Alacrity
Jan 19 2006, 04:26 PM
For those of you that have any interest, I have run a little curve fit analysis on the Open Payout tables. Why, you may ask would you do such a thing, if the table is readily available? There are several reasons; the first is that an equation can easily be put on a PDA or programmable calculator. At times this is much easier than carrying the tables around with you. It is also easier to do a calculation than a table lookup in Excel or Access.
Second it allows you to extend the table past 33rd place. If you have a large number of players in a particular division, you can calculate a smooth set of payouts. It will calculate out to 100 places with little to no adjustment required to assure % payout sums to 100%.
Thirdly, well it is a smooth 3d surface, which is just plain esthetically pleasing. It guarantees a well defined payout, consistent across all places. The equation below is very close to the PDGA generated formulas, but is not exact. The PDGA has tweaked teh table over the years and it is not a smooth curve. To use the equation you must first calculate the number of places to be paid out. This can be found from:
PLACES TO BE PAID OUT = ROUNDDOWN((Total number of players-1)*% Open Payout as fraction (.4, .45, or .5)+1)
This formula can also let you customize the percent payout. If you want something besides the normal suggested 40%, 45% or 50%. Once you know the places to be paid out then each position pay out can be calculated from:
0.9563*(Places paid out*Position Pay Out)^(-0.5937))/(0.9593*Places paid out^(0.09226-0.04832*LN(Places paid out))+0.0762*LN(Places paid out))
The divisor term is only to "normalize" the curve. What the divisor does, is cause the total of the pay out to equal 100%. There is a little difference in some of the totals, but it is very minor. The major deviation is if you are only paying out two places or less. The total payout will be off by no more than 3 tenths of a percent. For up to 100 places paid out the total payout will be off by no more than 1 tenth of a percent.
Now as an example, if you have a field of 67 Open players and you were planning to payout 50% of the field the total number of places to be paid out would be:
Rounddown((67-1)*0.50 + 1) = 34 places to be paid out
To find the payout at tenth place:
0.9563*(34*10)^(-0.5937))/(0.9593*34^(0.09226-0.04832*LN(34))+0.0762*LN(34)) =.030 times total cash
This formula is in my Excel score keeping spreadsheet, but it is only used if you go beyond the PDGA tables. I will be sending a copy out to in the next couple of days to several people. If you would like a copy, please e-mail me at [email protected]
I have performed a similar calculation for the Amateur tables, past the defined PDGA tables.
Second it allows you to extend the table past 33rd place. If you have a large number of players in a particular division, you can calculate a smooth set of payouts. It will calculate out to 100 places with little to no adjustment required to assure % payout sums to 100%.
Thirdly, well it is a smooth 3d surface, which is just plain esthetically pleasing. It guarantees a well defined payout, consistent across all places. The equation below is very close to the PDGA generated formulas, but is not exact. The PDGA has tweaked teh table over the years and it is not a smooth curve. To use the equation you must first calculate the number of places to be paid out. This can be found from:
PLACES TO BE PAID OUT = ROUNDDOWN((Total number of players-1)*% Open Payout as fraction (.4, .45, or .5)+1)
This formula can also let you customize the percent payout. If you want something besides the normal suggested 40%, 45% or 50%. Once you know the places to be paid out then each position pay out can be calculated from:
0.9563*(Places paid out*Position Pay Out)^(-0.5937))/(0.9593*Places paid out^(0.09226-0.04832*LN(Places paid out))+0.0762*LN(Places paid out))
The divisor term is only to "normalize" the curve. What the divisor does, is cause the total of the pay out to equal 100%. There is a little difference in some of the totals, but it is very minor. The major deviation is if you are only paying out two places or less. The total payout will be off by no more than 3 tenths of a percent. For up to 100 places paid out the total payout will be off by no more than 1 tenth of a percent.
Now as an example, if you have a field of 67 Open players and you were planning to payout 50% of the field the total number of places to be paid out would be:
Rounddown((67-1)*0.50 + 1) = 34 places to be paid out
To find the payout at tenth place:
0.9563*(34*10)^(-0.5937))/(0.9593*34^(0.09226-0.04832*LN(34))+0.0762*LN(34)) =.030 times total cash
This formula is in my Excel score keeping spreadsheet, but it is only used if you go beyond the PDGA tables. I will be sending a copy out to in the next couple of days to several people. If you would like a copy, please e-mail me at [email protected]
I have performed a similar calculation for the Amateur tables, past the defined PDGA tables.