When you hover your mouse over a player in the "list of tables", you will be shown the player's Elo rating, provided they have been ranked.
Wikipedia does a pretty good job of explaining how Elo ratings are computed.. There, an example is given of someone playing in a 5-round tournament:
Suppose Player A has a rating of 1613, and plays in a five-round tournament. He or she loses to a player rated 1609, draws with a player rated 1477, defeats a player rated 1388, defeats a player rated 1586, and loses to a player rated 1720. The player's actual score is (0 + 0.5 + 1 + 1 + 0) = 2.5. The expected score, calculated according to the formula above, was (0.506 + 0.686 + 0.785 + 0.539 + 0.351) = 2.867. Therefore the player's new rating is (1613 + 32 * (2.5 - 2.867)) = 1601, assuming that a K-factor of 32 is used.At World of Card Games, the process is very similar. The performance of each player against their opponents at the table is treated as a "round" in the tournament described above. Here's an example for a game of Spades.
Suppose there are 4 players: A, B, C, and D, with ratings 1512, 1562, 1484, and 1417, respectively. A and C are teammates, while B and D are their opposing teammates. The "expected" score for player A competing against player B is computed as 1 / ( 1 + 10(Rbavg-Raavg)/400 ). As of Dec 24, 2017, Rbavg is the average Elo rating for team B and D, (Rb + Rd)/2, and Raavg is the average Elo for team A and C, (Ra + Rc)/2. Using the average Elo rating helps to distribute the performance of the team more evenly, especially when a team is composed of players with widely mismatched skills. In this example, Rbavg is 1489.5 and Raavg is 1498. Prior to this change, the expected score was computed as 1 / ( 1 + 10(Rb-Ra)/400 ), where Rb was just the Elo rating for player B (1562), and Ra was the rating for player A (1512).
According to Elo, a player's actual score is given by 1 for a win, 0.5 for a draw, and 0 for a loss. If player A won against player B, then the actual score for player A would be 1.
In a Spades game, performance for an individual player is evaluated against 2 opposing players. If players A and C won over B and D, then player A's "actual" score is Sa = 1 + 1 = 2. The expected score for player A is the sum of [1 / ( 1 + 10(Rbavg-Raavg)/400)], evaluated for each player on the opposing team: Ea = 1 / ( 1 + 10(1489.5-1498)/400 ) + 1 / ( 1 + 10(1489.5-1498)/400 ). Note that it is not a mistake to add the same number twice; the computation is done once for each "match" against your two opponents. The total amounts to 1.024 approximately (previously, without using the average Elo, it was 1.06). You can plug the formula into Google, which can calculate this for you.
Player A's new Elo rating is computed according to the formula given in Wikipedia: Ra' = Ra + K * (Sa - Ea), where Ra is their current rating, 1512. At World of Card Games, I have used an Elo K factor similar to those found at other game sites
30 for experienced players (who have played more than 50 games) and 50 for inexperienced ones [Edit: In 2017, the Elo K was changed to 25 for all players.] Then Ra' = 1512 + 25 * (2 - 1.02). Google's handy calculator function says that is 1536, the player's new rating.
A similar computation is made for players B, C, and D. Each player's Elo rating is computed using their own Elo rating and the Elo rating of their two opponents.
Please check out the Wikipedia article for more details if you are curious. Obviously, there are flaws to applying a rating system that was developed for chess to a card game like Spades. Most game sites use this system, and I have followed suit.
You may want to try the Elo rating calculator for team games, to get a feel for how points are traded off between players during a Spades match.
In Hearts, your Elo rating suffers more if you quit a game because you automatically lose to all remaining players. In Spades this is not done. For one, rating a player against their teammate when they quit seems just too bizarre. It would put the player in a match against three other players, while the opponents would be matched against just two, and that would lead to a skewing of the ratings. Also, I've had a few protests about the way that a player's Elo is affected when quitting a Hearts game. Some people say that it is enough that they lose the game automatically, and they should not take a loss to all remaining players. So the Elo ratings in Spades do not place an additional penalty on a quitter. It's an experiment to see if a heavier penalty is needed for quitting or not.
Suppose 4 players with an Elo rating of 1500 start a ranked Spades game. Mary and Sue are teamed up against John and Peter. Halfway through the game, Peter realizes he must rush off to pick up his kids from school, so he apologizes and quits the game by clicking the "leave table" link. His Elo rating is immediately changed from 1500 to 1475, and he is banned from ranked play for 2 hours. The new Elo rating is computed from the formula Ra' = Ra + K * (Sa - Ea) = 1500 + 25 * (0 - 1) = 1475.
The Elo ratings of all remaining players are unaffected until the game is finished. Now suppose that John, whose partner quit, goes on to win the game. The resulting Elo ratings of the remaining players are computed with Mary and Sue winning against Peter, but losing to John, so their Elo ratings actually remain at 1500. As an example, Mary "won" over Peter (because he quit), and lost to John, so Mary's Sa = 1 + 0 = 1. Mary's Ea is also 1. So the formula Ra' = Ra + K * (Sa - Ea) = 1500 + 25 * (1 - 1) = 1500.Finally, John wins his 2 matches against Sue and Mary. His Sa = 1 + 1 = 2, and his Elo rating becomes Ra + K * (Sa - Ea) = 1500 + 25 * (2 - 1) = 1525.