What the model is asked
A live win probability model answers one question repeatedly during a match: given what has happened so far, how likely is each side to win? The output is a number that moves as events occur, often shown as a bar on a broadcast.
It differs from a pre-match forecast. Before play begins the only information is who the competitors are, often summarised by their ratings. As play continues, the state of the match becomes the main evidence, and the pre-match estimate fades in importance.
The starting point
Many models begin with a prior based on ratings. With Elo-style ratings, a 100 point gap corresponds to an expected score of about 0.64 for the stronger side. That number is then adjusted as the match unfolds. A good model starts from a sensible prior and weighs it less as more of the match is played.
A simple model built from rounds
Some games have a clean structure. Consider a format where the first side to reach 13 rounds wins, and suppose each round is a fair coin flip for simplicity. A side leads 10-5, so it needs 3 more rounds and the opponent needs 8.
The leader wins if it takes 3 rounds before the opponent takes 8. That is the same as asking for at least 3 wins within the next 10 rounds, since by then one side must have reached its target. The only way the trailing side wins is if the leader gets 0, 1 or 2 of those 10:
- 0 wins: 1 way
- 1 win: 10 ways
- 2 wins: 45 ways
That is 56 of the 1024 equally likely sequences, so the trailing side wins with probability 56/1024, about 5.5%, and the leader with about 94.5%.
The calculation uses the same counting as binomial outcomes elsewhere in probability, and it shows the usual shape: a lead that looks large in score terms translates into a high probability, and the probability moves most quickly in the late stages.
In a real game, rounds are not fair coin flips. Side choice, economy and player form all change the per-round probability. A better model would use a different chance for each round, and the answer would shift accordingly.
Richer models for richer games
Many games do not have such a tidy score. Sports and esports models typically describe the state with features such as:
- the score and the time or round remaining
- resources held, such as gold, economy, items or experience
- positions and objectives, for example towers taken or bomb sites controlled
- which characters, weapons or lineups are in play
- the pre-match rating gap
A common approach fits a statistical model, often logistic regression or a machine-learning method, to a large archive of past matches. For each moment in each historical match, the features are recorded along with who eventually won. The model learns which states tend to precede wins.
The logistic form is a convenient one. It takes a weighted sum of features and converts it to a probability between 0 and 1, so that a lead of a certain size maps to a certain probability. Doing this at every time step produces the curve shown during a broadcast.
Another approach is simulation. The model plays out the rest of the match many times using assumed probabilities for events and counts how often each side wins. That is the Monte Carlo method, and it is useful when the state is too complicated for a formula.
Why the probability swings
A live curve can jump when a major event occurs, such as a key player being eliminated or a large objective being taken. Those jumps are not a flaw. They indicate that the model sees the event as important evidence.
But large swings also come from the model’s limitations. If it has seen few matches with a particular situation, it may be overconfident. Features that matter in practice, such as team coordination or a player’s mental state, are not in the data. And features that look useful, such as gold lead, may partly be a result of already winning rather than a cause.
Checking a live model
A model is only useful if its percentages mean what they say. The main test is calibration: among all moments where the model says 80%, about 80% of those matches should end in a win for that side. Plotting predicted probability against actual frequency, in bins, shows where it is off.
The Brier score summarises accuracy in one number. A forecast of 0.8 for a team that wins scores (0.8 - 1)^2 = 0.04, while the same forecast for a team that loses scores 0.8^2 = 0.64. Lower is better, and averaging over many moments rewards models that are both right and appropriately cautious.
Two points are worth remembering when judging a model:
- Accuracy near the end of a match is easy, because the outcome is nearly known. A fair comparison looks at earlier points, when the answer is still open.
- Matches from the same game are not independent samples of the same situation, so a small test set can give a misleading picture. The same caution about sample size applies as with any stat.
Reading a probability bar
When you see a live percentage, treat it as a model’s estimate of the match as it stands, not a verdict. A side with 90% still loses about one match in ten. Comebacks from low probabilities do happen, and that is consistent with the model being correct, as rare events are expected to occur at roughly their stated frequency across many matches.
A model also depends on the game staying similar to its training data. After a patch or format change, past matches may be a worse guide. The numbers describe likelihoods given the information used, not what will necessarily happen next.