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I suggest the following average move time calculation so it is a moving average and it is just a simple change.
The idea is to cap the calculation for average to 50 average games(50x30=1500 moves).
Use this formula after 50 games:
Your average move time after a move is
(1500 x av move time + this move time) / (1500+1)
Not cpu intensive at all and it is quicker to lower average move time after a player moves quickly repeatedly.
I'm all for it. I want to join fast tournaments now but can't because in the past I played too slow. It is going to take me years to bring the average time per move down because of the weight of that history.
I wish chess.com would change this...
@Patzer24: Yes the average will go down if you play more speedily. But how fast do you think it will go down if you have thousands of games under your belt?
It is easy to calculate, say you played Nold moves at an average move time Aold. And now you want to bring your listed average move time down by playing Nnew moves at average move time Anew. Your listed average move time Alisted will be
Alisted = (Nold * Aold + Nnew * Anew) / (Nold + Nnew)
Rearranging terms to compute the number of games needed to bring your listed average move time down to Alisted
Nnew = Nold * (Aold/Alisted  1) / (1  Anew/Alisted)
There are three terms on the right hand side, they are all logical:
1. The number of games required is proportional to the gain wanted as seen in the term (Aold/Alisted1). Bring the listed average move time down by a factor 2 sets this factor to 1. Wanting a 3 times faster average, this factor will be 2.
2. The number of games required depends on the effort put in. Immediately answering all moves sets the term 1/(1Anew/Alisted) to 1, the best one can get. If Anew = Alisted, we will never get there.
3. The number of games required is also proportional to the number of games already played, Nold.
If we want to get or new average Alisted to be half our current average Aold, we see that we need to play faster than the desired average Alisted, or we will never get there.
Say we want to have or listed average Alisted twice as fast as Aold, i.e. Alisted = Aold/2, and to get there we are playing 4 times as fast as before, i.e. Anew = Aold/4
New = Nold * 1 / (1  Anew/Alisted) = Nold / (1  (Aold/4)/(Aold/2)) = Nold / (1  0.5) = 2 * Nold
If we have already played 1000 games at and average move time Aold, it will take us 2000 new games played 4 times as fast as before, just to bring just to half our new listed average move time.
If we played 10,000 games before and we decided to play 4 times as fast, it will take 20,000 new games just to adjust our listed average a factor 2.
So yes, the average will go down. But it is really an excessively slow process!
It is clear that it is very inpractical to substantially change one's listed average move time once a lot of games have already been played. It really should get some attention, there are a lot of better proposals in this thread than what has been implemented.
Late to the topic but agree that it should only take into account recent history.
Just looked at mine, currently 398 games at 5hours 45 minute per move. To get down to under a 3 hour average I'd need to play the next 400 games at 16 minutes per move. So in my case due to playing longer games in the past I will realistically never qualify for 3 hour/per move tournaments.
Your rating would probably take a pretty good hit but just find a few people willing to play some daily in a single sitting. Maybe a move every few minutes max. That should drop your average down pretty quickly.