A doubt on Codechef Rating System

As Codechef has explained their rating mechanism here, there is a formula used by them

And volatility weight of player is defined as , where timesPlayed is the number of competitions the player has participated so far

Here, what does timesPlayed represent?
Is timesPlayed the total number of contests or the specific type of contest the player has participated in so far ? Like if the rating is being calculated for a cook-off, the timesPlayed variable will represents the total number of rated contests the player has given or the total no of cook-offs the player has given?
Also, are the specific cook-off/lunchtime/long challenge ratings used in any way for calculating the new ratings?

All rated contest so far.