Now that seems fairly intuitive but it may not actually be true. This is because in order to always reach the hole, you need to pace your shot so that it plans to land a little bit past the hole. This is of so that if your shot doesn't go as far as planned then by being short of target it will still reach the cup. Also among strong players faster putts travel on a truer line and so tend to sink more often.
Consider the following situation. A golf pro and a casual player (handicap 15+) face a 12 foot putt. What strategy should be used. Now for the pro it's clear to be aggressive and attempt to hit it into the hole, aiming say 2 feet past the hole (so the putt reaches the hole and with enough speed). For the pro this strategy makes sense for a couple of reasons.
The pro's putts will mostly land within say a two foot radius of his target landing point. So if he misses the putt then he will still be in good shape on the next putt.
The pro can efficiently convert longer 4-7 foot second putts. So if say the pro is unlucky and his first putt lips out and ends up 6 feet away this isn't terrible as the 6 footer is very makeable for the pro. So the correct strategy for the pro is to be aggressive and make a strong putt with enough speed to land past the hole.
Now for the amateur things are different. The amateur is not able to control his landing radius as well so his radius is more like 3 feet and many, but still fewer, of his putts will land in this primary radius.
Also for the amateur being left with a second putt over 3 feet is a disaster as the amateur converts far fewer of these 4+ foot second putts.
From here we can see that it is possible that the correct strategy for the amateur may not be the same as the correct pro strategy. It is not difficult to devise a realistic circumstance where the amateur should aim at the cup, not past it, and accept coming up short half the time.
Consider this situation. An amateur is facing a 12 foot putt.
if he aims to land right at the hole
- 10% of the time he will be lucky and will sink the putt
- 80% of the time his second shot will be within 3 feet
- 10% of the time his second shot will be 4 feet or more
if he aims the putt a bit past the hole
- 20% of the time he will sink the putt
- 50% of the time his second shot will be within 3 feet
- 30% of the time his second shot will be 4 feet or more
in all cases this is his conversion efficiency on second putts
- within 3 feet he will convert 92% of the time and 3 putt 8% of the time
- from 4+ feet he will convert 24% of the time and 3 putt 76%
Plugging this into a simple spreadsheet we can see that the conservative strategy has an expectation of 2.04 putts. The aggressive pro strategy has an expectation of 2.07 putts (despite 1 putting twice as often). Thus the correct play is to ignore the tv pro advice and accept often coming up short.