Here' my two cents after playing in many leagues over the last 20 years.
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APA treats their players like cattle. Poor handicapping system. Their handicapping system is NOT a handicapping system at all when you compare it to other sports. It's completely inaccurate on all levels. If you took the same handicapping system and applied it to tennis, Peter Sampress would have been a 2. Doesn't make any sense.
Scoring is a set back. Counting balls is like counting chickens....after a while ya just get plain dizzy. Sandbagger friendly.
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BCA system is not player friendly and too much work for the League Operator. However, their game play rules are great. Handicapping system is much like APA's and it not accurate at all. Sandbagger friendly. Player support is pitiful. You don't get any.
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TAP scoring is ridiculous, I still don't get it after two years, and their player support gets a -1 on the quality scale. In fact I am not sure that anyone works at the main office anymore. Scoring is sandbagger friendly.
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UPA - I'm clueless on this one. But looking at their web site says a lot. If their web site is any reflection on the organization of their league I would be concerned. Someone there needs to hire an html developer. Looks like the league was formed at the playground
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VNEA - No idea because I refuse to play on Valley tables. Being forced to play on a particular table is like being forced to use a jump cue as your break stick.
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NAPA is impressive...perhaps ingenious. Supposedly the brainchild of one man, from arkansas of all places. Its run like an ACTUAL federation/association. Much detail goes into the player and not someones pockets. Just take 2 minutes and look at a player page on their web site. You are actually able to see a players entire history and make comparisons on their trends. It's very clear how and why a player moves up and down on their handicap scale. It's a variant of the ELO system which is used by many sporting associations around the world. Not too mention local and national rankings...not just in skill...but performance as well. According to my local LO everything is maintained at their data center. Player support is a +9 and their response time to league issues on league night is amazingly fast. One time we had a foul issue in our 8-ball league, we called the main office at 10:30pm and someone named Amy picked up on the second ring. Problem solved. Sandbagging in this league has no benefit. Simple, effective and allows players to focus on their game and not that darn score sheet. They do not count balls so you won't get dizzy. Very nice. Excellent web site and player search. Player skill levels are very broad from 0 to 100 or more and my local pro players can join in. It's like getting free lessons.
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Synopsis: NAPA offers the most for your game because it is simply done right and has more attention to the players. It's understandable why there is a new NAPA league popping up on their facebook page practically every hour. If they keep things the same they will be the only game in town in a few years.