To follow up on my putting stat, I had my brother-in-law in town this weekend and I revisited this calculation again (he has his doctorate in physics from Cornell and is a good person to ask these types of questions).
I told him about my earlier attempt to estimate the putting quotient based on distance, difficulty and return length. He liked the idea (statistically), but came up with a better estimation based on some simple yet elegant algorithms:
(Length of the putt) X (Difficulty factor) = weighted length (x)
Remaining Length = (y) where a made putt y=0
Difficulty factor should be somewhere in the range of 1-2. Imagine a putt so hard that is doubles the length of the putt. This is the interesting part to evaluate, but nevertheless, simple in its application to calculate.
All attempted putts that round are used for the following:
1 - (SUM(y/sqrt(x)) divided by SUM(x^2/sqrt(x)))
This gives you a value where the the closer you are to 100 the better putter you were that day. Long putts hit close to the hole count very good. Long putts actually made only count a little bit better, but not that much more.
e.g.
40 ft length putt,
1.0 difficulty (generally straight),
2 feet from the hole
= 95
40 ft length putt,
1.0 difficulty (generally straight),
10 feet from the hole
= 75
any length putt made = 100, but you get to factor in the actual length of the putt into the overall weighted score.
Do this calculation for every putt for that day and you end up with the overall value.
This gives me the ability to evaluate the actual "quotient" and this is something that would be important to me (to get to your overall first question), because if I make 28 putts one day and 30 putts another. How did I really putt? If the quotient is 87 on the 30 putt day, but 75 on the 28, I would actually say that I putted "better" on the 30 day. Even though I had more putts, it could easily had been because I had harder putts (overall longer length in combination with "harder") that I executed better (left it closer to the hole more often).
I now have the spreadsheet done, and it works perfectly...I can't wait to run it on my Blackberry the next time I play! (anyone who wants it I can forward it to you for a small fee
but I already gave you the key calculations above)