3ball against 4ball - best score advantage?

  I belong to the senior section of a golf club which meets regularly to play competitive social golf.  The question I have is a Mathmatical question.  At times we have 3ball and 4 ball teams with 2 out of 3 to count and 3 out of 4 to count.   My own feeling is that the 3 ball has an advantage over the 4 ball.  Can this be proved or disproved any help would be appreciated

Theoretically, you are correct Michael, but as we all know, golf is a funny old game.

I think in very simplistic terms if you are basing on the rounds being scored being played to handicap or better than the 3 ball is using scores from 66% of the team compares to the 4 ball using scores from 75% of the team so statistically the 4ball requires slightly better golf.

I think as John say's it a funny old game and I very much doubt anyone will have hard evidence to prove or disprove.

All comes down to mathematics and that would suggest the 3 ball have the advantage

Michael, you don't say how you adjust the three ball score from the two best players to equate to the fourball score from the three best. The threeball is likely to score in the 80's (Stableford points) and the fourball around 115-120, or do you take a simple average (in which case the threeball has a major advantage)? I would be interested to know how you allow for this.

However, I do have a solution for you which I developed several years ago and my Saturday group - typically between 7 and 14 players that often has a mix of threes and fours - has used it successfully ever since. I have also done some detailed analysis over that period and it does give very fair results.

Each group counts their best two scores only, but the fourball, with the advantage of the extra player, all play off three-quarters of their full handicap. Works like a charm.

If there is too much grumbling from the fourball about loss of strokes I suppose you could add one-third to the threeball's handicaps with roughly the same result. This would lengthen the round as players who might have picked up would still be putting out on several holes.

If we have just threes or just fours we discard the worst score on each hole, playing off full handicap, though, strictly, we should play off 7/8, as full handicaps should only be used when all of a player's strokes in the round count. As I'm the lowest handicap and would suffer least under that rule I am outvoted every time!

Let me know if you like this solution.

Hi, Michael.

Yes, I had assumed we were all talking about taking the best two (or three) Stableford scores on each hole, so even a player having an off day will contribute on several holes as one or two of the others have a disaster. We thoroughly enjoy the events as we are playing in a team and we all want each other to do well, so as to beat the other teams - of course, the teams will be totally different the next week!

I still don't understand how you compare two teams, one a threeball and the other a four. As I explained, we get a very even-handed game by taking the best two scores on each hole but making the fourball play off 3/4.

Mike, I don’t know what the problems are with the system today but I’ve tried to answer your comment four times and lost my entry every time. This time I’m typing it in offline so I don’t lose the detail again as I did with my first attempt.

Superficially it seems that the threeball will have an advantage in your system as you are comparing the average of the best two from three with the average of the best three from four.

However, if they were evenly spread the scores might look like this:

Threeball: 45, 36, 27 (total of the best, second and third best on each hole, not individual scores per player)

Fourball: 48, 39, 33, 24.

In each case the average score across all three or four is 36, so any system should put these two groups level or very close and, in fact, the average of the threeball’s best two is 40.5 and the fourball’s best three average is 40.0, which would suggest the problem is negligible.

However, in the real world things can be a little different. I’ve dug out a card (from my bin!) and analysed the scores using your method and my system.

The actual individual scores were 37, 33, 29, 27, a reasonably usual mix (actually off ¾, but this doesn’t affect the analysis). Taking the best, second, third and worst on each hole the totals were 47, 37, 26 and 16 respectively and the total of the best three therefore 110, giving an average of 36.7.

I then took each of the four possible combinations of three players in turn and assessed their scores. The results were:

Without the 37-point player the best two on each hole totalled 71, averaging 35.5;

Without the 27-point player the best two on each hole totalled 78, averaging 39;

Without the 29-point player the best two on each hole totalled 79, averaging 39.5;

Without the 33-point player the best two on each hole totalled 76, averaging 38.

Thus, the threeball had an intrinsic advantage, winning three of four combinations, in two cases by a statistically significant margin, and losing only the case where the highest-scoring player was not counted. Of course, this is a fair test as the same scores were used for each group. It would suggest that the averaging method is unfair to the fourball.

I then used the same card to evaluate (not for the first time) the fairness of my system.

In this case the best two from the fourball, off ¾ handicap, totalled 84 points. In the case of the threeballs:

Without the 37-point player the best two on each hole totalled 77;

Without the 27-point player the best two on each hole totalled 85;

Without the 29-point player the best two on each hole totalled 85;

Without the 33-point player the best two on each hole totalled 83.

Thus, the threeballs won two and the fourballs won two, in all cases but one by the closest possible margin and, in the other case, with the best scoring player taken out, the threeball would hardly expect to be competitive.

On another occasion four players who scored 35, 32, 30 and 29 would have totalled 109 scoring the best three on each hole, averaging 36.3, but combining them as the four constituent threeballs they would each have scored 76, 74, 75, and 72, averaging 38, 37, 37.5 and 36. The threeballs in this case would have won three times by between 1.2 and 0.7 and lost once by the narrowest of margins, 0.3. This seems to confirm that the threeballs are given an unfair advantage using the “best two average” method.

I would be happy to let you have the details of the calculation if you need to use your own group’s results to prove the point, or I could analyse one of your fourball cards as above.

Hi, Mike. Enlightened self-interest - I wanted to know if your system or a derivative would work for our group! It's taken several analyses over the years to convince people, especially when three or fourballs have a run of wins, but overall there is a very good balance. I've just done a final check with another fourball card and it shows the same result - using your system threeballs win 3 out of 4, with our system it's 2-2. Looking at the three analyses the average advantage the threeballs have is 0.9, so you could consider retaining your system but just giving the fourball a one-point start!

Using my system with a 7/8 handicap will give the fourball, counting the best two only, an advantage. This will depend on the typical handicaps in your group. If they are relatively high the advantage will be quite large, as each16 handicapper will only lose 2 strokes not 4. Our group is 5-16 handicap, mostly around 9-12.

The benefit of your system is that each group only drops one score per hole - the disadvantage of ours is that the fourballs drop two so the players are less involved. Here's a compromise: each player in the threeballs have to play off one stroke less than their usual handicaps! This would typically only reduce their overall score by one point (averaging the best two) and would strike the balance perfectly. It would still mean that three players counted on every hole in the fourball/s.

In fact, I might suggest that method to my group (except we would miss the countback afterwards!).

Good luck, let me know how you get on,

Terry

Michael,

Do these groups play 3's and 4's in the same competiton, on the same day?

If they do, you should look at the whole thing.

Play the Comp as "Best TWO scores on each hole" plus one hole where all scores count.

Then into the 3ball groups you introduce "Harry" or "Hilda".

Who are Harry & Hilda? They are a Blind Draw Score, usually Nett level par or 2pts per hole. You can have any number of ways to produce these scores, but giving a level par score on each hole allows the 3balls to 'know' how they stand.

You send everyone out in fours, which will end with only 1, 2 or 3, 3ball groups to deal with.

TheLyth