You can see your skirimish rating on this link, just replace the red part with your realm and character name.
https://eu.api.battle.net/wow/character/stormscale/Smnzq?fields=pvp&locale=en_GB&apikey=vy33bberqfnzydm3rjb4uy485m47gyu6
This is what the arena ladder uses. And every time you level up your MMR and win/loss ratio resets.
And if I remember this correctly a player with 0 wins, 0 losses give as much skirmish rating as a player with 1500 MMR. But after they have lost a game they are counted as lower than 1500. So if you are farming levelers they will most likely be at 1500 MMR or lower.
