The Tour finally has gone to statistical record-keeping that allows us to see how good … “These Guys Are Good” … really are.

Let’s take one of my intermediate benchmarks in testing… 18 footers. The Tour “make %” average from 18 feet is actually 17%, but as we modify upward all Tour averages to account for the repeated same distance (but different line) putts effect, we boost that up to 18% in our models. If we were to boost for “reading break” advantage, the number goes to approximately 21%. But for this example, we’re sticking at 18% for our benchmark probability.

Now, suppose a Tour player (who was a composite, or average of them all) hit all 18 greens, and had eighteen straight 18 footers for birdie. This would of course be a (near) impossibility, but it’s illuminative for our purposes, so imagine it happens. How many birdie putts should the Pro make?

Simply put, 18% of 18 = 3.24, so on average, the number would be… Three (and maybe Four on a good day). But, will he repeatedly make 3? Nope.

The way to estimate the “spread” of results, is simple mathematics, courtesy of a Calvinist minister turned Mathematician named Jacob Bernoulli long ago… (you can learn about it here…

If we plug the probability (0.18), and trials (18) into the formula, it yields these probabilities (rounded)…

0 makes… 3%

1 make… 11%

2 makes… 21%

3 makes… 24%

4 makes… 20%

5 makes… 12%

6 makes… 6%

7 makes… 2%

8 or more… 1%

So the probability of making 7 or more is about the same as making 0. About 3% each. But both are fairly likely, at any given round.

Oh yeah, the odds on making 17 of 18? Three in a trillion… try to make that many!

What does the above tell us? It tells us that it is not possible to find causality in a single round, for an “input” factor, like for example, changing the putter used. You need statistical data that is of significance… enough to give a level of confidence to your assertion. Just as you wouldn’t flip a coin three times, observe two heads occurances, and declare that two-thirds of all future flips would be heads with that coin.

The make values here are quite a spread… graphically, it looks like this… and on another post, I’ll show how many rounds are necessary, and why, to draw valid inference from the data.

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