Elo has a hard structural assumption baked in at the bottom: it is defined for a pair. Two ratings go in, an expected score comes out, one result updates both. Everything built on top of it inherits that shape.
A free-for-all has no pairs. Ten people drop into a battle royale, or six sit down at a Mario Kart cup, or eight teams enter a multi-team match, and what comes out is not a winner and a loser — it's an ordering. There's no obvious place to put that in a formula that wants exactly two sides.
This is one of the genuinely underserved corners of competitive rating, and it's worth walking through properly: how the ordering gets converted, the quadratic problem that conversion creates, and — the part most treatments skip — where the whole approach stops describing reality.
Manufacturing Pairs
The standard answer, and the one Team Up implements, is pairwise decomposition: treat one N-player free-for-all as a set of simultaneous head-to-head matches, one for every possible pairing.
You "beat" everyone you outplaced. You "lost to" everyone who outplaced you. Finish 3rd of 6 and you have won four virtual matches — against 4th, 5th and 6th — and lost two, against 1st and 2nd. Each of those is a normal Elo calculation against that specific opponent's rating, and your rating change for the event is the sum.
Players finishing on the same placement are treated as a draw against each other, which is what you want for genuinely tied results and for formats where several people are eliminated simultaneously.
That's a satisfying answer because it doesn't invent any new mathematics — it decomposes an unfamiliar result into the familiar one, and every property of Elo comes along for the ride. It also immediately creates a problem.
The Quadratic Problem
An N-player free-for-all contains N(N−1)/2 pairings, and each individual player appears in N−1 of them.
That number grows fast. A 6-player FFA is 15 pairings. A 10-player lobby is 45, with each player in 9 of them. A 100-player battle royale is 4,950 pairings, each player in 99.
So without a correction, one FFA moves your rating up to N−1 times as far as a single 1v1 would. Nine times, for a ten-player lobby. Playing one battle royale would move your rating as much as ninety-nine ranked duels.
The correction is to divide the summed delta by the number of rated opponents, which is on by default. Here's the difference on a 6-player FFA where everyone is rated 1000 and K=32:
| Placement | Divisor on | Divisor off |
|---|---|---|
| 1st | +16.0 | +80.0 |
| 2nd | +9.6 | +48.0 |
| 3rd | +3.2 | +16.0 |
| 4th | −3.2 | −16.0 |
| 5th | −9.6 | −48.0 |
| 6th | −16.0 | −80.0 |
Two things worth reading off that table.
It's zero-sum. The column sums to exactly zero. Points move between the entrants and none are created — the same property a 1v1 has, preserved through the decomposition. (Non-rated entrants, like players marked casual, are excluded from the sum precisely so this stays true among the players who are rated.)
The middle barely moves. Finishing 3rd of 6 among equals is worth +3.2 points. That's correct and it's a feature: mid-pack in a free-for-all is a genuinely uninformative result. You beat some people and lost to some people, and the rating shrugs. All the signal is at the edges.
With the divisor on, first place in a 6-player FFA gains exactly what a 1v1 win against an equal opponent would — 16 points at K=32. That's the design intent: one event, one match's worth of rating movement, regardless of lobby size.
What the Divisor Is Actually Deciding
It looks like a scaling knob. It isn't — it's a claim about how much you learned.
Divisor off says an FFA is worth N−1 matches of evidence. Divisor on says it's worth exactly one. The truth is in between, and which end you should sit nearer depends on your format.
An FFA genuinely is more informative than one duel — you placed against nine people, not one. But it is nowhere near nine times more informative, because the nine comparisons aren't independent. One event determines all of them at once. Get third-partied at the first rotation and you simultaneously lose to everyone still alive — that's a single piece of bad luck producing nine correlated "losses", not nine separate assessments of your play.
This is the same effective-sample-size trap that the fighting game post runs into with games inside a set, but arriving from the opposite direction. There the dependence is sequential — game two is shaped by game one. Here it's structural: one cause, many simultaneous outcomes. Both end at the same place, which is that counting raw comparisons overstates what you know.
Leave the divisor on. If your FFAs are long, low-variance and skill-dominated — a six-player strategy game rather than a battle royale — you can afford a slightly higher K-factor to compensate, which is a cleaner control than turning the divisor off and getting a 9× multiplier you can't tune.
Placement Sets the Order, Expectation Sets the Sign
Here's the part that surprises people the first time they see it, and it's the strongest argument for doing this properly rather than with placement points.
The same 6-player FFA, but the entrants have different ratings. They finish in the order listed:
| Placement | Rating | Delta |
|---|---|---|
| 1st | 1400 | +4.2 |
| 2nd | 1000 | +13.9 |
| 3rd | 1200 | −1.6 |
| 4th | 900 | +5.1 |
| 5th | 1100 | −9.9 |
| 6th | 1000 | −11.7 |
Look at 3rd and 4th. The 1200-rated player who finished 3rd loses points, and the 900-rated player who finished 4th gains them. Placement did not determine the sign of the rating change — expectation did. The 1200 was supposed to beat most of that lobby and only managed third; the 900 was supposed to finish last and beat two people.
And the winner gains 4.2 while the runner-up gains 13.9, because a 1400 winning is barely news and a 1000 taking second in that lobby is.
No placement-points system can do this. Award 100 for first and 70 for second and the 1400 banks the most points for doing the least impressive thing in the lobby. That's the difference between scoring an event and measuring skill, and it's the reason to convert placements into ratings at all. (You can poke at these numbers directly in the Elo calculator, which runs this exact code with the FFA distribution toggle exposed.)
Where This Genuinely Breaks Down
Being honest about the limits, because they're real and they're specific to this format.
Placement is ordinal, and the gaps are not equal. Pairwise decomposition treats every adjacent pair identically — the 1st/2nd comparison and the 40th/41st comparison carry the same weight. In a battle royale that's plainly false. First versus second is a final fight between the two best-positioned players; 40th versus 41st is a coin flip about who happened to be standing nearer a bad rotation. The model has no way to express that, and it will read noise at the bottom of the field as signal.
Luck is a much larger share of the result. In a 1v1 both players face identical conditions. In a battle royale the landing spot, the circle, and the identity of whoever happens to be nearby dominate any single match. FFA ratings therefore need substantially more matches to converge than 1v1 ratings do, and deserve a lower K to compensate.
Very large fields are mostly untracked anyway. A 100-player battle royale has 99 opponents but only a handful of meaningful placements, and recording it means listing an ordering nobody has. In practice you record the placements you actually know — the tooling takes up to ten — which is why "score only the top N and treat the rest as unplaced" is usually the right call rather than a compromise.
If your format is a genuine mass battle royale, the honest read is that a placement Elo describes the top of the field well and the bottom of it barely at all. Rating only the top 10 and being explicit about it is more truthful than manufacturing 4,950 comparisons out of one drop.
Multi-Team Matches
Everything above generalises: four teams of three, eight duos, a six-way multi-team match. The decomposition happens at the team level — each team is compared pairwise against every other team by placement, using the team's rating against theirs, and the divisor applies the same way.
Two things to decide before you start.
Rate the team or the players? If the same rosters play together repeatedly, rating the team directly is cleaner — the team is the real competitive unit and you sidestep the attribution problem entirely. If rosters shuffle, rate the players and accept that a team result attributes imperfectly to individuals, which the attribution post covers in depth. Both can run side by side.
Don't double-count. If you're recording a multi-team match as team results and as individual results on the same leaderboard, one event moves the same people's ratings twice. Pick the unit that matches how your league actually competes.
Setting It Up
- Record the full ordering, not just the winner. The placements are the entire input; a match recorded as "player X won" throws away everything the FFA measured.
- Leave the FFA divisor on. One event should be worth about one match of rating movement.
- Use a lower K than you would for 1v1. FFA results carry more luck per match, and the divisor doesn't change that — it only stops the movement compounding by lobby size.
- Score the top N for large fields, and say so publicly. Ten meaningful placements beat fifty noisy ones.
- Group genuine ties on the same placement rather than breaking them arbitrarily — they're handled as draws between those entrants.
- Expect slow convergence. More than 1v1, an FFA ladder is a volume game.
Frequently Asked Questions
Why did the winner gain so few points?
Because the rating expected them to win. Elo updates a prediction rather than paying out a prize — a heavy favourite taking first in a lobby they were supposed to top is close to zero new information. If that reads as unfair to your community, the thing you want is a placement-points season standing alongside the rating, not a change to the rating.
Can I weight first place more heavily?
Not within the pairwise model, and it's worth understanding why before working around it: first place already earns the most, because that player won every one of their comparisons. Adding an extra bonus on top breaks the zero-sum property and starts inflating the ladder over a season. If you want to reward winning an event beyond what it says about skill, that belongs in a separate points standing.
How does this handle a player who leaves early?
However you record them. If they're placed last, they lose to everyone, which is usually right for a rage-quit and clearly wrong for a disconnect. There's no way for the rating to distinguish the two, so this is a rules question rather than a rating one — decide whether disconnects are recorded or the match is voided, write it down, and apply it consistently.
Is this the same as how chess tournaments rate Swiss events?
No, and the distinction is instructive. A Swiss event is a sequence of actual pairwise games, each rated normally — the pairs are real. An FFA has no real pairs, so the comparisons are manufactured from an ordering, which is exactly why the divisor and the correlated-outcome problem exist here and not there.
Do co-op matches work the same way?
No — a co-op result is one outcome shared by everyone on the same side, so there's no ordering to decompose. Free-for-all scoring specifically needs an ordering with more than two distinct positions in it.
Running FFA or multi-team formats on Discord? Team Up records full placement orderings, converts them with pairwise Elo and lobby-size distribution, and runs FFA queues that form matches automatically. Start with the leaderboard setup guide, or try the numbers yourself in the Elo calculator.