[We'd like to thank Paul Jakus (@paulj) for this guest installment on "Reba"'s absence at Dick's – ed.]
In 2011, Dick’s Sporting Goods Park became a venue of lore almost instantaneously, a place where Phish’s Greatest Hits appear in unconventional set placements with spectacular jamming. Except, curiously, "Reba." The lack of a Dick’s "Reba" was a topic of discussion going into last year’s run, and it seemed quite unusual when, once again, it was not played. Maybe so, but then again, maybe not.
Since 2011, "Reba" has been played 33 times in 254 shows, or about once every 7.7 shows. "Reba" has taken long vacations before—a couple of double-digit gaps in 1997, and again in 1999 when she had a 25 show gap—and she’s just come off the longest gap to date: 31 shows between July 23, 2016 and July 21, 2017. Given these long gaps, is "Reba"’s absence from Dick’s really all that odd?
There are a several ways to look at this, but let’s stick with two. First, we’ve had 18 shows at Dick’s since 2011, so one could ask how likely it is to have not appeared at 18 randomly selected shows. The probability of playing "Reba" at any given show during the 2011-2017 period is 13.0%, so the probability it will not be played on a given night is fairly high, 87.0%. Assuming independence of each show (more on this later), the probability of not seeing "Reba" in 18 shows is 0.870 raised to the 18th power, or about 8.2%.
Put another way, if 100 people each attended 18 randomly selected shows since January 1, 2011, about 92 of them would have heard at least one "Reba," while 8 people would have missed it. Now, is 8.2% all that small and unusual? Some stats-minded folks would say, “No, this could just be some kind of strange, random anomaly; wait until the odds get under 5% and then get back to me.”
Another thing one might hear is that shows are not independent of one another—if Phish played "Reba" last night then we sure ain’t gonna get one tonight. That is, the probability for tonight falls to zero—it is not constant at 13% for each show. That makes me suspicious of the previous result. Instead, we’ve got to figure out how to control for dependence across shows.
As it turns out, we can take advantage of the fact that Dick’s shows are always three-night stands. Since 2011 there have been 28 three-show stands, from Bethel Woods in 2011 through Northerly Island 2017. Three-show runs are separated by both time and space, which increases the likelihood that the songs played during any given three-show run will be independent of those played during another run.
"Reba" has been played at 11 of the 28 three-night stands since 2011: this means you’d have about a 39.3% chance of hearing a "Reba" at any given three-show run. If you chose to attend six randomly selected three-night stands, the odds of not hearing a "Reba" is 0.607 raised to the 6th power, or about 5.0%. This is getting pretty darn small… to date we’ve actually had a 95% chance of having heard "Reba" at least once at Dick’s.
So it does seem to be an unusual absence, but it’s right on the edge. And if we don’t see "Reba" at Dick’s 2017 (when the odds of no "Reba" at seven three-show stands falls to 3%), well, even those stats geeks might start wondering what’s going on.
Finally, if you’re interested in an amusing "Reba" stats thread—one that dives down the rabbit hole of Bayes’ Theorem, irregular distributions, the Gambler’s Fallacy, and the importance of Trey’s “free will”—check out this one from @Capt_Tweezerpants:
TL;DR: No "Reba" at Dick’s is not statistically unreasonable… unless we don’t get one this year. Then it’s weird.
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