AUTHOR’S NOTE #1: The blog post includes underlined numbers to indicate that the numbers that are underlined are repeating decimals.
AUTHOR’S NOTE #2: The projected scoring system described below is not to be confused with the “most likely score” method that is part of the U.S. Golf Association (USGA) handicap system and designed mainly for recreational golf.
Unlike most sports, it’s not fair to end a round of a stroke-play golf tournament early because of bad weather or some other condition that prevents the round from being completed on its scheduled day. That’s because it wouldn’t be fair to allow one golfer to play fewer holes than another golfer in the same tournament, as, depending on the scores being set by the golfers playing the entire course, it would either be a huge advantage or disadvantage to the golfer playing fewer holes. Also, because each round of a stroke-play golf tournament is usually scheduled for most of the available daylight hours on a given day, and golf courses don’t have artificial lighting of any kind to allow for nighttime play, any suspension of play for a significant length of time will invariably result in golfers who were among the last to tee off not being able to complete their rounds before darkness.
However, a projected scoring system, in which a mathematical formula is used to project an full-round score for a golfer who is unable to complete the full round due to the suspension of play, would eliminate the unfairness associated with ending a round of a stroke-play golf tournament early. At least one sport that I know of, cricket, uses a projected scoring system for some events. In One Day International (ODI) and List A limited-overs cricket matches, the Duckworth-Lewis method, a mathematical formula that produces a projected result if the second team to bat cannot complete their innings due to bad weather, darkness, or some other reason, can be employed in certain situations.
In order to speed up stroke-play golf tournaments (most, but not all, professional golf tournaments use the stroke-play format) that are affected by bad weather or other conditions resulting in play being suspended before the completion of a round, I’m proposing a projected scoring system that can be used if a round is suspended after all golfers have completed at least 12 holes on an 18-hole golf course (at least 6 holes played by all players for 9-hole courses), but before all golfers complete the round, and play cannot be restarted later in the day.
If a golfer had completed a hole other than the final hole he or she was scheduled to play, but had not yet hit his or her tee shot on the next hole, at the time of suspension of play, the formula used to calculate a golfer’s projected score is p/f = s/c, in which p is the projected score relative to par for the round, f is the number of holes in a full round (this is universally 18 for professional tournaments), s is the score relative to par for the holes completed, and c is the number of holes completed. Since p is the variable, one must solve for p in order to get a projected score relative to par. Should p be a number with one or more decimal places, it shall be rounded to the nearest whole number. Should p be a non-whole number ending in .5 or greater, it should be rounded away from zero (i.e., 1.67 is rounded to 2, while -1.67 is rounded to -2). Should p be a non-whole number ending in anything less than .5, it should be rounded towards zero (i.e., 1.33 is rounded to 1, while -1.33 is rounded to -1).
After the projected score relative to par is calculated, the second step involves assigning projected birdies or projected bogeys to holes that the golfer did not play because of the suspension of play. The formula used to determine how many projected birdies or projected bogeys should be assigned is |p| – |s| = b, in which |p| is the absolute value of the projected score relative to par, as rounded per the rounding rules that I described in the previous paragraph, |s| is the absolute value of the score relative to par for the holes completed, and b is the number of projected birdies or projected bogeys to be assigned. The variable in this formula is b, and whether or not p is positive or negative, not |p|, is used to determine whether to assign projected birdies or projected bogeys.
Here’s how the assignment of projected birdies and projected bogeys for each golfer would be conducted:
- Should b be zero, projected pars shall be assigned to all holes that the golfer did not play prior to the suspension of play.
- Should p be a negative number, b be a non-zero number, and the number of birdies to be assigned is less than the number of holes the golfer did not play (i.e., b < (f – c)), a number of projected birdies equal to b shall be assigned to the easiest b holes that the golfer did play, and projected pars shall be assigned on all other holes that the golfer did not play.
- Should p be a positive number, b be a non-zero number, and b < (f – c), a number of projected bogeys equal to b shall be assigned to the most difficult b holes that the golfer did not play, and projected pars shall be assigned to all other holes that the golfer did not play.
- Should p be a negative number, b be a non-zero number, and the number of birdies to be assigned is equal to number of holes the golfer did not play (i.e., b = f – c), projected birdies shall be assigned to all holes that the golfer did not play. Should p be a negative number, b be a non-zero number, and b > (f – c) but 2b < (f – c), a number of projected eagles equal to b – (f – c) shall be assigned to the easiest b – (f – c) holes that the golfer did not play, and projected birdies shall be assigned to all other holes that the golfer did not play. Should p be a negative number, b be a non-zero number, and the number of birdies to be assigned is twice the number of holes the golfer did not play (i.e., 2b = (f – c)), projected eagles shall be assigned to all holes that the golfer did not play.
- Should p be a positive number, b be a non-zero number, and the number of bogeys to be assigned is equal to number of holes the golfer did not play (i.e., b = f – c), projected bogeys shall be assigned to all holes that the golfer did not play. Should p be a positive number, b be a non-zero number, and b > (f – c) but 2b < (f – c), a number of projected double bogeys equal to b – (f – c) shall be assigned to the most difficult b – (f – c) holes that the golfer did not play, and projected bogeys shall be assigned to all other holes that the golfer did not play. Should p be a positive number, b be a non-zero number, and the number of bogeys to be assigned is twice the number of holes the golfer did not play (i.e., 2b = (f – c)), projected double bogeys shall be assigned to all holes that the golfer did not play.
- Should p be a negative number, b be a non-zero number, and the number of birdies to be assigned is more than twice the number of holes the golfer did not play, one shall use the formula a = b/(f – c), in which a is the number of projected strokes under par divided by the number of holes the golfer did not play, to calculate how many strokes under par should be assigned to each hole. Should a be a whole number, the number of strokes that shall be assigned to each hole that the golfer did not play shall be the par of the hole minus a. Should a be a fraction, a shall be rendered as an improper fraction in which the denominator shall equal (f – c), the numerator shall be divided by the denominator in order to yield a quotient with a remainder, the number of projected strokes on the easiest number of unplayed holes equal to the remainder shall be the par of the hole minus the sum of a rounded down to the nearest whole number and one, and the number of projected strokes on all other unplayed holes shall be the par of the hole minus a rounded down to the nearest whole number.
- Should p be a positive number, b be a non-zero number, and the number of bogeys to be assigned is more than twice the number of holes the golfer did not play, one shall use the formula a = b/(f – c), in which a is the number of projected strokes over par divided by the number of holes the golfer did not play, to calculate how many strokes over par should be assigned to each hole. Should a be a whole number, the number of strokes that shall be assigned to each hole that the golfer did not play shall be the par of the hole plus a. Should a be a fraction, a shall be rendered as an improper fraction in which the denominator shall equal (f – c), the numerator shall be divided by the denominator in order to yield a quotient with a remainder, the number of projected strokes on the most difficult number of unplayed holes equal to the remainder shall be the par of the hole plus the sum of a rounded down to the nearest whole number and one, and the number of projected strokes on all other unplayed holes shall be the par of the hole plus a rounded down to the nearest whole number.
To determine which holes projected birdies and bogeys are to be assigned, either average scores relative to par for each hole (counting only those who completed their round and if at least eight players completed their rounds prior to suspension of play), each hole’s handicap rating, or the lengths of the holes can be used.
For golfers who were playing a hole at the time of suspension of play, two separate projected score calculations are made. The first calculation, called the calculation for completed holes, treats the golfer as if he or she did not tee off on the hole he or she was playing at the time of suspension of play. The second calculation, called the calculation for played holes, treats the golfer as if he or she recorded a score of the number of strokes he or she made on the hole he or she was playing at the time of suspension of play, plus one stroke. The calculation that results in the higher score relative to par is the calculation used for the projected score for a golfer who was playing a hole at the time of suspension of play, then the calculation and assignment of projected birdies and bogies is done using the projected score calculation that results in the higher score relative to par.
Had this system been in use in the 2005 PGA Championship at the par-70 Lower Course at Baltusrol Golf Club in Springfield, New Jersey, the final round would have been not restarted on Monday (as it was in real-life), projected scores would have been used for several golfers who did not complete their rounds on Sunday due to play being suspended, and the tournament would have been declared over on Sunday. This is because all golfers had played at least 12 holes (in fact, all golfers played at least 13 holes) prior to play being suspended on Sunday. I’ll use two real-life examples from that tournament in order to explain how the projected score system works.
In the 2005 PGA Championship, Steve Elkington (who finished in a tie for second place with Thomas Bjorn in real-life with a final round of 1-over-par 71 and four-round tournament score of 3-under-par 277) had finished the 15th hole and was one over par for the round at the time final round play was suspended on Sunday. Had projected scores instead of Monday play been used to determine the outcome of the 2005 PGA Championship, here’s how Elkington’s projected score would have been determined:
p/18 = 1/15
p = 1.16, rounded to 1
|1| – |1| = 0
Projected pars on all holes not played by Elkington prior to suspension of play
Projected final round score of 1-over-par 71 for Elkington
Projected tournament score of 3-under-par 277 for Elkington
In the 2005 PGA Championship, Phil Mickelson (who won the tournament in real-life with a final round of 2-over-par 72 and four-round tournament score of 4-under-par 276) had made three strokes on the par-4 14th hole, but had not yet holed out on the 14th hole, and was two over par for the round, and four under par for the entire tournament, at the time final round play was suspended on Sunday. Had projected scores instead of Monday play been used to determine the outcome of the 2005 PGA Championship, here’s how Mickelson’s projected score would have been calculated:
Calculation for completed holes
p/18 = 2/13
p=2.769230, rounded to 3
Calculation for played holes
p/18 = 2/14
p=2.571428, rounded to 3
Calculation for completed holes used to project Mickelson’s score
|3| – |2| = 1
Projected bogey on hardest hole not completed by Mickelson prior to suspension of play
Projected par on other four holes not completed by Mickelson prior to suspension of play
Projected final round score of 3-over-par 73 for Mickelson
Projected tournament score of 3-under-par 277 for Mickelson
The next example that I’ll give is a completely fictional example that takes place on a fictional par-72 golf course in the first round of a stroke-play tournament. Because of a late-afternoon thunderstorm that hit the golf course after Bogey McSandtrap (the name of the fictional golfer) finished the 12th hole of his round (McSandtrap began his round at the 1st hole), and all players in the first round were able to complete at least 12 holes prior to the suspension of play due to the thunderstorm, projected scores were used to determine first-round scores for McSandtrap and the other golfers who did not finish their rounds. The fictional golf course has a total of 16 par-4 holes, a par-3 8th hole, and a par-5 12th hole. McSandtrap did extremely poorly in the 12 holes that he played, taking a whopping 104 strokes to complete the first 12 holes of the golf course, or 56 over par. Based on average scores for each hole relative to par among those who completed their rounds prior to the suspension of play, of holes 13-18 (all par-4 holes), 18 was the most difficult (average score of 4.74), followed by 14 (average score of 4.38), 17 (average score of 4.33), 13 (average score of 4.04), 16 (average score of 3.85), and 15 (average score of 3.72). Here’s how McSandtrap’s projected score would be calculated under this fictional example:
p/18 = 56/12
p=81
|81| – |56| = 25
25/(18 – 12) = 25/6 = 4 R 1
Projected quintuple bogey (five-over-par for the hole) on hole 18 for McSandtrap
Projected quadruple bogey (four-over-par for the hole) on holes 13-17 for McSandtrap
Projected first-round score of 81-over-par 153 for McSandtrap
My projected score method cannot be used in all situations. A notable example of an instance where my projected score method couldn’t have been used was the second round of the 2015 Open Championship at the Old Course at the Royal and Ancient Golf Club of St. Andrews, Scotland, which was suspended twice on Friday (first suspension due to heavy rain; second suspension due to darkness) and once on Saturday (due to high winds), with play being suspended on Saturday for nearly 10 1/2 hours! However, in regards to the second suspension of play, projected scores couldn’t have been used in that scenario since a number of golfers were waiting to play the 11th hole at the time play was suspended. However, if play has to be suspended for any reason after all players have completed at least 12 holes of a round of golf, and the round can’t be resumed later in the day, using my projected scoring system is a great alternative to finishing the round on another day.
The Progressive Midwesterner 