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.
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The maximum handicap is determined by the base used for handicap calculation. For example, if the base is 230, then the maximum handicap could potentially be 230 depending on the percentage used for calculation. If the base was 300, then the maximum could potentially be 300.
Yes - most leagues will not give bowlers with an average over 220 a handicap so technically the highest handicap a bowler could receive would be one based on an average of 219 or under.
A bowling handicap resulted with you average, The higher you average is the Lower the Handicap.