Yes, there a specific equations to calculate the Elo wins / lose after a game.
This thread might be interesting for you as well. The devs did never explain the Elo system, but based on the standard Elo system and based on the data we can found on for example aoe2.com we are able to found most of the rules.
This explain how basic Elo works. It will give the basic equations behind the basic elo calculations. I think the devs used K=30 or K=32. On average you will gain by a win 15 (k=30) or 16 (k=32), but if you win against higher rated players, then you will gain more. If you win against lower rated players, then you will gain less. The same is true for losses. If you loose against some one with lower rating, then you will loose more. If you loose against someone with higher rating, then you will loose less. In the most extreme cases you win the full K-value. This will happens if you win against someone which elo is more the 400 higher then yours. In basic elo, it holds that the amount of elo won by one player, is equal to the amount of elo lost by the other player.
Until now this is the basic Elo calculations. There are some adjustments:
- In the first games, you gain/loose more elo. There is some kind of factor applied in the first 10 games (this number can be some higher/lower). Afaik how this mechanic exactly works, isnt known. It looks like they start with a factor 3 or something like that. So they dont win or loses 15 elo on average, but around 45 elo each game. This way you can climb the ladder more easily in the first games.
- Elo is designed for 1v1. So it needs some adjustments for TGs. In DE the elo is calculated for each player individually. It uses your elo and compare this to the highest elo of the enemies. This rule is the reason why team games are inflated. If you win, then your elo will be compared to someone with high elo. Standard elo rules say you need to gain a lot of elo. If you loose, then your elo will be ompared to someone with high elo. Standard elo rules this time say that you need to loose a few points. So overall the average Elo on the ladder will increase no matter what.
Hopefully i helped you understanding the Elo calculations a bit more.