**Player Rating Algorithm**

To calculate your rating at a particular round the following formula is applied:

………. [1]

Where,

s is the players score for that round.

is the average Open Pro score for that round.

R_{o} is the rating given to the average Open Pro score for that round.

K is a factor that determines how many rating points each stroke is worth for that round.

R_{o} has been given a **fixed** value of 955. This means that if you shoot a score equal to that average of Open Pro players playing that round, your rating will be 955. This is independent of who played Open Pro, which course was played, and what the weather was like. This fixed rating average works for Duck Golf tournaments because, roughly and in general, the same group of players play Open Pro at each tournament.

K is a variable factor that depends on the length of the course (L), the par for the course (P), and how close the lowest score is to the 'perfect round’, where the ‘perfect round’ is defined as all birdies (s=P-H, where H is the number of holes). The formula for K is:

………. [2]

This formula looks a little intimidating, but can be explained with words. K is composed of three factors, K_{1}, K_{2}, and K_{3}. K_{1}=8.0 and is generally about 80% of the value of K. This means that K_{1} gives 8 rating points for each stroke of a round (i.e., if you shot 50 and your friend shot 55, you would have a rating (55-50)*8=40 points higher if only K1 is used). K_{2} gives the influence of course length (relative to par) – the larger L/P, the larger K_{2}, and the more each stroke is worth. K_{3} gives the influence of a nearly perfect round. The closer the lowest score (s1) is to the ‘perfect’ round of all birdies (s1=P-H) the more the rating is amplified. The graphs below show the ranges for K_{2} and K_{3}. From all DG rounds, the range of K (= K_{1}+ K_{2 }´ K_{3}) is from 9.4 to 11.0.

This rating system is better than the previous rating system which used the standard deviation of round scores to determine the value of K - the less spread out the scores, the larger the value of K. The current system has a smaller range of K, meaning that each stroke is worth roughly the same number of rating points in each tournament. Also, the range of K is properly influence by direct measures such as course difficulty (large L/P) and a score approaching the ‘perfect’ round.

**Player Ratings**

To get your player rating at given date, use the following steps:

- For each round you played in a Duck Golf tournament prior to that date, compute your rating using equations [1] and [2] above. Everything you need (including K values) is given in the tournament results file for that round. Note that in order for your round to be given a rating, you must play the exact same course (including tee pad, O.B.'s, etc.) as the open men, otherwise it is impossible to give a rating based on this system. If you are really into ratings, try to convince your TD
*long before the event*to let your division play the same course as Open Pro (sometimes, due to time/space limitations it's not possible, so respect your TDs decision). - Order all your round ratings from most the recent to the oldest.
- Take no more than the most recent 20 round ratings from Step 2.
- Remove all round ratings left in Step 3 that are 18 months or more older than the most recent in the list.
- Remove the 15% worst ratings. This is a safeguard against the 'sandbagging' issue.
- Calculate the overall player rating from the remaining ratings based on the formula:

………. [3]

Where is the ith round rating and is the associated weighting factor,

………. [4]

Where is the time (in months) between round i and the player's most recent round (from Step 2). A rating counts less towards the overall rating the further back in time it occurred. A round within the first six months of the most recent counts the same as the most recent rating. Rounds older than six months of the most recent count less - at 12 months they count half as much, and finally at 18 months they don't count at all. This means that your overall player rating is based on play within the last 18 months of your most recent round with the value biased towards your play in the last 6 months. NOTE: since we normally have about a 4-5 month gap between duck golf seasons, this means that ratings can change more quickly at the start of the season due to the limits of 6 and 18 months in the formula.

**Sample Player Rating Calculation Ratings Calculations **

From the tournament file (http://www.bcdss.bc.ca/ssi/tournaments/DGR/2002-3/Kamloops.html) the tournament has 3 rounds with averages of 55.05, 55.40, and 55.00. The tournament file also gives L/P = 6209/57 = 108.93 for all three rounds. This give K2=1.316 for all three rounds from formula [2] above. The lowest score for each round is 50, 46, and 48, giving K3 = 1.320, 1.623, and 1.446 from equation [2] (in this tournament, P-H=39 is the ‘perfect’ round). This gives the K values for each rounds as 8+1.316*1.320, 8+1.316*1.623, and 8+1.316*1.446 = 9.737, 10.136, and 9.903

Now we can calculate Dave’s ratings using [1]. For round 1, R1=955+9.737*(55.05-53)=974.96 rounded to the nearest whole number is 975 – the same as in the tournament file. Similarly for round 2 and round 3, R2=955+10.136*(55.40-46)=1050 and R3=955+9.903*(55.00-53)=975.

Now we can calculate his player rating of 1000 for Oct 1 2002, as given in his personal file. Following steps 1-5 above, we can see that all three Kamloops rounds are the only ones prior to the rating date and are within the 18 month cutoff, so all are included. 85% of 3 is 2.55 which is 3 when rounded to the nearest integer. This means we keep all three rounds. Since all three rounds are within 6 months of Oct 1 2002, they all get a weight of 1.0 from equation [4]. Using equation [3] we get:

R = (1.0*975+1.0*1050+1.0*975)/(1.0+1.0+1.0)=1000.

Hank