So, perhaps a summary of Elo would be helpful here:
Starting with some basic assumptions:
1) Both plays have completed 21 games.
2) Neither player forfeits or quits unless it is a concession at or above 50% game progression, which has no effect on the Elo results
3) Neither player has won 3 or more consecutive games against the opponent.
4) Both players are at or above 120 Elo
5) The game is PvP (meaning, 2-players).
Elo facts:
1) The Elo gained by one player will be
exactly the same as the Elo lost by the other player. That's how the formula works.
2) If both players have identical Elo ratings (regardless of what those Elo ratings actually are), the winner will gain 10 Elo and the loser will lose 10 Elo.
3) The greater the Elo disparity, the greater (or lower) this result will be. For example, if the Elo differential is 100, and the higher Elo player wins, that player gains 7.2 and the opponent loses 7.2. If the lower Elo player wins, that player gains 12.8 and the opponent loses 12.8. Notice those two values add up to 20. That's not an accident. That's the result of the Elo formula and the standard k-factor of 20.
4) If Elo differential is:
200, then the numbers would be 4.8 and 15.2
300, then the numbers would be 3.0 and 17.0
400, then the numbers would be 1.8 and 18.2
500, then the numbers would be 1.1 and 18.9
5) MEANING: Yes, you gain a much bigger Elo reward for beating a much higher rated player than you do for beating a much lower rated player. Obviously.
6) That being said, winning against high rated players is one way to progressively gain Elo. It can also be accomplished by beating low-rated players. In the game "Earth", I have been successful at both methods. (I play Arena, so I have no filter controls over the Elo of my opponents). SO, yeah, if I lose a game, I sometimes need to win 6 or 7 or 8 games to get that Elo back. That's fine with me, because, well, I'm a top 5 player, and I should be able to win those 6-8 games for each loss. If I couldn't do that, I wouldn't have nor deserve a top 5 rating.
7) Someone said "Elo [in some circumstances] should be zero-sum". In fact, it IS zer0-sum. The Elo gained by one player equals the Elo lost by the opponent. (Assuming the above 4 assumptions are true.)
8) Players who complain about this situation are simply not good enough to maintain the Elo they believe they are capable of maintaining. Or, the game has too much luck for anyone to achieve and maintain those Elos. Spades is a high-skill game, yet, nobody is good enough to reach a 500 Elo rating. In Spades, the margins are too narrow, the nuances too nuanced, among other factors. That said, generally speaking, the 300+ Elo spades players are very good, and the 150- Elo players are not.
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Going back to the 4 listed assumptions and why they matter:
1) A player who has not yet completed 21 games will have a k-factor of 40 or 60, and thus will appear to be gaining or losing 2x or 3x as much Elo as expected based on the formula. This is not a bad thing. The goal of these higher k factors (for a player's first 11 games and first 21 games) are designed to get a player's Elo to the appropriate level faster rather than slower.
2) When a player forfeits or quits, TWO things happen that skew overall Elo. First, the winner only gets partial Elo, based on game progression percentage, which will make it seem as though the results are wrong, because you might see one player take -9 while the winner takes +4. As explained in the posts prior to this one. Second, the player who quits or forfeits gets hit with an extra -10 Elo penalty (regardless of what either player's Elo was.) SO, forfeits and abandoned games really wreak havoc with the overall Elo system, and contribute to it not being zer0-sum all the time.
3) TO prevent multi-account Elo dumping, a player who wins 3 or more consecutive games against the same opponent will be assigned an Elo decay that starts at 10% and gets increasingly higher. This can make it seem as though the results are "wrong", and it WILL also contribute to Elo not being zero-sum. (This is a bad policy especially in Arena where we don't even get to choose our opponents.)
4) Players can never lose Elo when they are below 100 Elo. This can have the same effects as listed above; the results might seem "wrong", and it will not be zero sum. (I personally think this is a completely absurd feature.) Also, a player who reaches 100 Elo will never go below 100. SO, that player could lose 40 games in a row without losing ANY Elo, then win one game and go up to anywhere from 101 to 120. This is also a really silly feature, further skewing Elos and making it not zero-sum overall. That is why some sites start players at 1500 Elo as the default Elo. That 1500 Elo should, in theory, mean "exactly average". A player at 2000 would be 500 above average (expert level, to some extent equivalent to a 500 ELo here on BGA). Starting everyone at 1500 allows players to go below 1500 when they lose, which makes sense. That way, Elo would in fact be zero-sum. If two 1500 players play, the winner will be at 1510 and the loser at 1490. But, here, if two 50 ELo players play, the winner will increase, but the lower will remain at 50 Elo. Losing a game but not losing any Elo makes no sense.
5) All sorts of silly and difficult-to-comprehend things happen with Elo in 3+ player games. It took a lengthy thread involving numerous experienced players and some developers to reverse-engineer the convoluted formulas for games of different player counts above 2p.
Bottom line: If you want to reach high Elos and continue to increase Elo, you need to win games. And avoid losing games. To suggest it's impossible to gain ELo by playing lower rated players, that's just false. Look at my game results for "Earth". Or Pente.
