Somebody asked me for the golf putting data from Don Berry’s book, which Deb and I use as an example for nonlinear modeling in this article and our Teaching Statistics book. Here they are:
distance(feet), #tries, #successes
x n y
2 1443 1346
3 694 577
4 455 337
5 353 208
6 272 149
7 256 136
8 240 111
9 217 69
10 200 67
11 237 75
12 202 52
13 192 46
14 174 54
15 167 28
16 201 27
17 195 31
18 191 33
19 147 20
20 152 24
I’m still pretty amazed that the pros miss nearly half their 5-foot putts. I mean, sure, I’d miss it all the time, but the pros??? Phil and I discussed this and decided that 5 feet is not so close–when I was first thinking “5 foot putt,” I was really visualizing something closer to 3 feet.
Thanks for the data….
The average golfer learns to fear four-foot putts. I believe it's because anything under four feet is a 'tap', while anything above that is a stronger 'hit'.
I'm not surprised that pros make 3/4 of their four-foot putts, they should perform a lot better than the average duffer.
I don't have the numbers to back this up, but just from watching golf a lot, when Tiger Woods wins, he seems to make an awful lot of six-foot putts, which quickly puts him ahead.
Great data. Fear is definitely one of the most pressing external variables when addressing a 5 foot and under putt. It's the psychological aspect of discounting the putt as easy, as a putt that should be made, and as the focus of scrutiny from one's peers and colleagues if it is not made.
I think the estimate here underestimates the proficiency of pro-golfers since the bad golfers have more tries i.e. a bad pro fails at 10 feet so gets another try at 2 ft (say) whereas a good pro probably gets it in at 10 feet. The worse the pro the more he (she?) appears in the data, the better the pro the less he appears.
There seems to be some "steps" in the data and I was wondering if it's to do with choosing which putter to use i.e. the 5-8 ft group, 9-14 ft and 15+ ft group. Presumably, at pro level, there is some accepted wisdom about what putter to use at what distance. Perhaps the caddies object to carrying too many clubs for the between distances (e.g. 7-10ft)? :-> (I don't play golf so I don't know if that makes sense.)
I guess the other problem is the error in x is not accounted for. It doesn't seem reasonable to assume that the ball lands uniformly in the foot range since the players are actually intending to get to the hole i.e. you'd expect more balls 1.55 ft away then 2.45 feet away in the 2 foot range. If so, you ought to see it in the data (at a distance where it's not likely to be a second attempt) – more balls landing 10 feet away then landing 11 feet away, then landing 12 feet away but it's not really there :-> . Perhaps to get a ball that distance from the hole the golfers weren't aiming for the hole but the green and in that case their distance from the hole is more random.
It might not make sense to have each foot range one unit apart. Perhaps, we need little GPS units in the golf balls to get a better understanding of where golf balls land around the hole.