Assume two players both get to 4 SG:P for the day. A does so by holing four 33' putts. B does so by holing 8 8' putts. They're both average on the remaining putts.
- A has a 0.000625% chance of that happening, since a 33' putt is holed about 5% of the time.
- B has a 0.390625% chance of that happening, since an 8' putt is holed about 50% of the time.
With the average hole proximity on tour being 37, and 32 on shots hit from the fairway, a player on any given day having 4, 33 putts would seem to be moderate to highly probable. But what would need to happen for the average tour player to have a day in which they have 8, 8 putts? How frequently does that occur?
A ball resting anywhere on the green most likely arrived there by one of three methods; as the result of an approach shot, as the result of a chip/pitch, or as the result of a putt.
Comparing a ball laying at 8 and a ball laying at 33:
A ball at 33 has a greater than 93% chance to be the result of an approach shot and a near zero chance to be the result of a putt.
A ball at 8 has a 45% chance to be the result of an approach shot and a small, but recognizable chance to be the result of a putt. Meaning close to 50% of all 8 putts will be for par or worse.
With their approach performance being considered average on all other holes...
If all 8, 8 putts were the result of an approach shot, resulting in 44% of that players approach shots that day ending up at 8, that would probably be the greatest SG:App round ever. At the other end of the spectrum, if all 8, 8 putts were the result of missed greens and recovery shots, the SG:App for that round would probably be very poor.
In actuality, the average player with 8, 8 putts in a round would most likely have less than 4 of the putts come from approach shots and more than 4 of them come from other shots. As the average tour player hits ~12 greens a round, 2/3rd of those missed greens would result in a recovery shot ending up at 8 from the hole, which would be a well below average scrambling distance. Suggesting the approach shot was fairly wayward and hurting their SG:App.
It would then seem unlikely for a player that makes 8, 8 putts over a round to do so with a stellar approach game.
Over the course of the 2020-2021 season there were 10,343 putts struck from 8 and ~11,554 putts struck from between 30-35. (33 stats were not available, but I presume the SG:P variance between 30 and 35 is close enough to 33 for this exercise) If a player had 8, 8 putts over the course of a round, the probability would say they would also have 9, 33 putts. But of course neither is true. Odds are a player would have less than 1 of each putt in a round. So to have 8, 8 putts is twice as unlikely as having 4, 33 putts.
While it may be feasible to putt at an average rate for 11 holes and make 8 consecutive 8 putts, the probability of the situation even presenting itself appears to be rather low.