Welcome to everyone who has gotten to this site via the link in Carl Bialik's Wall Street Journal "Numbers Guy" blog! For those of you who've gotten here other than through the Numbers Guy, this is what I'm referring to.

Bialik's topic was "Jacqueline Gagne, a 46-year-old Rancho Mirage, Calif., resident, [who] has hit 10 holes in one in the last four months, over a stretch of just 75 rounds of golf." In this connection, Bialik was kind enough to mention and put a link to the Hot Hand page.

The most similar thing I've ever written about is the case of Danny Leake who, right here in my home city of Lubbock, Texas last July, made a hole-in-one on the same hole on two straight days.

Bialik's blog posting on Jacqueline Gagne has generated a huge number of comments. One issue I've seen mentioned, which I would like to discuss, revolves around the fact that the kinds of statistical formulas that have been used to estimate the probability of Ms. Gagne's feat assume independence of observations (i.e., the outcome of one shot or one round does not affect the outcome of the next).

Independence characterizes such exercises as coin-tossing and dice-rolling. Because of this independence, we can, for example, calculate the probability of rolling double-sixes with two dice as 1/6 (which is the probability of a six on one die) X 1/6 (the probability of a six on the other die) = 1/36.

Whether human athletic performances -- such as shooting rounds of golf, taking shots in basketball, or getting hits in baseball -- should be discussed analogously to coin-tossing and dice-rolling is controversial. A person can vary in his or her mood, energy levels, etc., whereas a coin or die cannot. In fact, a prominent statistician was once quoted as saying, "...the thought of comparing dice with shooting baskets is silly."

Yet, studies have shown that sequences of athletic performances often match sequences generated by random processes such as coins, dice, and spinners. Interested readers are invited to peruse a write-up I did on the fifth anniversary of the Hot Hand page, in which I offered my reflections on what research on this topic has shown. In particular, please see the section where I summarized my spinner-simulation studies of Texas Tech women's basketball players' three-point shooting.

I hope those of you for whom this is your first foray into streakiness analyses have found this introduction to be thought-provoking and will be interested in coming back!