There's a formula for that.
DAVE MCGILLIVRAY, for Runner's World
How does a race director determine how many porta-potties to order for their race?
Having to “go” is arguably the most important and nerve-wracking thing any runner needs to do before the start of a race. However, many races underestimate this and truly don't spend enough time or effort determining how many porta-potties to order.
An often-used formula is a ratio of one unit per 100 runners. A better formula is one unit per 75 runners, and even better is one unit per 50 runners. Runners often have to go multiple times before the race, and this takes that into account. And, the more women in your race, the more units you may need.
Just do the math. Say you have 5,000 runners in a race and 50 porta-potties. Say each runner takes an average of two minutes in the unit. That means each unit could accommodate 30 runners an hour. Thus, 50 units multiplied by 30 runners only equals 1,500 runners per hour. So, if every runner in the race had to go, some multiple times, you can see how the one unit per 100 runners formula can send hundreds heading for the woods. One unit per 50 runners could handle 3,000 runners per hour—a much better result.
Where to place the units and how to actually manage them is also a very important part of making sure all the runners have a positive experience. If they are not all in the same place, then long lines may form at one bank of units in one location while others go unused. Additionally, if your assembly area (i.e., athletes' village) is in one location but your start line is elsewhere, you may have to almost double your original quantity of units.
Allowing one long line to form is a big mistake: It scares off runners into taking their “business” elsewhere, and it leads to an inefficient use of all the units.
Placing a strong volunteer with a bullhorn near the bank of porta-potties well before long lines form to direct runners is helpful. You can also tape a flier on the door of each unit that reads “FORM SINGLE LINE HERE,” which may help to alleviate these long lines and frustrated runners.
Instead of lining the units up in one long row, you can try separating them in say five-unit clusters, with all clusters in the same area where people can see all of them. Then, lines form in front of each cluster. If runners can only see some of the units, then they will automatically think those are the only units you have provided and thus create an uneven distribution.
The point is: You want to get maximum use out of each unit.
And, those of us who direct races also need to beware of pranksters who target porta-potties. They sometimes “lock” the units from the outside, giving the impression that a unit is occupied when it is empty, while others have been known to knock over units overnight. I even once had someone who "torched" the units, and all that was left in the early morning when I arrived at the race site was melted plastic. Yes, these things can happen! Plan accordingly.