The science behind why the flagstick should be pulled 99.9 percent of the time
EDITOR'S NOTE—PGA Tour rookie Davis Thompson's 48-foot birdie putt on the 17th hole Sunday at the 2023 American Express was tracking all the way to the cup. But with the flagstick still in the hole, the ball didn't seem to have the room to fall in, instead clanging away and leaving Thompson a short clean up for par. Unfortunately for the 23-year-old, that missed opportunity proved costly as he would lose to Jon Rahm by a stroke. If only he had read the research below, first published by Golf Digest in 2019 shortly after the USGA and R&A amended the Rules of Golf to allow for the flagstick to remain in while putting.
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When you question the standards and practices of PGA Tour players, multiple expert teachers and perhaps even golf's ruling bodies, you better bring in some heavy thinking. Especially when you say that not only is leaving the flagstick in questionable, it’s no benefit for 99.9 percent of putts. But this conclusion is not made lightly.
There’s loads of science behind that number. But then this is what you should expect when you put a Ph.D. on the case, which is what Golf Digest did in its May issue in an effort to answer the debate over the flagstick and whether in or out is the best way to putt.
Tom Mase, professor of mechanical engineering and former associate chair of the department of mechanical engineering at California Polytechnic State University (Cal Poly), is no amateur golf scientist. He’s been on the vanguard of golf equipment research for much of his 30-plus years in academia, as well as stints at both Callaway and Titleist and as an original and long-time member of the Golf Digest Hot List Technical Advisory Panel.
His research on the value of leaving the flagstick in was precise, painstaking and perfectly clear. His findings upend the conventional wisdom that the flagstick is some kind of backstop, gathering wayward putts back into the hole. The facts of his study suggest the opposite, that the flagstick does much, much more to hurt your chances of a putt going in than help turn a bad putt into a made one. Here’s how he got to that incredibly definitive number:
What was Prof. Mase’s testing methodology?
The testing occurred over six separate sessions at the Cal Poly golf team practice facility at Dairy Creek Golf Course. Some of the preliminary sessions determined a model and methodology for the final testing, but the main testing involved rolling putts with the Perfect Putter training aid, which is a ramp-like structure that sends the ball on a consistent path and at a consistent pace. The Perfect Putter was set up two-and-a-half feet from the hole to eliminate the irregularities in the putting surface that might have skewed results on putts from a longer distance. Given that the focus of the study was the pace of the putt as it reached the hole, this speed could be regulated more consistently from close range.
Putts were rolled six at a time during various scenarios and speeds. Those included:
—Flagstick in (with three different flagsticks: fiberglass, tapered aluminum, dual-diameter
There were five main areas of focus in the testing:
So where does the 99.9 percent number come from?
“Let’s say that a golfer is an extremely good putter,” Mase says. “He or she seems to hit the hole or get a piece of the hole every time. Of course, they are not perfect, so assume their putts adhere to what scientists call a ‘normal distribution.’ A normal distribution is basically what we know as a bell curve. For our really good golfer, we’ll assume that the middle of the hole gets the most activity (the top of the bell curve) and then the range of all putts drops off equally left and right of dead center, stretching at the extremes beyond the edges of the hole. These dropoffs, or standard deviations, are broken down into six regions across the 4.25-inch diameter of the hole. Divide 4.25 inches by 6 and you get 0.7083 inches per standard deviation. That means our really good putter only hits the area of the hole 99.73 percent of the time.”
Now, Prof. Mase’s theory explains that hitting the flagstick directly means hitting a half-inch wide area in the center of the hole, or less than the width of one standard deviation. Using a Matlab script, he calculated the probability density function and concluded that this theoretical “really good putter” is hitting the flagstick straight on only 27.6 percent of the time.
So basically, there are two scenarios to consider: the approximately 28 percent of putts that hit the flagstick straight-on; and the approximately 72 percent of putts that otherwise catch some portion of the flagstick and the hole.
First, let’s consider putts that hit the flagstick straight-on.
In Prof. Mase’s exercise, for putts rolling at a pace equal to 2 1⁄2 feet past the hole, 100 percent of putts went in. That was true regardless of the scenario: flagstick in, flagstick out, straight in or off-center and regardless of flagstick type. For straight-on putts that would hit the flagstick dead center, there also was no difference on attempts for putts that would have rolled 4 1⁄2 feet past the hole. Whether the flagstick was in or not, 100 percent of the putts were made. That 100-percent make rate also remained true for attempts on putts rolling eight feet by the hole.
However, once that velocity was exceeded, the putts holed dropped precipitately. At nine and 10 feet past the hole, the make rate drops well below 50 percent with the flagstick out to ultimately zero. With the flagstick in, it generally remains at 100 percent—even at a pace 11, 12 and 13 feet past the hole (see chart below). (One caveat: The dual-diameter aluminum pin showed make rates dropping below 50 percent at nine feet past the hole and higher.)
What does this tell us? For that theoretical 27.6 percent of putts that would hit the flagstick straight on, the advantage of leaving the flagstick in vs. out for holing those putts only begins to manifest itself when the pace of the putt is greater than rolling nine feet past the hole. But how often does that happen? Here’s where we get to the 99.9 percent solution, although hold on, because we’re about to hit you with a lot of math.
Using PGA Tour statistics from 2018, on putts of more than 25 feet, the make percentage is 5.48 percent. So under our model, this very good PGA Tour putter is then only hitting the flagstick dead center a little more than one-fourth of those putts, or approximately 1.37 percent of the time. Now, according to the PGA Tour’s ShotLink data, the number of putts that finish 10 or more feet from the hole is less than one percent. Admittedly, that number is for all putts, but let’s get real. Tour players don’t miss putts by 10 or more feet very often when they’re putting from less than 25 feet. Basically, though, using these statistics and our model, about one percent of one percent of putts from 25 feet or more are hitting the flagstick dead on at a speed that would take them 10 feet or more past the hole. That’s .01 percent of the time.
So that’s the only time the flagstick will help a putt go in the hole that would not have gone in otherwise. The rest of the time—99.99 percent—the better play is to putt with the flagstick out of the hole.
But doesn’t the flagstick help on off-center flagstick strikes?
As Prof. Mase’s data and study establish, it is much more likely that a putt would be striking the flagstick off-center as opposed to dead on. According to our probability calculations above, putts that contact the flagstick off-center with a glancing blow occur almost three times more often (72 percent vs. 28 percent). So does the flagstick help in these situations? Once again, the answer is an overwhelming “No.” In Mase’s testing, he chose a pace where the ball was rolling 4 1⁄2 feet beyond the hole. (Remember that at 2 1⁄2 feet by the hole, 100 percent of the putts were made whether the flagstick was in or out.) Here are the results of the off-center testing performed with the Perfect Putter at Cal Poly. For the first round of 30 rolls, the order of testing and number of putts holed were:
For the first round of 30 rolls, the order of testing and number of putts holed were:
Fiberglass pin: 15/30
Pin out: 22/30
Taper pin: 15/30
Multi-diameter pin: 11/30
The second round kept the same order as the first round. The putts holed were as follows:
Fiberglass pin: 15/30
Pin out: 29/30
Taper pin: 2/30
Multi-diameter pin: 9/30
A final round of 30 putts:
Fiberglass pin: 25/30
Pin out: 30/30
Taper pin: 15/30
Multi-diameter pin: 14/30
For a putt traveling 4-1/2 feet past the hole. The total numbers are as follows:
Fiberglass pin: 55/90
Pin out: 81/90
Taper pin: 32/90
Dual-diameter pin: 34/90
In total, the make percentage with the flagstick out was 90 percent. The average with a flagstick in was 45 percent, as high as 61 percent with the fiberglass pin and as low as 36 percent with the dual-diameter pin. In general then, a putt that would have struck the flagstick off-center is twice as likely to go in with the flagstick out as it is with the flagstick in.
What about the belief that the flagstick may have some benefit in distance or break perception?
Prof. Mase’s brief study of this aspect was inconclusive. To assess whether people are better processing a 25-foot putt with the pin in or out, players putted from two spots on the practice green to holes running in opposite directions. Players made one attempt on each of the putts. The first putt taken by the players alternated between the flagstick-in and flagstick-out conditions. The players tested were mostly collegiate golfers playing in the Bruin-Wave Invitational. Schools helping us with the testing were San Diego State University, New Mexico State, University of New Mexico, University of Washington, University of California, Stanford, Pepperdine, San Francisco University, UCLA, and Cal Poly.
There was no difference in the distance from the hole between the two scenarios. Whether the flagstick was in or out, putts finished about two feet from the hole. With the flagstick out, the misses were slightly closer (23.6 inches) than with the flagstick in (25.7 inches). With the flagstick in, 56 percent of the putts finished past or in the hole. With the flagstick out, 39 percent of the putts finished past or in the hole. Here is a chart for how putts finished in the two scenarios.
Jeff Troesch, mental coach to several college teams, explained that how players perceived and used the flagstick was still very much a work in progress.
“I speak with dozens of golfers every week and what is notable about the visual/mental perceptions of the pin is that the golfer reactions are quite varied. Some see having the pin in on shorter putts as visually intimidating and this feels distracting. Others perceive the hole to look smaller with the pin in (on shorter putts) and find this disconcerting. Others appreciate with the pin in that there is the sense of a “backstop”- particularly for putts that are downhill and/or are longer where there might be an overall increase of top putting speed. Still more have spoken about a sense of having greater hole awareness for short to mid-range putts as they can see the pin in their peripheral vision when in the address position. There is a group of golfers who don’t like the sight/notion of something that is “so radically different” from how they’ve always putted. They articulate finding themselves internally distracted from relevant cues that have worked in their pre-putt routine or during the execution of the putt itself. Others find themselves open and receptive to it and are particularly influenced by the perspectives of pros (e.g. Bryson DeChambeau and Adam Scott).”
So where does all this science leave us?
Leaving the flagstick in may have some benefits but from a physics standpoint, there is zero evidence to suggest that the flagstick helps in any but the rarest of situations. What the flagstick may do is occasionally reduce the length of a second putt and therefore possibly help reduce three-putts. Of course, it also will clearly and substantially reduce the number of one-putts. It’s also clear from our research that the fiberglass type of flagstick is the least detrimental (but still nowhere near as good as taking the flagstick out). Finally, there is some evidence that tour players putting on really fast greens may benefit slightly because the ball may be rolling slower as it comes in contact with the pin. This benefit however remains miniscule compared to the benefit of pulling out the flagstick completely. Perhaps the best benefits to leaving the flagstick in are the optics and distance perception. Several sports vision experts we contacted suggested there would be such benefits especially from longer distances, and noted putting instructor Mike Shannon said his research suggested players read greens better because the flagstick acted as a plumb line. So the obvious solution might be to have the flagstick attended. In other words, a return to the preferred method from before the new rule was enacted. We shall see if tour players will see this data and change their minds.