It's a bit belated, but I definitely want to comment on Phil Mickelson's victory in last weekend's Master's golf tournament, driven by his back-to-back eagles (making a hole in two shots below par) on Day 3. And Mickelson nearly eagled the next hole! According to an ESPN.com blog posting:

Lefty [Mickelson] became only the third player in Augusta National history to make back-to-back eagles -- and came within 6 inches of pulling off another one -- briefly stealing the lead from [Lee] Westwood with one of the most remarkable three-hole stretches Augusta has ever seen.

During Mickelson's remarkable third-round, he made the par-5 13th hole in 3 shots and the par-4 14th in 2. Aggregate statistics from this year's 13th hole, taking the third and fourth rounds combined (to restrict the sample to players who made the cut after the first two rounds), there were 6 eagles out of 96 player visits to the hole. It was the 14th that was really the stingy hole: Mickelson's Saturday eagle was the only one of the entire tournament.

Rather than try to estimate the statistical probability of Mickelson's feat, I would instead fall back on its historical rarity. The Masters tournament has been around since 1934 and, as noted above, back-to-back eagles have been achieved only three times. If one thinks of all the golfers who've participated in the tournament's 77 years and all the rounds and holes they've played, the number of opportunities for consecutive eagles would be astronomical.

In Mickelson's first Master's win (2004) of his three, he got five birdies (one under par) in the last seven holes. Although extensive research has shown a "hot hand" in golf to be elusive, Mickelson has seemed capable of one in at least some years' Masters.