I propose the following events for starters:
Marathon. How many periods in a row can you go without a bathroom break? (Edge probably goes to elementary school teachers on this one, who also get the pleasure, in many cases, of twenty-six first-graders right outside the door while it's all happening.)
100-meter dash. Oh no! You're five photocopies short for your first period class! Can you make it to the staff room and back in time? (And, when you get there, will there be a working photocopier and paper?)
Gymnastics, floor exercise. There are 37 desks in your classroom big enough to accommodate 25. How will you maneuver among all the students in order to give them each 17 seconds of your undivided attention?
Shot put. How far can you hurl the latest binder full of DOE directives? (Bonus points for style; i.e. how many and how exotic your profanities as you perform said hurl.)
Swimming. You've said many times that you'd do anything to get away from your crazy principal. Really? Anything? This 3.5 mile race in the dead-body-and-petroleum-products-lined East River will prove how serious you are, as you sprint towards the Statue of Liberty and the promise of the open water.
Gymnastics, balance beam (endurance). Can you pull off a phone call to the touchiest parent you know, couching your concerns about their darling angel's behavior and grades in both gentleness and, well, honesty?
Beach volleyball (upper DOE management only). Imagine that the ball is the blame for, say, the spectacular shortcomings of the Acuity program. How long can you volley the blame back and forth until it eventually hits someone square in the face?