I’m not an athlete by any definition. I tried playing sports growing up and did not enjoy it. However, I started playing pickleball this past spring with some friends, and I was hooked after the first day. It’s very approachable for people like me (refer to the first sentence). If you’re unfamiliar with the sport, think small-scale tennis played with large paddles and a wiffle ball. It can be played singles or doubles. If you’re wondering what pickles have to do with it, many believe it was named after the creators’ dog named Pickles. But it was actually named after the rowing term “pickle boat” referring to a thrown together crew boat. The dog story is cuter.
One night I was invited to the pickleball courts at the Opelika Sportsplex to play with a group of friends I hadn’t played with before. There were a lot of us there, and we divided up and played some pickup matches. After half an hour had passed, everyone decided we needed to have a small tournament. There were ten of us to be exact, so we could make five teams of two. About five of us there were experienced, and the other five of us beginners (me in the latter squad).
Fairness was on people’s minds, so it made sense to put each beginner on a team with an experienced player. We easily could’ve decided in two seconds who was going to be on whose team. But my friends are a bit more complicated than that.
“We can’t just pick teams,” someone from the experienced side said. “Someone will be left without a choice.” He was right; if we had five captains pick among five choices, the last captain would not have a choice. This wasn’t fair.
“Ok, well how are we gonna do this?”
I’m a grad student studying mathematics. Scenarios like this come up all the time in the classroom. I was very intrigued to watch my “non-math” friends engage in mathematical reasoning without realizing it.
The problem of captains choosing teams fairly has been solved before. One team captain gets the first pick, and then the next captain gets the next pick, and so on. This works great when you have few captains picking large teams from a large group. Even though the first captain gets the advantage of first pick, there are usually plenty of players considered just as good as the first of whom the second captain gets to choose from. Is it a perfectly balanced method? Eh, maybe, maybe not. It gets the job done.
My friends noticed something important. Even though this solution works well enough for few captains choosing from many people, it breaks down when you have five captains choosing from five people. The perceived fairness fades away.
Here’s the snag we hit. While they could see this solution wasn’t going to work, the only alternative solutions they could offer were simply variations of the first.
“What if we did…”
“Well, no, that’s still not fair because…” this went on for about a minute or two as I quietly observed.
We’re creatures of habit. If something works, it’s hard for us deviate from it even when it stops working. But we’re also creatures of creativity and collaboration, and we can eventually break away.
“I have a solution,” I spoke up. “Team captains go huddle up and assign the numbers 1-5 to each captain. The rest of us five will huddle up and do the same. Then we’ll come together, reveal our numbers, and matching numbers will be teams.”
“Of course, the mathematician has the answer,” my loving friend said jokingly! Everyone was very satisfied with the solution. Why? Every alternative solution offered before this one still gave choice to some and no choice to others. With this, no one had a choice, and everyone agreed it was fair. We had teams decided in seconds and we were ready for our tournament.
Later that night, being the mathematician, I wondered if this was really the best solution. Eh, maybe, maybe not. It got the job done. I’ll leave finding a better solution to the reader because we have another problem.
How do you schedule a fair 5-team pickleball tournament?
Disclaimer: The views and opinions in this work are those of the author and do not necessarily reflect the views of Auburn University.