## Monday, May 21, 2018

### Quota System Vs. Stableford System

The Quota System and the Stableford System are two common methods for tournament scoring.  In the Quota System a player is given a quota equal to 36 minus his handicap (e.g., a 15 handicap would have a quota of 21).  As shown in the table below, a player earns points based on his gross score on each hole.  A player’s tournament score is the total of points earned minus his quota.  For example, if a player earned 24 points with a quota of 21, his tournament score would be +3.  In the Stableford System, a player earns points on his net score as shown in the table. The total number of points earned is his tournament score.

Table
Points for Quota System and Stableford System

 Quota System Stableford System Gross Double Eagle 5 Net Double Eagle 5 Gross Eagle 4 Net Eagle 4 Gross Birdie 3 Net Birdie 3 Gross Par 2 Net Par 2 Gross Bogey 1 Net Bogey 1 Gross Double Bogey 0 Net Double Bogey 0

It would seem a system based on gross scores would not necessarily produce the same winners as one based on net scores.  A closer analysis reveals that is not the case.  (For simplicity, eagles and double eagles have been excluded from the proof.)
The Quota System is described by equation 1):

1)                  Q= 3(Xs + Xn) + 2 (Ps + Pn) +1(Bs +Bn) – (36-H)

Where,
Q= Quota Score
Xs = Number of birdies on stroke holes
Xn = Number of birdies on non-stroke holes
Ps = Number of pars on stroke holes
Pn = Number of pars on non-stroke holes
Bs = Number of Bogeys on stroke holes
Bn = Number of Bogeys on non-stroke holes

The Stableford system is described by equation 2):

S = 4∙Xs + 3∙Xn + 3∙Ps +2∙Pn + 2∙Bs + 1∙Bn + 1∙Ds

Where,
S = Stableford Score
Ds = Number of Double Bogeys on stroke holes

Now a player’s handicap must equal:

H = Xs +Ps + Bs + Ds

Substituting equation 3) into equation 2):

S = H + 3Xs + 3Xn + 2Ps + 2Pn + 1Bs +1Bn

The difference between a player's Stableford score and his Quota score is shown in equation 5):

S – Q = H + 3(Xs + Xn) 2(Ps + Pn) + 1(Bs +Bn) – (3(Xs +Xn) + 2(Ps + Pn) + 1(Bs +Bn) - (36 – H)) = 36

In summary, a player’s Stableford score will be 36 points higher than his Quota score.  The rank order of player scores, however, will be the same under both systems.