Ratings & Leaderboard

[Stef]

Since release 1.2 players have a rating, based on glicko-2.

Every player is assigned a level, which we try to keep between 0 and 100.
- New players start at 20.
- You can go up by winning games.
- The only thing that matters is win/tie/lose (point margin is irrelevant; resigning is the same as losing).
- You can also go up if the system gets to know you better (e.g. after winning a game and losing one).
- You will go up more if you beat a higher ranked opponent.

There are two rating systems. One for 2-player games, one for 3-4 player games. This is because we intend to add an automatch queue for 3-4 player games in the near future. These rating systems are completely independent of each other. If you win a 3 player game, it counts as a win against both opponents. If you end up 2nd in a 3 player game, it counts as a loss against the winner and a win against the loser.

The leaderboard will update on a daily basis at 0:00 UTC. Players who haven't played any games that day will see their level go down a tiny bit. You will not be visible on the leaderboard if you haven't played any rated games. The leaderboard displays you, your friends and the top 20 players.

If you don't use automatch but create a table of your own, you can select whether or not this game will be rated. Games with bots, games with 5+ players and games respecting familiar cards will always be unrated though.

While it's possible to beat up dummy accounts in order to game the leaderboard, this is not a good idea if you're interested in the longevity of your account.

[Stef]

Automatch basic

• Two Player will find you a rated game against a human opponent of similar level (your own level +/- 10).
• Three Player will find you a rated game against two human opponents of similar level (your own 3P level +/- 10).
• Practice Game will find you an unrated game against a human opponent of similar level (your own level +/- 10). The game will respect the familiar card settings of both players.
• Bot Game will create an unrated game against the computer. The game will respect your familiar card settings.

Automatch advanced

• Two Player will find you games with one other human.
• Three Player will find you games with two other humans.
• Rated game will find you rated games that don't respect familiar cards.
• Practice games will find you unrated games that do respect familiar cards.
• Wait for expansions means you'll only accept games with at least half the expansions. If you subscribed yourself this option is meaningless because all your games will have expansions anyway.
• Min Rating Is the minimum level of your opponent compared to your own. It will use your 2-player-level for 2-player-games, and your 3/4-player-level for games with 3 players.
• Max Rating is the maximum level of your opponent compared to your own.

you can search for both two and three player games; you'll be looking for either.
you can search for both rated and practice games; you'll be looking for either.
you can change your options while searching; this will affect your search.
when you search the server will automatically save your search options.

Automatch queue
(this is only visible if you have 'advanced' checked and are currently searching)
This box gives you a bit of feedback about the other searching users, and tries to explain to you why you're not in a match with any of those players. If you click on the name of another player, the colors of the searching options will change to reflect this. Green means there is no problem with this option. Red indicates there is a problem you can't solve (but the other player can). Yellow implies there is a problem which you could solve by relaxing your search criteria.

[Stef]

This post is only for people interested in the underlying details

Your rating in glicko-2 consists of three numbers (μ, φ, σ).

μ is your estimated skill which starts at 0 and will go up for players better then average and down for players below average.
φ is your deviation, which starts at 2 and will go down whenever results come in and go up when they don't.
σ is your volatility, which starts at 0.06 and impacts how quickly your skill will change based on new results.

Glicko2 claims it's 95% certain your actual skill is between (μ-2φ) and (μ+2φ), and suggests using (μ-2φ) for rating / leaderboard, so we're doing that. It's also common to translate this (μ-2φ) to a more human-friendly number. We decided to go with levels, which are 50 + 7.5 * (μ-2φ), rounded to the nearest integer, but never below 0.

The 2P leaderboard updates are computed with τ=0.4; for 3-4P τ=0.3. These are relatively low values, because Dominion is a game with a relatively high chance that a weaker player beats a stronger player.

It's quite possible that 50 + 7.5 * (μ-2φ) is not very good at mapping everyone to the 0-100 range. If too many people end up at 0, or if someone goes above 100, we'll change the 50 or the 7.5 later on, but that won't impact the actual rating system under the hood.

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There is only one queue with ranked players, even though there are several buttons to enter this queue. When you enter the queue, the system first looks at eligible opponents already in the queue. For every opponent it tries to assess the suitability on a scale of 0-1 on three different factors:

- level suitability = 1 - (atan(levelDifference / 20) * 2 / π)
- waiting suitability = atan(duration / 10000) * 2 / π
- familiar cards suitability = percentage of cards your opponent familiarized of the cards that you "expect to see". (you "expect to see a card" if you both subscribed to it and are familiar with it).

Both players have to say yes to eachother. For this decision, both the time and the familiarity factor are irrelevant.

- players who are "searching for a suitable opponent" will say yes to anyone with level suitability > 0.6 (~14.5 levels)
- players who are "searching for any opponent" will actually say yes to anyone with level suitability > 0.2 (~61 levels)
- players who are "waiting for expansions" will say yes to anyone who has subscribed to half the sets or more.

If there is at least one match (i.e. both players say yes to eachother) you will instantly find a game. You will be matched with the player where (level suitability + waiting suitability) is highest. If you're not matched, you're added to the queue.

familiar cards suitability is only used for the unrated queue, because that's the queue that will actually respect familiar cards. In that queue, players say yes to eachother if the familiar cards suitability is at least 0.4, and when selecting the best opponent this is based on the sum of all three (level suitability + waiting suitability + familiar cards suitability).