How Many People Are You Who Saw All 17 MSG Shows?

“Everyone knows wookies can’t do math.” 

– Jon Fishman (almost)

Phish fans are even more rabid with their fandom than many of them are with actual rabies. In the normal world, seeing the same band 10 times is considered highly strange. In the Phish world, 100 is when you’re finally ready to celebrate your N00b Mitzvah. But in 2017, Phish put the die-hards to an unprecedented test, by playing 17 shows in a single venue in a single year.

The question is, how many fans were crazy enough to ace the test by hitting all 17 shows?

To get something approaching an answer, I ran a Twitter poll, starting Monday night and continuing through Tuesday night, asking people how many they saw.

Before I even mention the results, a disclaimer: this poll is massively unscientific. For starters, if you’re following an account that exclusively tweets statistical minutiae and dumb jokes about Phish, you are more into Phish than the average audience member. Second, it’s easy to imagine that people who saw lots of shows are more inclined to want to log their answer than those who didn’t.

As for the results: 937 responded. Of those, 5% saw all 17, 31% saw between 6 and 16, 35% saw 1-5, and 29% saw none at all. (One more note: yes, this is a decent-sized sample; but a sample as big as Mike’s scarf collection is useless if it’s not representative of the population you’re surveying. And again, this is not a representative sample. So don’t overestimate the importance of the sample size.)

Now you might think the math is easy: just take the 5% who saw all 17, divide it by the 71% who saw any at all, and multiply that by the capacity of MSG (20,789) and you’re done! Right?

Wrong. The math is a bit trickier than it looks at first glance. The reason is that 5/71 isn’t the fraction of people at a single show who saw all 17. It’s the fraction of people who went to any shows who saw all 17. At any given show, every single one of the 17ers was in the building, but only some of the 1-16ers were. So the number of 17ers is actually more than 5/71 of 20,789. To figure out what exactly that number was, we have to calculate the total number of tickets purchased, then use our poll results to find out how many of those were distributed to the 1-16ers, and how many were hogged by the 17ers.

Warning: algebra ahead.

Okay. First, let’s assume that Phish sold 20,700 tickets to each of the 17 shows. That means they sold a total of 351,900 tickets. Now, because Twitter only allows 4 options on polls, we don’t know exactly how many shows each respondent saw. Let’s assume that the average person in the 1-5 group saw 3 shows, and the average person in the 6-16 group saw 11. (Note: these estimates may be way off, and they introduce yet another source of error into our final numbers.)

Let’s put everything we know in an equation. Let x = the total number of 17ers, y = the total number of 6-16ers, and z = the total number of 1-5ers.

351,900 = 17x + 11y + 3z

Translation: 351,900 tickets were sold; this is the sum of all tickets bought by the 17ers, the 6-16ers, and the 1-5ers. The 17ers bought 17 tickets apiece; the 6-16ers bought an estimated average of 11 tickets apiece, and the 1-5ers bought an estimated average of 3 tickets apiece.

Now, we know that the number in group x is 5% of our total sample, in group y is 31%, and group z is 35%. Or in other words,

y = 6.2x

z = 7x

Substituting these into our previous equation gives us

351,900 = 17x + 11 * 6.2x + 3 * 7x

or

351,900 = 17x + 68.2x + 21x

Adding the coefficients on the right, then dividing each side by that number leaves

x = 3313.56

This would imply that 3,314 people saw all 17 shows. Substituting back in for y and z, we get 20,544 people who saw 6-16 shows, and 23,195 people who saw 1-5 shows — for a grand total of 47,053 individual fans who saw Phish at MSG in 2017.

With all of this said, imagine the biggest grain of salt you’ve ever seen. Take that grain, double it, and then dance your way over to your friend Jennifer’s gravy and throw it in, because again, this poll is not scientific. The chances are that the actual number of people who saw all 17 shows is far lower than 3,314. Likewise, the actual number of individuals who saw any shows is probably higher than 47,053 — people who saw only a single show were probably disproportionately unlikely to even see this poll. This entire exercise is simply an opportunity to get some vague, ballpark idea of how crazy we all are. And an opportunity to combine Phish and nerdiness, which go together like second jams and Mike’s.