Originally posted by The Swine Down Hope
The solution is simple and statistically more correct:

on a win where the loser is more than -400 points add the current rating into the average formula.

on a loss where the winner is greater than 400 add the current rating in average formula.

Most such proposals (please forgive me if I've misunderstood yours) have the problem that a person with a choice of games to finish or defer finishing (whether by checkmate or resignation) could make a significant difference to their rating by choosing the order in which they did this.

The provisional rating system has the merit of closing in very fast on a fair rating; it has the disadvantage of involving big swings, sometimes in an unexpected direction, at the beginning. Providing a way for the player to manipulate the big swings would result in the worst of all worlds.

(The normal system can also be manipulated by choosing when to end games, but not to so great an extent.)

The provisional system was introduced when I had completed about 15 or 17 games - I worked out that it would have made no more than 20 points difference to my rating if it had come in earlier, so it's pretty fair to the new player while minimising the impact on existing players who risk their rating against newcomers.

It occurs to me, however, that an interesting idea would be to have newcomers play unrated matches against five or so active players of various ratings, have each of them estimate a rating, take the average and let that be the new player's (non-provisional) rating.