Why not simply use a well established rating system, like ELO, or Glicko? There are plenty of sports out there that use them regularly. I think what @Player of 0ADsaid pretty much sums it up.
That is how it works, at least in online chess, which I play a lot, if you stop playing rated your rating will fluctuate more when you next play, also this is the case when new players start until their rating is adjusted to their level, with each game played the uncertainty decreases.
As asides, a system like in tennis of "defending" points as I saw mentioned above doesn't really fit here, in my opinion, as we don't have regular, fixed calendar events. Also, I don't think we should care about possible "inflation", it doesn't matter if the lowest rated used to be 1250 and now it is 1000 or whatever, what matters is that the difference between a good player and a not so good one will show in their rating difference, after all this is not a professional competitive game (although people can be very competitive even when no stakes are on and that is ok) and I also think the relatively small pool of player is to be blamed a bit as it makes harder for ratings to stabilize overall.
Finally, I also agree with @LetswaveaBook that rating shouldn't be reset between alphas for the reason he just exposed, players that know best the underlying mechanics will inevitably crop up to the top.