Has anyone bothered figuring out how many different team combinations are possible?

[Elway]

:confused: I'm sure the math and the final number would boggle everyone.

250 players, 3 tiers, 11 on each team, 3 different possible strategies for all the made up/scrub players.....

It has to be in the tens of thousands.

Anyone want to figure it out?

[Elway]

That's replay value enough for me. I was never really into the cribs thing in 2K5 and to tell you the truth I never brought a franchise past 2 full season before I started simulating before eventually getting bored with them.

[acoolperson]

:confused: I'm sure the math and the final number would boggle everyone.

250 players, 3 tiers, 11 on each team, 3 different possible strategies for all the made up/scrub players.....

It has to be in the tens of thousands.

Anyone want to figure it out?
I believe that would be 250 factorial multiplied by 3 factorial multiplied by 11 factorial multiplied by 3 factorial again...correct me if I am wrong.

[ninetyfourniner$]

It has to be in the tens of thousands.



I don't know the numbers, but I do know this. It is MORE than "tens of thousands."

Here's what I DO know. In baseball, if you have NINE players and can arrange them in any batting order, you have 9! possible arrangements. That is equal to 362 880 different combinations.

This is a FACTORIAL. A HUGE number.

Since the order is not important, lets use this formula (a different one we used for baseball):

nCr = n!/(r![n -r ]!)

I am NOT a mathematician, I am a physics major, and I have NOT studied number theory, or anything other than calculus, so hopefully I am not off on this. But I'll give it a try.

Now, if we want to be accurate, we will do this formula for gold, silver and bronze players and then add them up or combine them in the appropriate way (I'm not sure what that is right now). If we wanted to be TERRIBLY accurate, we would also break it down by position, and assume that no one will take a legend of the same position twice, but I don't have the time for that (and again, I might be off).

Lets assume there are exactly 240 legends. Let's also assume that 60 of them are gold, 80 of them are silver, and 100 of them are bronze. You can take 2 gold, 4 silver and 6 bronze. (I don't know the numbers, honestly, so that's a guess, as most of this is).

Number of possible Gold combinations:

60!/(2![60 - 2]!) = (8.32098711 × 10^81)/((2 x [2.35056133 × 10^78])}

= (8.32098711 x 10^81)/ (4.70112266 x 10^78)

= 1770

1770 different combinations of gold players.

Number of possible Silver combinations:

80!/[4!(80-4)!] = (7.1569457 × 10^118)/[24 x (1.8854947 × 10^111)]

(*my calculator won't crunch that number, so bare with me, I might be wrong)

** ha! nevermind! google calculator to the rescue!

= (7.1569457 x 10^118)/(4.52518728 × 10^112)

= 1,581,580 different possible combinations for silver if you can pick 4. if you can pick 5, that number will probably be an order of magnitude higher (or more). If you can only pick 3, it will significantly lower, I'd wager.

Number of possible Bronze combinations:

100!/[6![100-6)!] = (9.33262154 × 10^157)/ [720 x (1.08736616 × 10^146)]

= (9.33262154 × 10^157)/ (7.82903635 × 10^148)

= 1.1920524 × 10^9 different possible combinations for bronze players. Translated out of scientific notation, that is 1,192,052,400 different possible combinations, assuming you can pick 6 out of 100.

Now, this is NOT complete, because we STILL have to find out what combinations of TEAMS you can have. I don't think I can do that.

Anyway, you get a little bit of an idea. It is a HUGE number, no matter what.


DISCLAIMER: Again, I am NOT a math major and I have ONLY taken calculus courses. I have NEVER had a number theory class or any math specialty class including statistics. Therefore, I could very well be wrong. But the formula I posted is correct for calculating different possible combinations of numbers.

Also, maybe tomorrow I'll think about how to combine the three possibilities into one to determine exactly how many possible team combinations there are. From my position right now I'd say average the three numbers to get a decent guess or perhaps multiply them. GUESS being the operative word. That would probably be WAY off... but hell, I can think no more tonight. Apologies.


EDIT- I have a hunch that the correct thing to do would be to multiply the three together... IF that is right, then just for ****s and giggles, the total number of combinations would be...


3.33702744 × 10^18

In normal notation that is:

3,337,027,440,000,000,000 (EDIT- This number is incorrect because I originally thought you could pick FOUR silver players. It really should be 346,704,149,000,000,000. Notice that that number only has 18 digits, while the previous one had 19. It is a smaller number, but it is still obviously huge)




different possible combinations




*taking into account all the assumptions I made, of course. Oh, and this does NOT take into account the NON-legends players (for example, you can pick pass blocking linemen, run blocking linemen or ballanced, etc.) That would make the number even larger. Oh, and remember, I might have misunderstood when to use the formula, which would effectively turn this entire post to **** :D I am thinking of one possible way I have misunderstood this- if taking the SAME picks but in different ORDERS is counted as more combinations, then this is going to be off by a large margin. I'll research it.

EDIT-2: Rest your fears aside (if wiki is right)

According to wikipedia "When the order does not matter and each object can be chosen only once, the number of combinations is the binomial coefficient [the forumula I used]."

Therefore, my numbers for each gold, silver, or bronze are close to accurate (assuming wiki is right and I made the correct initial assumptions about how many of each you can have and how many of each are available).

Even so, I will talk with one of my professors about this.

[ninetyfourniner$]

I believe that would be 250 factorial multiplied by 3 factorial multiplied by 11 factorial multiplied by 3 factorial again...correct me if I am wrong.


Maybe, but I don't know if you can straight up use the factorial formula because the order of the players does not matter. But then again you are suggesting multiplying them together. Btw, where did you get your numbers (the 3's specifically)?

EDIT- it's good to know I'm not the only nerd here :)

[ninetyfourniner$]

Ah hell... I just realized that it's only THREE silver per team, 2 gold, and 6 bronze. Refigured (still assuming there are 60 possible gold, 80 possible silver, and 100 possible bronze- we don't have that info so this is all assumption):

Number of possible Silver combinations:

80!/[3!(80-3)!] = (7.1569457 × 10^118)/(3 x 1.45183092 × 10^113)

= 164,320 a lot smaller than before...

Ok, now, multiply 1770 possible gold combinations x 164,320 possible silver combinations x 1,192,052,400 bronze combinations.

Which = 3.46704149 × 10^17

Which is 346,704,149,000,000,000 different possible combinations.

Which is a great deal smaller than my first estimate.

* The following "problems" exist for this estimate:

1.) The ACTUALLY numbers of how many golds, silvers, and bronzes exist to choose from could possibly drastically affect the final number (when the game comes out, I will once again refigure this).

2.) There are additional choices/ options on how to design your team not factored in, for example, the different types of generic players/positions you can choose from.

3.) It doesn't take into account the FREQUENCY of different teams you will see when playing online. The fact is, not all players are equally popular. Even though there is a HUGE number of possible teams, there are certainly going to be more popular choices than others, which means certain combinations will be statistically more prevelant than others. How much? Only God knows...

[twsn88]

I don't know the numbers, but I do know this. It is MORE than "tens of thousands."

Here's what I DO know. In baseball, if you have NINE players and can arrange them in any batting order, you have 9! possible arrangements. That is equal to 362 880 different combinations.

This is a FACTORIAL. A HUGE number.

Since the order is not important, lets use this formula (a different one we used for baseball):

nCr = n!/(r![n -r ]!)

I am NOT a mathematician, I am a physics major, and I have NOT studied number theory, or anything other than calculus, so hopefully I am not off on this. But I'll give it a try.

Now, if we want to be accurate, we will do this formula for gold, silver and bronze players and then add them up or combine them in the appropriate way (I'm not sure what that is right now). If we wanted to be TERRIBLY accurate, we would also break it down by position, and assume that no one will take a legend of the same position twice, but I don't have the time for that (and again, I might be off).

Lets assume there are exactly 240 legends. Let's also assume that 60 of them are gold, 80 of them are silver, and 100 of them are bronze. You can take 2 gold, 4 silver and 6 bronze. (I don't know the numbers, honestly, so that's a guess, as most of this is).

Number of possible Gold combinations:

60!/(2![60 - 2]!) = (8.32098711 × 10^81)/((2 x [2.35056133 × 10^78])}

= (8.32098711 x 10^81)/ (4.70112266 x 10^78)

= 1770

1770 different combinations of gold players.

Number of possible Silver combinations:

80!/[4!(80-4)!] = (7.1569457 × 10^118)/[24 x (1.8854947 × 10^111)]

(*my calculator won't crunch that number, so bare with me, I might be wrong)

** ha! nevermind! google calculator to the rescue!

= (7.1569457 x 10^118)/(4.52518728 × 10^112)

= 1,581,580 different possible combinations for silver if you can pick 4. if you can pick 5, that number will probably be an order of magnitude higher (or more). If you can only pick 3, it will significantly lower, I'd wager.

Number of possible Bronze combinations:

100!/[6![100-6)!] = (9.33262154 × 10^157)/ [720 x (1.08736616 × 10^146)]

= (9.33262154 × 10^157)/ (7.82903635 × 10^148)

= 1.1920524 × 10^9 different possible combinations for bronze players. Translated out of scientific notation, that is 1,192,052,400 different possible combinations, assuming you can pick 6 out of 100.

Now, this is NOT complete, because we STILL have to find out what combinations of TEAMS you can have. I don't think I can do that.

Anyway, you get a little bit of an idea. It is a HUGE number, no matter what.


DISCLAIMER: Again, I am NOT a math major and I have ONLY taken calculus courses. I have NEVER had a number theory class or any math specialty class including statistics. Therefore, I could very well be wrong. But the formula I posted is correct for calculating different possible combinations of numbers.

Also, maybe tomorrow I'll think about how to combine the three possibilities into one to determine exactly how many possible team combinations there are. From my position right now I'd say average the three numbers to get a decent guess or perhaps multiply them. GUESS being the operative word. That would probably be WAY off... but hell, I can think no more tonight. Apologies.


EDIT- I have a hunch that the correct thing to do would be to multiply the three together... IF that is right, then just for ****s and giggles, the total number of combinations would be...


3.33702744 × 10^18

In normal notation that is:

3,337,027,440,000,000,000




different possible combinations




*taking into account all the assumptions I made, of course. Oh, and this does NOT take into account the NON-legends players (for example, you can pick pass blocking linemen, run blocking linemen or ballanced, etc.) That would make the number even larger. Oh, and remember, I might have misunderstood when to use the formula, which would effectively turn this entire post to **** :D I am thinking of one possible way I have misunderstood this- if taking the SAME picks but in different ORDERS is counted as more combinations, then this is going to be off by a large margin. I'll research it.

EDIT-2: Rest your fears aside (if wiki is right)

According to wikipedia "When the order does not matter and each object can be chosen only once, the number of combinations is the binomial coefficient [the forumula I used]."

Therefore, my numbers for each gold, silver, or bronze are close to accurate (assuming wiki is right and I made the correct initial assumptions about how many of each you can have and how many of each are available).

Even so, I will talk with one of my professors about this.


so...in lamens terms you say we can replay this game until the end of time?

[sleepyjay]

thanks a lot, you guys gave me a headache lol

[IMDVS2]

EDIT- it's good to know I'm not the only nerd here :)
Yeah, you are definitely a nerd. Do you listen to Weird Al, too?:)

Not that it's a bad thing. :cool:

[Prince_RIP4eVa]

yea, looks like someone else did it first, but it's pretty simple. Just need to understand some algebra skills like factorials...

[Prince_RIP4eVa]

hmm, i might recheck that.. that looks like a huuge number and i'm not sure if that's right... then again, I am pretty lazy and it's summer break so I may not check it also..lol..

*edit* also, we don't know the amount of gold, silver, and bronze, so it's really not calculable

[somnus93]

A LOT! and then some.

[ninetyfourniner$]

Yeah, you are definitely a nerd. Do you listen to Weird Al, too?:)

Nope. But that white and nerdy thing was pretty damn funny. I listen to Nirvana, Doom metal and anything Indie.



hmm, i might recheck that.. that looks like a huuge number and i'm not sure if that's right... then again, I am pretty lazy and it's summer break so I may not check it also..lol..

Well, the formula I used is right (if you are picking a certain amount from a larger set of numbers and order doesn't matter [i.e. Picking Joe Montana and then Jerry Rice is counted as the same as picking first Jerry Rice and then Joe Montana], then you use the formula I posted). I might have crunched the numbers wrong though (and keep in mind my FIRST number is NOT correct because I assumed the WRONG number of silvers you can choose). Also, the other thing I wasn't sure of is if you're supposed to multiply the three together.

But one things for certain: If there are 100 bronze legends, then there are AT LEAST 1,192,052,400 different combinations of teams (of course, this is ABSOLUTELY off because THAT number is how many possible combinations of BRONZE PLAYERS ALONE- iff there are 100 bronze legends to choose from), unless I did the number crunching wrong.

EDIT- here's a wiki link that shows that I did use the right formula

http://en.wikipedia.org/wiki/Combination

*edit* also, we don't know the amount of gold, silver, and bronze, so it's really not calculable

Yep. This enire thing is based on several assumptions. But no matter what, it WILL be a HUGE number.

Of course, I blame google calculator if I'm off.

[Prince_RIP4eVa]

well, I know the formula and how to do it we did this stuff in math class last year. It just seeems like a huge number and i'm too lazy to check. i'll take your word for it though

[ninetyfourniner$]

well, I know the formula and how to do it we did this stuff in math class last year. It just seeems like a huge number and i'm too lazy to check. i'll take your word for it though


So that begs the question... why on EARTH would you know this? :D

Just kidding. What's your major? Did you learn this in a statistics class? Or prehaps from an advanced algebra class?

I actually learned this one on my own. Never had this in algebra, trig, or calc, so I ASSUME it's either stats or some advanced math class ( I can't stand statistics, so needless to say I've shunned all that sort of math up until this point...)

[Prince_RIP4eVa]

So that begs the question... why on EARTH would you know this? :D

Just kidding. What's your major? Did you learn this in a statistics class? Or prehaps from an advanced algebra class?

I actually learned this one on my own. Never had this in algebra, trig, or calc, so I ASUME it's either stats or some advanced math class.

Actually, I was in 10th grade last year... i'm just really good at math so was in an honors advanced algebra class..