Does anyone have any data sets from which two professional golfers, for example from the PGA or Euopean tour, who are approximately equal matched and the likelihood that the shoot the score score in an individual round? I was looking at some of the betting odds and it seemed to imply the probability was between 10-15%.

Specifically it would involve two players who have roughly the same mean score, so what the SD would be.

If they are equally matched it's higher than 15%. Pro golfer scores don't vary by much for a single round on the same course, maybe a three to four strokes range.

This is not true. At this year's PGA Championship in the first round, the low score was a 67 and the high 84. Out of 157 entrants, 18 shot 74 and 17 shot 73 (including the eventual winner), 2 and 3 shots over par respectively. I think these are the most common scores that round (I just did a quick count). One of the first round leaders, 67, shot a 78 on the second day. The PGA is always a very competitive field, so I think it closely mirrors the parameters given. I think the answer to the question is likely lower than 15% chance.

That field is definitely not evenly matched players, which is what OP specified. Look at the 4 rounds played by each individual golfer and you will usually find a 3-4 stroke range of scores. We aren't talking about the score range of a diverse field of over 100 golfers.

That is just not true. The reason I chose the PGA is that it is a major championship and players need to qualify for it. It is a very tough field. And as far as the four rounds, the spread between the winner and 75th, the last person to make the cut, was 23 strokes. But if you meant the range between the rounds of individual players, here are the spreads of the top six finishers for their high and low rounds: 7, 10, 6, 3, 6, 9.

Today's event is the BMW Championship. It is part of golf's "playoffs" that people have to actually qualify for with their play throughout the year. This is the third event of the "playoffs" where only the top 70 golfers are included. It is the very definition of "evenly matched" and hardly a "diverse field".

The leader after the first round is at 62. Last place is 77. The person in last was ranked 24 coming in. Are you saying that the 24th ranked golfer in the world is not evenly matched with anyone?

Golf scores for the very best players are not bunched as closely as you think.

This is the part that matters, so I concede the point. It is wider than I thought.

I did a fair amount of research on this subject. The bookmakers don't differentiate between Speith vs Matsuyama and Speith vs Chalmers. They believe that the skill levels of pro players are more or less irrelevant. I did some modest sampling and they seem to be correct - comparing 100 matches with one player greater than a 6/4 dog and 100 matches with both players less than 5/4, both samples had 11 ties.

Those samples were based on actual matches. The situation however becomes somewhat confused when you look at "simulated" matches i.e. take the finishing order of a tournament and see how likely the 1st and 2nd 9th and 10th etc players are to have the same score. I looked at 18215 of these simulated matches from the 4th rounds of several years PGA tournaments and the number of same scores was 3969 (21.7%)! In order to stop the shouts of "double counting"* here is the complete breakdown of differences of scores:

0 3969
1 5353
2 3138
3 2047
4 1378
5 945
6 669
7 355
8 192
9 108
10+ 61
total 18215

So there appears to be dynamics in actual twoballs that make tied scores less likely than between "random" players


*I can't find any double counting anyway disclaimer

Can you expand on your methodology for this? Did you pick your matches based on tournament finishing order and then use each golfer's final round? If so that seems like you are cherry picking results based on golfers that have already performed well in the tournament.

hmmm there is a bias of some sort but not sure its due to players performing well, think its more likely to be players scoring average scores and maintaining their position.

Anyway I reordered by player name which is close to random and

1853 0
3543 1
3200 2
2758 3
2117 4
1603 5
1144 6
778 7
525 8
309 9
423 10+
18253* total

*slight difference because excel

So about 10% seems to be the number.

Still seems strange that players skill level doesn't materially affect the odds. I suppose it must be because the win/lose margins are very flat around zero, "1" on the table is the total of players winning matches by 1 stroke, 1788, and losing by one stroke, 1755.

Aren't you also limiting your player pool to the top ten finishers in the tourney?

No the top 70-80

You can have the spreadsheet if you want

The figures in the R1 R2 etc are below or above the average round of the day

https://1drv.ms/x/s!AtKSOpG8b_uugTKaMxMD1XVNFSYc