The Fastbreak
Put your league on the floor and let them run it. Everybody breaks from their own baseline at the same time, and the order they get to the rim is the order they pick in. It is free, nobody needs an account, and the link you get at the end replays the same race for anyone who missed it.
Two to twenty runners, which is the same range of league sizes the rest of the site works with. Blank lines are ignored, so you can paste a list straight out of your league page.
Some leagues reward the winner of the race with the first pick and some hand it to whoever finishes last. Both are here, and the floor says which one is running.
The draw happens before the first step. The order is settled by the random number generator your browser uses for encryption, and every possible order is exactly as likely as every other. The race is then built to end in that order, which is why the replay link always finishes the same way and why nothing that happens on the floor can change the result. That includes the run itself: everybody angles in toward the basket at the end because that is what a break looks like, and the lane already lined up with the rim wins no more often than any other.
On the break
On the floor
The order
The replay link carries the names and the race itself inside the address, so nothing about your league is stored anywhere and the link keeps working for as long as this page does. Sending it to somebody shows them the same race, ending the same way.