The next part of trueskill that begs attention is the model of what happens to a player's skill *between* games. Trueskill has this 'tau' parameter, which basically says that if we reckon a player has skill 1800±50 based on the results of game N, then maybe by the time he enters his (N+1)th game he has skill 1800±60 because we know that human skill doesn't stay the same, it keeps changing. Probably something happened in between game N and game N+1 and his skill changed a bit in some unpredictable way.

Well if we imagine reasons why it might have changed, we might be able to go some way towards reducing the unpredictability of it. Two obvious factors that come to mind are rust and experience.

Rust: the longer a player abstains from playing, the more his technical abilities diminish and the more he forgets the nuances of his coveted and polished build orders.

Experience: Having lost one too many games by forgetting to build energy, maybe now, after this game, he can finally remember to build energy. Or maybe he just watched a few replays and learned some tricks. That all ought to be worth a few points of skill at least.

So in order to model rust and experience, I added some stuff to reduce the mean and increase the variance of player's skill depending on the time since last game, and also increased the mean just a little bit just for playing on the assumption that players will generally learn something by playing.

As before there was a great reduction in NLML, and also an interesting change in the optimal 'tau' parameter. This reduced from 18 down to 10. Now the situation isn't quite as simple as previously with the 'beta' parameter because while the 'tau' parameter is lower, we are adding variance elsewhere through the rust model. But what we can say is that we're not indiscriminately blanketing all games with the same amount of 'tau'. Only games where the player has had significant amounts of down-time do we add any significant amount of variance beyond tau. And that tau is now much lower so we can say that we've reduced the amount of residual uncertainty in our model - another win!

Again with the distribution of outcome probabilities we see a general, if slight, shift to the right. A reduction in number of games in the 50-60% region and an increase in the number of games in the >70% region. Player rating progressions show significant differences again. I've included Photon's progression this time because he has an interesting step change after a haitus just after the 200th game that I can point to. Without the rust model, his loss of points is kind of gradual, whereas with the rust model the loss of points is very rapid. But after that, the subsequent recovery of points is quite similar. And generally the ratings are much less eratic.

btw, it looks like the average player might initially lose points at a rate of 8pts/month of inactivity with uncertainty 30pts(stdev)/month. And he learns maybe 0.6 points just by playing a game.

Next to come: What happens if we control for factional imbalance?