There are no quality points in the ATP, and the tournaments aren't broken down into Tiers (though the same logic applies). Go here
for an explanation of the Champions Race, and this is from Steve G, who runs a rankings website at www.stevegtennis.com
The ATP determines its rankings on a formula of 4 grand slam results + 9 masters series results + 5 best other events over a rolling 52-week calendar -- this means that the points given for a player's results using this formula over the previous 52 weeks make up the player's entry point total. For each mandatory event a player is not eligible to play in because of ranking, he may substitute another non-mandatory result. The Entry System period is the immediate past 52 weeks, except for the Tennis Masters Cup, which is dropped on the Monday following the last ATP event of the following year. For a breakdown in tournament entry points, go to http://www.stevegtennis.com/entrypoints.txt
*Number of tournaments represents all tournaments played that count towards the rankings. Qualifying losses in events that don't award points in qualifying or first round losses of futures events do not count towards this total. The four-week satellite circuits count as 1 event.