Kevin C. Cox
Four games. Four different lineups. And I know what you were thinking. How many possible lineups can Larry drew possibly go with this season? We did the math. We're here to help.
First, you have to understand how to calculate the possible combinations given the variables, which are starting lineup spots (five) and the total amount of players in the selective pool (14).
Now, for the purpose of this exercise, we are going to lock down the roster at 14 and assume that no new players enter the season, thereby reasonably controlling this calculation.
I am also assuming no order is required, so it doesn't matter if Al Horford is playing small forward or center, just his inclusion here matters. Likewise for the guards...I am not figuring different combinations for Jeff Teague and Devin Harris with one at the point, the other at shooting guard and vice versa.
Now, let's show the formula that will help us understand how many possible lineups Larry Drew can create with his 14 players and five lineup slots.
(X, Y) = X! / Y!(X-Y)!
Y = 5
To figure for the !, you take the number (in X's case, 14) and multiply it backwards as such: (14*13*12*11*10 and so on down to 1)
So 14! = 87,178,291,200
Now 5! times (14-5)! = 120*9! or 43,545,600
87,178,291,200 divided by 43,545,600 = 2,002
This means Larry Drew can create 2,002 possible starting lineup combinations from his 14 man roster! Wooohooo! Good times! Let's get it started!
Drew would have to have a 24 year contract (playoff games excluded) as well as all the players to make this happen. Alright, well, would be fun to watch, right? Ok, maybe not.
Now the flaw in this calculation is assuming that Drew would play ANY possible combination on the floor. Sure, as much as I would love to see a starting lineup that was comprised of Al Horford, Josh Smith, Anthony Tolliver, Zaza Pachulia and Johan Petro, it's only slightly probable in happening.
So what we can do is narrow the variables down a bit and dedicate players in the three frontcourt starting slots and those for the backcourt starting slots.
Frontcourt player pool:
Backcourt player pool:
So for the frontcourt combinations, we have eight players for three slots.
8! / 3! * (8-3)!
8! = 40,320
3! = 6 and (8-3)! = 120, so 720
40,320 divided by 720 = 56
So there are 56 possible frontcourt combinations. Sweet, right?
Now the backcourt...
We have six players and two spots.
6! / 2! * (6-2)!
6! = 720
2! = 2 and (6-2)! = 24, so 48
720 divided by 48 = 15
There are 15 possible backcourt combinations here. Almost there. Stay with me.
Now, you have to take the 15 possible backcourt combinations and multiply it by the total frontcourt combinations to get the total amount of combinations possible here with our stated parameters of common sense lineups. Well, so to speak.
The 56 frontcourt combinations times the 15 backcourt combinations yield 840 possible starting lineup combinations, meaning Larry Drew, theoretically, would need 10.2439 seasons more with this roster in tact to start every possible combination. Hey, better than 24, right? At least everybody on this roster could make it up and down the floor in 10 years.
Now that we know what's possible, let's send Robby in with this information and make this happen -- what does everybody say? Fellas? Guys? Fellas?
Disclaimer: Jason Walker did graduate from the University of Florida and, therefore, is not responsible for the accuracy of his theories or his math. He watches the NBA. He is not Mr. Wizard. Carry on.