MMR gap gives the higher-rated side roughly a 95% expected win probability. That doesn't guarantee a win — the underdog can still take an individual game — but over any series of matches, a 500-point favorite should win the large majority.

Is a 200 MMR gap between two Dota 2 teams fair?

Using the Elo formula, a 200-point gap gives the favorite roughly a 76% expected win probability, which most groups would consider a noticeably lopsided, though not hopeless, matchup. Gaps closer to 100 points or less, at roughly 64%, tend to feel more like genuinely fair games.

Does Valve use Elo for Dota 2's actual matchmaking?

Not plain Elo — Dota's MMR rises and falls with wins and losses the way Elo does, but Valve said with the 7.33 update in 2023 that ranked matchmaking runs on a Glicko-style system with a per-player confidence value, and the exact formula is unpublished. The Elo expected-score formula in this article is a standard approximation for reasoning about rating gaps, not Valve's internal math.

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