Yeah, the difference between 15 inches and 30 inches is really huge. A 15 inch putt can break on you, but it likely won't break outside of the hole. It takes a horrible stroke or a real tricky downhill breaking putt to miss a 15 incher. You can also be pretty firm, relatively speaking, with a 15 inch putt to hit the back of the cup with confidence.
36 inch putts can be missed. Even a good putter might miss a 36 inch putt 1 out of 5 times. 36 inch putt with break can break outside the hole. Also, you cannot be as firm, relatively speaking, on the 36 footer.Once
you get to 60 inches, we're talking about a 45-40% miss percentage for pga pros.
Just some examples of PGA tour pros stats (range for top 100 golfers:
Inside 5 feet:
96-98.9%
3-5 feet:
86-96% (only Oosthuizen is above 93%)
(this means these guys are very high 90% from inside of 36 inches)
5-10 feet:
54-65% (so if you can make 2 out of 3 of these, you are better than the best pga tour pros)