Typically, the average and handicap are recalculated after every session of a Bowling league. For tournament leagues (such as the Amateur Bowlers Tour), averages and handicaps are recalculated after every tournament.
Bowling Green Handicap was created in 1975.
There are three variables that affect a bowler's handicap: 1) Their current average, 2) the handicap basis, and 3) the percent of the difference between their average and the handicap basis that is used for the handicap. For example, a typical league may calculate handicap as 80% of 200, meaning that a bowler with a 150 average would have a 40-pin handicap (80% of the 50-pin difference between their 150 average and the 200 basis). With a 40-pin handicap, the highest handicap game this bowler could roll would be 340. Theoretically, you could have a 600 handicap game: A bowler with a 0 average bowling in a league with handicap based on 100% of 300 would get 300 pins of handicap, making a perfect game worth 600 pins. In reality, I don't think I've seen many handicap games over 330.
Each league votes on the handicap system. Common rules is to assign each bowler a handicap based on 90% of the difference between the bowlers average and 200. Team handicap commonly is calculated by summing each bowlers handicap on a team. There is software that does this for you, such as Bowling League Secretary by CDE Software, which the majority of centers in the US use.