# Equality Now! BBall Substitutions dilemmaFebruary 23, 2011 2:11 PM   Subscribe

MathStoryProblem: I coach youth bball and need help with equal playing time substitutions with a line-up that varies week to week. I think some kind of formula or counting trick should help, but my math skills are failing me. Up to 15 kids, 10 substitutions per game (25 min halves - subs every 5 min). As close to equal amount of floor time as possible (obviously, this can't always be the case).

Is there a way to make this functional? Printing a few pages of roster i can fill in when the game starts so i don't have to do subs all game instead of coaching (yelling futile encouragement)? I never know how many kids will be there until tip-off. Embarrassingly, I have very little basketball knowledge but the local Salvation Army needed some help and what the hell, right? The kids are 7 or 8 and very very aware of who gets how much playing time.
posted by ten year lurk to Grab Bag (6 answers total)

Up to 15 kids, 10 substitutions per game (25 min halves - subs every 5 min)

If I'm reading that right, that means every kid is on the court for periods of 5 minutes. So to get your target playing time, take [10 sub periods]*[5 players on the court]/[total number of kids]. Which for a full team would be 10*5/15 = 3.333... which means everyone should be in for 3 or 4 out of the 10 five minute play periods.

The easiest way to keep track of this would probably be to have the roster list with checkboxes next to each name for how many 5 minute play periods they get. There will always be 50 checkboxes total, the number each kid gets will vary based on the number of ones playing that day. Every 5 minutes, check off a box for each of the kids on the floor and make any necessary subs. At the end of the game you should have all of the boxes checked off.
posted by burnmp3s at 2:27 PM on February 23, 2011

If you're allowed 10 substitutions, you can get 5 per half. With 25 min halves you'd be subbing every 4 minutes - at the 4, 8, 12, 16, and 20 min mark. Unfortunately, the last chunk of time will be 5 minutes, unless you want to get really technical and sub every 4.16 minutes.

Are you allowed to swap more than one kid per substitution?
posted by cgg at 2:27 PM on February 23, 2011

Let's presume for a minute that you're not making pro-style distinctions of position (1,2,3,4,5), and you care only about providing equal playing time.

Before each game, divide your roster into guards and forwards. You'll always need two guards and three forwards. Swap them out like hockey lines -- e.g. every five minutes, swap out an entire "line" of three forwards for the next three, and swap out a "line" of two guards for the next two. Keep doing this throughout the game, and adjust as necessary for uneven splits.

What you're doing is ensuring not that a specific player is getting enough time, but that his entire line is. It's easier to keep track because you're dealing with groups of players, not one undifferentiated mass. And then you can mix and match (e.g. ensuring that each line of forwards includes one guy that can play center).

Your next step is to automate your offense and defense as much as possible. Just run a 2-3 zone on defense, and a motion offense ("pass and screen away"). In other words, take as much minute-to-minute thought out of the process.
posted by Cool Papa Bell at 2:27 PM on February 23, 2011

If they're 7 and 8, there's not even really much point in distinguishing between guards and forwards. Just write down everyone's name on an index card with one card per player. Shuffle. First five up are your starting five. At the first substitution, the next five are up and the starting five go to the bottom of the deck.
posted by ewiar at 2:40 PM on February 23, 2011

Here's a really simple system that would work for any number of players.

When the kids arrive, write their names down in any order. Lets say: Alf, Bert, Chris, Dan, Eddie, Frank, Greg, Henry and Izzy.

Start with Alf, Bert, Chris, Dan and Eddie on the floor. After 5 minutes, take out Alf and Bert, and put in Frank and Greg. After 5 more, take out Chris and Dan, and put in Henry and Izzy. After 5 more, take out Eddie and Frank, and put in Alf and Bert. Keep looping round like that.

The only thing the kids will notice as potentially 'unfair' about that is which kids get to start, since kids view gratification now as inherently better than gratification later. So, to solve this, just vary your ordered list each week so different kids are starting.
posted by piato at 12:11 AM on February 24, 2011