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Paul Bourgeois
ODGC Tuesday Night Coordinator

Joined: 21 Aug 2005
Posts: 1687
Location: Ottawa, Ontario

PostPosted: Tue Apr 24, 2007 1:31 pm    Post subject: TOSS 2007: The Calculation of Round and Player Statistics Reply with quote

TOSS utilizes a USGA-style handicap system to rate players and to determine how many strokes each person receives at any given event. The USGA system provides a simple means of comparing golfers, because the comparison is based on strokes. It is expected that a player with a golf handicap of 10 would take 3 more strokes than a player with a golf handicap of 7.
Where the USGA handicap system excels in simplicity in this regard, it is reliant on a static course scratch score, and a static course slope as determined by course rating experts once every few years. A static course scratch score and slope rating do not account for difficult playing conditions like wind, rain, and temperature extremes. Any of these could greatly affect the score a player would turn in at the end of an event.
The PDGA rating system utilizes a formula for determining scratch scores and adjustment factors based on the expected score that a field of players should turn in. In this manner, environmental factors are accounted for, and individual course characteristics need not be ascertained by a panel of experts.
In 2007, TOSS handicaps will be calculated by combining the best characteristics of each of these systems to deliver a simple to understand golf handicap system that doesn’t rely on static numbers for determining round scratch and slope values. Here is how it works:

Warning! The following details the algorithm used to determine round results and player handicaps. If math isn’t your thing, don’t worry. This work will be done for you as a service by the ODGC to its members.

Scores for players are recorded, and those players that have a history of at least three differentials are used as “seeds” in determining the round scratch score and slope value.
1) An adjusted score is calculated for every player based on their differential history (only the 20 most recent scores are considered, and only those differentials within a single standard deviation of the player’s average differential are considered).
2) An adjusted round score (The player’s score minus their adjusted score as calculated in step 1) is recorded for each player having a record.
3) All adjusted round scores are averaged and a standard deviation is calculated.
4) Any players with adjusted round scores outside of 1.4 standard deviations of this calculated average are removed from the pool of eligible scores. (Note: If fewer than five players remain, then the score cannot be accurately calculated, and a course average will be used to determine the round ratings. Typically, if six or more players record a round, there should be at least five players in adjusted pool. Statistically, if ten players record rounds, at least five players will have eligible adjusted scores.)
5) From the remaining players in the pool, the scratch score is then determined by recalculating the average adjusted round score. This score becomes the scratch score for the round.
6) Using the differential history of the remaining players and taking into account their scores, the slope is then calculated. Using the least squares method of analysis, a slope of score versus adjusted differential is calculated.
7) As a means of adjusting the slope, the calculated score for a hypothetical player having adjusted differential of 18 is considered. This hypothetical player is a “bogey golfer”. The slope of the line joining the expected score for a player having a differential average of 18 and the scratch score as calculated in step 5 is then used to determine the course slope for the round. The course slope is the slope of this line times 113.
These values are then used to determine round differentials for all players that participated in the round. As per last season, a player’s differential is calculated as follows:
1) Determine the score for the round, minus the calculated scratch score.
2) Multiply this by 113, and divide this by the calculated slope.

Handicaps are then calculated based on the differential history. The average of a player’s lowest differentials, rounded up to the nearest tenth, forms their handicap. The following table is used to determine how many differentials are used:
RoundsDifferentials Used
1, 2 0
3, 4 1
5, 6 2
7, 8 3
9-11 4
12-14 5
15, 16 6
17 7
18 8
19 9
20 10

Only the 20 most recent differentials are considered. As a player adds more scores to their record, the oldest score is discarded and replaced by the newest score.

Copyright (c) 2007, Ottawa Disc Golf Club, All Rights Reserved.

Last edited by Paul Bourgeois on Tue Apr 24, 2007 1:37 pm; edited 1 time in total
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Paul Bourgeois
ODGC Tuesday Night Coordinator

Joined: 21 Aug 2005
Posts: 1687
Location: Ottawa, Ontario

PostPosted: Thu May 03, 2007 3:40 pm    Post subject: Reply with quote

The method of calculating player differentials and handicaps has been described above, as well as the method for calculating round scratch scores and slope values. One important facet in making handicaps meaningful is determining what the value of a stroke is, or what exactly a scratch round is. This is a matter of calibration.
Each of the 2006 TOSS rounds was evaluated using the PDGA rating system to determine the PDGA scratch scoring average (the scratch score), and the round’s adjustment factor (AF *113 = slope). This was done by utilizing players’ PDGA ratings as of the date of the round. The exercise was repeated for the 2005 League Night rounds, and the respective average of those blue and yellow teepad rounds was use to rate the 2004 League Night rounds as well. Finally, the 2006 season averages were used to assign scratch and slope values to the 2006 World’s Biggest tournament results.
Finally, using the method described in the post above, scratch and slope values were determined for players participating in blue and yellow teepad rounds at the Plaid Jacket, the Plaid Jacket Super 9, and at League Night Finals.
The result is a collection of almost 100 player records, nearly 40 round results, and over 600 individual scores. 50 players now have disc golf handicaps, and almost as many are only a round or two from establishing one for themselves.
What all of this translates into is an amazing opportunity for members of the disc golf community in Ottawa to track their performance and improve their game by participating in Tuesday League nights and ODGC sanctioned tournaments.
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