As you can see, the metagame of Mario Golf is very mathematical, with numbers on every corner of the screen. Perhaps the place where it is easiest and most consistent to save precious seconds in Speed Golf (or any category, really) is making fast and accurate putts. I am going to list what I have generally discovered through a lot of gameplay and experimentation:

1) The hardest putt that doesn't skip over the cup will most often be the fastest, with an average upper threshold of 5-6 feet over the minimum distance required (which due to slope is different than the nominal distance to the cup).

2) When it is raining, you have to putt harder (obviously). The longer the putt, the smaller the minimum "ratio" seems to be. I find that for putts under 20 feet, a 3:2 (or 1.5:1) ratio works well. For anything longer, you can mentally assigning a sliding scale that takes the ratio anywhere from 4:3 (or 1.33:1) on up. For the longest putts, the ratio might be as low as 1.2:1.

3) Shooting uphill requires about an extra 1.5-2 feet of power on the meter for every 1 foot climbing uphill.

4) For putts exceeding about 18 feet (after all factors), switching to Middle strength can prove faster than staying on Short due to waiting less to hit your mark on the meter (hitting the 1/4 mark on Middle will aggressively sink 18-22 foot putts and slowly sink 23-24 footers). Switching to Long might prove riskier but useful for the rare 75+ foot putt (3 marks short of 50% of Long works nicely), especially for putts from the Fairway.

5) Disregarding slope, assuming you split the distance to the cup into 2 parts (X for distance to Green and Y for distance from Fringe to Cup), then a good rule of thumb for strength is 2X+Y

6) It might not be a bad idea (say, you are behind in a race), to try a putt to escape from a tiny amount of Rough. In that case, Rough commands about a 16:1 ratio of resistance. Use this wisely (safe option, hit a low Approach at 1.5-2x the distance to the cup, maybe).

7) If the 50% Middle mark is too hard and the one less than it is too little (for 43-48 foot putts), go for a 25% Long instead. This comes up way too often to forgo mentioning.

If there are other things you can share and discuss about putting, I'm all ears! Especially since there are at least a dozen nasty Greens that cost a ton of time if you get stuck in the wrong areas.