The hole is 4.25 inches wide, the circle's diameter. The "minimum" capture width is the thinnest but longest route across the hole where the ball will actually drop and stay in the hole. This line is centercut, so 4.25" across for length, but the thinness is basically one dimple wide. The "maximum" crossing speed along this "minimum width" / "maximum length" path is a smidgen over about 9 revolutions per second ball speed at the front lip. This actually varies a bit due to the grass on the edge and the firmness of the dirt near the top edge, etc.
The "maximum width" / "minimum length" path is 100% wide minus iota and 0" long front to back plus iota, "iota" being a conventional expression in mathematics for "a tiny bit more". So a ball that arrives with zero revolutions per second plus iota speed at the far left or right edge of the hole that has the bottom of the ball and the ball's center of gravity actually traveling over air inside the column of the hole, can possibly go in and stay in.
When the ball arrival speed is in between these extremes, the hole has an "effective capture width" that increases from one dimple to the entire width of the hole left-right in relation to the crossing path of the ball, and the steps in width increase at about 0.4 inch for every one revolution per second decrease in ball arrival speed. If 9 rps just hits below the rim on the back of the hole across a centercut path, 8 rps hit in the dirt in the first 1" from rim down inside the column of the hole and this path is effectively about 0.4 inch left and right of the centercut line, so that a ball that crosses 0.4 or less inch left of centercut at 8 rps can still stay in the hole. The total "effective path width" at this arrival speed is about 0.8".
At 8 rps the width is about 0.4" either side of center (total 0.8"), will usually run past the hole 40"-45";
At 7 rps the width is about 0.6" either side of center (total 1.2"), will usually run past the hole 35"-40";
At 6 rps the width is about 0.8" either side of center (total 1.6"), will usually run past the hole 30"-35";
At 5 rps the width is about 1.0" either side of center (total 2.0"), will usually run past the hole 25"-30";
At 4 rps the width is about 1.2" either side of center (total 2.4"), will usually run past the hole 20"-25";
At 3 rps the width is about 1.4" either side of center (total 2.8"), will usually run past the hole 15"-20';
At 2 rps the width is about 1.6" either side of center (total 3.2"), will usually run past the hole 10"-15"';
At 1 rps the width is about 1.8" either side of center (total 3.6"), will usually run past the hole 5"-10";
At 0 rps + iota the width is about 2.0" either side of center (total 4"), will usually run past the hole 0";
Each slower speed allows the ball to drop lower before impacting the back wall, except the curving of the vertical back wall means that balls crossing near the left or right edge don't get all that low inside the hole before hitting the back wall.
Once the bottom of the ball gets within 1/2 the ball diameter (1.68" is the ball diameter, and 0.84" is half that), or when the bottom of the ball crosses the front lip closer than 1.705" left or right of the centercut line to the left or right edge, the ball faces the possibility of "ringing out" as it tries to drop. This is when the dropping of the ball is blocked to some extent by the edge of the left or right side of the hole, so that the whole diameter of the ball is not really clearly inside the hole's column of air. Even though balls arriving at 0 to 1 rps out to the edges of the hole have a chance of dropping and staying in the hole, these far-edge paths also pose the danger of rimming out. So while 0-1 rps sounds great in theory, using that much width is not really a great plan, so there is not all that much need to slow down to less than 2 rps, since these far edges for holes wider than 3.4" aren't all that great a crossing path.
So there are those two considerations about the maximum width of the hole for effective capture. The "effective" capture width at the maximum width is not all it appears to be.
Basically, so long as the ball arrives inside a hole so the entire ball is over the air of the hole's column, then it's good. That "width" is 1.705" left or right of centercut and a total crossing width of 3.41". That corresponds to a ball arrival speed at the far margin of this wide path of between 1 and 2 rps, and that speed is good for all of that 3.41" hole. And faster balls will also go in this 3.41" hole so long as the crossing path matches the speed limit for that path.
The reality, however, is slightly different, as 1 rps is not really something golfers perform with any regularity or consistency. For a variety of reasons, almost all golfers use AT LEAST 2-3 rps as a delivery speed, and most amateurs regularly use more than this, while pros don't really use much more. That being the case, the REAL maximum width is more like 2.8" to 3.2", or roughly 3" wide, 1.5" to either side of centecut.
There is also another REALITY at the minimum extreme. No golfer whacks the ball at a hole with the speed that sends it crazy past the hole except by spastic putting or by really shoddy lagging. Within 20 feet, any golfer who sails the ball over 4 feet past the hole is not very good at putting touch. This sometimes happens in long lags even to the best putters, though, and long lags start to cause substantial worry of three-putting only after about 30-35 feet on Tour. So no decent golfer sails the ball more than 3' to 3.5' past the hole on purpose, and that corresponds usually to keeping within a maximum ball delivery speed of about 4-5 rps at the front edge of the hole. Hence, the MINIMUM effective capture width in reality is about 2.0" to 2.4" on center, or 1"-1.2" left or right of the centercut path. No hole is ever really less wide than this unless the golfer is a spaz.
So, the REAL answer is:
Minimum width, about 2" on center (under 5 rps, go-by comeback inside 2' past back of hole, a gimmie);
Maximum width, about 3.4" on center (about 2 rps, go-by or comeback inside 6-10" past back of hole).
Putting Coach and Theorist