How to work out match chances from Elo ratings: a guide to the Elo calculator
The Elo calculator turns the gap in strength between two clubs in our club rankings into the chances of a home win, a draw and an away win, and into fair odds for 1X2, double chance and draw no bet. Once you enter a bookmaker's odds, it shows where the ranking sees more than the market, and it also works out how many Elo points each club would gain or lose with a given score. A gap of 150 points, home advantage included, gives the home side a 52.6% chance and fair odds of 1.90. In this guide we show how to use the calculator, how to read its results and what Elo does not know.
Key takeaways
- 1
An Elo gap of 150 points, home advantage included, gives the home side a 52.6% chance of winning and fair odds of 1.90.
- 2
Home advantage depends on the league, about 50 Elo points in the Premier League, 60 in the Eredivisie and 75 in LaLiga, and at 60 it gives equal teams about 6.5 percentage points more chance of a home win.
- 3
In the example Elo rates the away side 2.6 points above the market, so odds of 5.00 show an EV of +9.8% against Elo's fair odds of 4.55, but only if Elo's chance is right.
- 4
Elo knows nothing of line-ups, injuries or motivation, so a gap to the market is a reason to look at the match more closely, not a ready-made tip.
How the ranking itself is built, where its parameters come from and how we tested its forecasts is covered separately in our article on club Elo ratings.
What the Elo calculator works out
- 1X2 chances from the Elo gap between the two clubs, increased by home advantage.
- Fair odds, that is odds without a margin that follow from those chances: for 1X2, double chance (1X, 12, X2) and draw no bet.
- A comparison with the bookmaker: the market's margin, the chances without the margin, the gap between Elo and the market and the EV of every bet.
- The rating change: how many Elo points each club would move after scores from 3-0 to 0-3.
How to use the calculator
Ranked clubs
By default, in Ranked clubs mode, you pick two clubs from the ranking: the home side and the away side. The search covers every club in the ranking, and under each club you can see its league, its current Elo and a link to its profile with its rating history.
The calculator chooses the model's parameters itself:
- a match within one league: that league's home advantage and draw rate. In the Premier League, for example, the home side gets about 50 Elo points, in the Eredivisie about 60 and in LaLiga about 75,
- clubs from different leagues: the international parameters, as in cup matches (home advantage of 80 points).
The Neutral ground switch sets home advantage to zero, which is useful for finals and matches played at a neutral stadium.
The chosen pair goes into the page address (?home=…&away=…), so you can save the link to a particular match or send it to someone. From the "Who wins?" calculator on the club rankings page you come here with the pair already chosen.
Own Elo
In Own Elo mode you type any ratings for both teams and the Home advantage in Elo points. The Competition switch, League or Cups, chooses the draw rate and the K factor for the rating changes. This mode is useful when you want to check a hypothetical match, apply a correction of your own (a weakened line-up, for example) or work out chances for teams outside the ranking.
The third mode, Attack and defence, works from the attack and defence ratings of two teams from one league instead and shows their expected goals, the chance of over 2.5 goals, of both teams scoring and of each correct score.
Example: how an Elo gap turns into chances
Take a league match in Own Elo mode: the home side on 1800, the away side on 1710 and home advantage of 60 points. The gap with home advantage is +150.
| Outcome | Chance | Fair odds |
|---|---|---|
| 1 | 52.6% | 1.90 |
| X | 25.5% | 3.92 |
| 2 | 22.0% | 4.55 |
From the same chances the calculator works out fair odds for double chance (1X 1.28, X2 2.11) and draw no bet (DNB 1 1.42, DNB 2 3.39).
A few reference points to get a feel for the scale (with home advantage of 60 points):
| Home Elo | Away Elo | 1 | X | 2 |
|---|---|---|---|---|
| 1500 | 1500 | 42.3% | 27.9% | 29.8% |
| 1500 | 1500 (neutral ground) | 35.8% | 28.4% | 35.8% |
| 1800 | 1710 | 52.6% | 25.5% | 22.0% |
| 1800 | 1600 | 64.7% | 20.8% | 14.5% |
| 2000 | 1500 | 87.8% | 8.0% | 4.1% |
Home advantage alone, with equal teams, adds about 6.5 percentage points to the home side's chance of winning.
Comparing with a bookmaker's odds
In the Compare with bookmaker odds section, enter the 1X2 odds. The calculator shows:
- the bookmaker's margin on that market,
- the market without margin: the chances that follow from the odds once the margin is removed (by normalisation),
- Elo − market: how many percentage points more or less the ranking sees than the bookmaker,
- EV: the expected value of a bet at the odds you entered, at Elo's chances.
For the match in the example the bookmaker pays 1.80 / 3.60 / 5.00 (a margin of 3.33%):
| Outcome | Elo | Market without margin | Elo − market | EV |
|---|---|---|---|---|
| 1 | 52.6% | 53.8% | −1.2 pp | −5.4% |
| X | 25.5% | 26.9% | −1.4 pp | −8.2% |
| 2 | 22.0% | 19.4% | +2.6 pp | +9.8% |
Elo rates the away side higher than the market, and at 5.00 the bet shows an EV of almost +10%. The break-even price is Elo's own fair odds, 4.55: any higher price shows a positive EV, but only on the assumption that Elo's 22.0% is right. That assumption is the weak point, and in our tests the market predicted better: against Pinnacle's prices none of 89 simple betting rules built on our own ratings made a profit (more in why a betting model alone is not enough), and even the Elo with closing odds closes only 57% of the gap to the market. How to check whether a price has value, with the margin removed from a whole market, is covered in our guide to calculating fair odds.
A gap between Elo and the market is a signal to look at the match more closely, not a ready-made tip. The market knows the line-ups, the injuries and the situation in the table, and Elo sees only the results.
What a result would change
The What the result would do section shows how many points both clubs' Elo would move after scores from 3-0 to 0-3. The rules are the same as in the ranking:
- points pass from one club to the other, so the changes add up to zero,
- the size of the change depends on the surprise: a favourite gets little for a win and loses a lot for a draw or a defeat,
- a bigger win counts for more, but with restraint, and a big win is worth less to the favourite than to the underdog,
- the K factor is 15 in a league match and 30 in a match between clubs from different leagues, so cup matches move the ranking twice as much.
For the match in the example (1800 against 1710, league):
| Score | 1-0 | 2-0 | 3-0 | 1-1 | 0-1 | 0-2 | 0-3 |
|---|---|---|---|---|---|---|---|
| Home side | +4.4 | +6.6 | +8.8 | −3.1 | −10.6 | −17.1 | −22.8 |
A draw costs the favourite more than 3 points, and a 1-0 defeat costs more than two 1-0 wins would bring. Hover over a change to see the club's Elo after the match.
The Elo calculator for tennis
The Tennis tile above the calculator switches it to tennis matches. You pick two players from the tennis Elo rankings (Men and Women separately) or type your own Elo, then the Surface and the Format: Best of 3 or Best of 5.
- The win chance follows from the Elo gap. On a hard, clay or grass surface each player gets the average of their overall Elo and their Elo on that surface, as in our match forecasts.
- Fair odds are the inverse of those chances.
- The score in sets (for example 2-0, 2-1, 1-2, 0-2) is derived from the match chance, on the assumption that sets are independent of each other. That is an approximation: in a real match fatigue and the course of play tie the sets together. How often each set score lands in real matches is in our piece on first set and set betting.
- The Elo change after a win and a defeat is worked out as in the ranking: K = 250 / (n + 5)^0.4, where n is the player's number of matches in the ranking, so a newcomer gains and loses more than a veteran.
What Elo does not know
- Line-ups and injuries. The ranking changes only after matches, so it does not know that the star will miss the game or that the manager will field the reserves.
- Motivation and the fixture list. A dead rubber at the end of the season and a relegation decider look the same to Elo.
- Changes at the club. A new manager or a transfer window shows up in the ranking only after a few rounds.
- Leagues without cup matches. If a club plays in a league that cup matches do not connect with the rest of the ranking, the calculator warns that the result for a pair from different leagues is only a rough guide.
That is why Elo works best as an independent benchmark: a quick way to check that the odds have not drifted away from the teams' strength and to spot matches worth a closer look.
FAQ
The calculator takes the Elo gap between the home and away sides, adds home advantage and turns the result into chances of 1, X and 2 with a model fitted to hundreds of thousands of matches, with a separate draw rate for every league. The formulas are described in our article on club Elo ratings.
It depends on the league, usually 50–100 points, and 80 points in matches between clubs from different leagues. With equal teams that means a few percentage points more chance of a home win.
Yes. Switch the mode to Own Elo and type the ratings of both teams and the home advantage. You can also choose whether it is a league or a cup match.
Yes, for 1X2, double chance and draw no bet. These are odds without a margin, which follow only from Elo's chances.
Not automatically. The EV in the calculator assumes that Elo's chances are true, and Elo knows nothing of line-ups or injuries. In our tests the market's prices predicted results better than our ratings, so treat a gap to the market as a reason to look into the match, not as an edge.
The calculator uses the same ranking as the club rankings page, which is updated after the matches are played.
Yes. Once you choose the Tennis tile, the calculator works out the chances of a tennis match from the tennis Elo rankings, taking the surface and the best-of-3 or best-of-5 format into account, along with the distribution of set scores and the Elo change after the match.
Yes. In ranked clubs mode the chosen pair and the neutral ground setting are saved in the page address, so all you need to do is copy the link.