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Quota vs Handicaps

The idea behind both Quota system and Handicaps are the same: To make for a level playing field for golfers of different abilities. Here are the general differences, and your quota system may be slightly different than what I'm going to explain, but the concept is the same.
 
Golf League Tracker does not support the "quota" system, and instead, calculates a handicap for a player based on the scores they shot, rather than the points they won for the previous rounds. We believe Handicaps are a better and more equitable way of running a Stableford Competition. The main reason for this is that by calculating a Handicap, it is calculated based on the difficulty of the course and tee box they played. If your league plays different courses, has players playing from different tees, or if the difficulty of the front side vs the back side is significant, this can have an impact to a player's handicap calculation which cannot be accounted for in a quota system. Having a handicap also allows leagues to change formats seamlessly, since handicaps can be used for any other format of play, including the use of a Net Skins game using the same handicap as for the stableford competition.

QUOTA SYSTEM

With a quota system, each player has an "expected" number of points to win each week. That expected number is based on the number of points they won in the previous rounds (That number of rounds determined by you). If your expected quota is 10 points, and you won 14, then in your league standings you would be "+4" in points for that round. If your expected quota is 20 points, and you won 17, you would be "-3".
 
With the quota system, the points are determined by your gross score on each hole relative to par.  In your settings, you have a BOGEY=3, PAR=4 points, a BIRDIE=5 (among other point values). Gross score means no handicap is applied to the player's score. It is the actual score the player made for that hole. 
 
As you can see, a better player would have a higher quota for each week, therefore they need to score better than someone with a lower quota.

HANDICAP SYSTEM

With a handicap system, each player has a handicap based on the previous scores they shot, rather than the number of points. When a player plays a round, that handicap is used to reduce their gross score on some or all holes to calculate a net score. The hole in which the handicap is applied is based on the "Hole Handicap" value for each hole. A Standard 18 hole golf course has hole handicaps from 1 through 18, with no duplicate values across the 18. The lower the hole handicap, the "harder" the hole is.
 
If you're a 6 handicap on a 9 hole league, then you would apply a 1 stroke reduction on the 6 hardest holes (the lowest 6 Hole Handicap values on the card).  If you're an 11 handicap on a 9 hole league, you would apply a 2 stroke reduction on the two hardest holes, and 1 stroke reduction on the next 7 holes, thus adding up to 11 stroke reduction.
 
Stableford points are then awarded based on the NET SCORE for a hole according to your point system. Let's assume a point system of the following:
 
Double Bogey or Worse = 0 , Bogey = 1, Par = 2, Birdie = 3, Eagle = 5
 

HANDICAP EXAMPLES

Example 1

A player is a 6 handicap, which means they will get 1 stroke on the hardest 6 holes. On this course, the front 9 hole handicaps are all odd numbers (which is very typical), therefore they will get 1 stroke on hole handicaps 1, 3, 5, 7, 9, and 11, and get 0 strokes on hole handicap 13, 15, and 17.

  Hole 1 2 3 4 5 6 7 8 9 TOTAL HDCP NET
  Yards 345 321 142 487 400 156 412 492 355      
  Hdcp 1 7 17 5 11 13 3 9 15      
  PAR 4 4 3 5 4 3 4 5 4 36    
Player 1   6 5 3 5 7 3 5 5 5 44 6 38
Strokes on Each hole   1 1 0 1 1 0 1 1 0 6    
NET SCORE   5 4 3 4 6 3 4 4 5 38    
POINTS   1 2 2 3 0 2 2 2 1 15    

Example 2

A player is a 13 handicap, which means they will get 2 stroke on the hardest 4 holes, and 1 stroke on the next 5, for a total of 13 strokes. On this course, the front 9 hole handicaps are all odd numbers (which is very typical), therefore they will get 2 strokes on hole handicaps 1, 3, 5, and 7, and get 0 strokes on hole handicap 9, 11, 13, 15, and 17.

  Hole 1 2 3 4 5 6 7 8 9 TOTAL HDCP NET
  Yards 345 321 142 487 400 156 412 492 355      
  Hdcp 1 7 17 5 11 13 3 9 15      
  PAR 4 4 3 5 4 3 4 5 4 36    
Player 1   5 7 4 6 6 4 4 6 5 47 13 34
Strokes on Each hole   2 2 1 2 1 1 2 1 1 13    
NET SCORE   3 5 3 4 5 3 2 5 4 34    
POINTS   5 1 2 1 1 2 3 2 2 19