THE REAL ODDS OF SCORING A DOUBLE EAGLE
Below is correspondence I received from Scott Hovde from the the USGA who responded to my question "How are the odds determined for scoring a Double Eagle? Most sports writers quote the odds to be 1,000,000/1 or 6,000,000/1. Please advice".
June 10, 2015
Looking at professional data, there are very few double eagles. According to the PGA Tour there have been 32 double eagles (so roughly 3 per year on average) in the last 10 years. I found a link from 2013 (http://www.pgatour.com/news/2013/09/25/2013-by-the-numbers.html) that shows about 281,000 holes of golf were played for the season with about 218,000 of them as par 4/5 (impossible to score a double eagle on a par-3). In that particular year there were 2 double eagles (both on par 5’s) so the odds would be about 109,000 to 1. So assuming the same number of holes played in most years, and a recent average of about 3 double eagles per year, the odds drop to about 72,000 to 1 for a PGA tour player. I’d imagine the odds are similar for the other professional tours. In looking at holes in one on a par-4 hole, there has only been one officially recorded on the PGA tour (Andrew Magee 2001), so you can imagine what the odds are based on decades of golf. If the PGA tour had more short par 4’s, the odds would surely get better. In general there are maybe 1 or 2 holes at most at a typical tour event that are legitimate chances to reach the green in one shot.
Regarding amateurs, we would probably have to break it down by handicap, as the odds would be vastly different for a scratch amateur compared to say a 36.4 Index. We have a fairly large database of hole by hole scores for players of various handicaps and for some, the odds are basically zero (no recorded 1’s on a par-4 or 2’s on a par-5) for players in the 25.0 and up categories, as 99% of them do not have the length to ever do it. For players in the 5 or less Handicap Index range, the odds are not far off from the PGA Tour stats…however the distances that the PGA Tour plays compared to amateurs is significantly different, so there are more legitimate opportunities to score a double eagle for the amateur players. For example, many of the double eagles in our amateur database are very short, right on the break point for par (i.e. a 460 yard par-5 or 240 yard par-4). Plus the database only lists the official hole length…so if tees were moved up say 30 yards for weekend play or maintenance, it wouldn’t be reflected. When we get into the 5-25 Handicap Index range, the odds start to go up as expected from 100,000 to 1 up to 1 million+ to 1…and ultimately zero at 25+. So there isn’t a single number that represents the odds. If we define an amateur golfer as say a 15-20 handicap male (about the average), then the million to 1 odds are not unreasonable and may be reflected in a large set of data. But depending on the data set and the handicap, the odds can change a lot since we are looking for rare occurrences instead of predictable patterns.
I hope this info helps.