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## #1 2020-02-28 14:57:57

UCanCallMeMitch
Member
Registered: 2020-02-28
Posts: 24

### Combinations For Fantasy Football Roster

First, I am person with limited math skills and the concept of permutations and combinations is basically beyond my reach.  With this in mind, I hope someone can assist me with the following.

I`m struggling with the number of combinations (no repetition) that a fantasy football roster can have with the following minimum / maximum positions and a cap of 14 players for the total roster.

QB:  Min = 1; Max = 2
RB:  Min = 3; Max = 6
WR: Min = 3; Max = 6
TE:  Min = 1; Max = 2
PK:  Min = 1; Max = 2
TM:  Min = 1; Max = 2

For instance one valid roster would be: 1QB, 4RBs, 4WRs, 2TEs, 1PK, 1TE & 1TM (a total of 14).

Another would be: 2QBs, 3RBs, 3WRs, 2TEs, 2PKs & 2TMs. (again, totaling 14)

How many different combinations (without repetition) would there be?  And can I get list of these combinations?

A position cannot have 0 players.

Any guidance would be greatly appreciated.

Thanks - Mitch

"The more you explain it, the more I don't understand it."
-- Mark Twain

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## #2 2020-02-28 21:54:29

Bob
Registered: 2010-06-20
Posts: 8,930

### Re: Combinations For Fantasy Football Roster

hi Mitch,

Welcome to the forum.

As you have got to have at least one of each and three for some positions that means that ten players are compulsory:

QR  RB  RB  RB  WR  WR  WR  TE  PK  TM

So that leaves a list of the remaining ten:

QR  RB  RB  RB  WR  WR  WR  TE  PK  TM

It's actually the same list but I got it by subtracting the first list from the maximum list.  It's just a coincidence that it came out the same.

You can choose any from this second list without restriction so the answer is found by considering how many ways you can chose any four from this list.

I need to examine each possibility separately.

(1) Suppose I choose QR TE  PK  TM.  There are no repeated positions so there's just 1 way of picking this.

(2) Suppose I choose QR  RB  and 2 from {TE  PK  TM}.  There are 3 ways I can make that choice.

(3)    QR  WR  and 2 from {TE  PK  TM} is similar … 3 ways

(4) Suppose I choose QR  RB  RB  and 1 from {TE  PK  TM}  There are 3 ways of picking this.

(5) Similarly QR  RB   WR  and 1 from {TE  PK  TM} … 3 ways

(6) Similarly QR  WR  WR  and 1 from {TE  PK  TM} … 3 ways

(7) {QR RB RB RB} and {QR WR WR WR} each have one way.

That covers all the ways that have QR as a choice

So now repeat (2) to (7) with TE instead of QR at the start and don't include QR later in the list.

(8) TE RB and 1 from {PK TM} …. 2 ways

(9) TE WR and 1 from {PK TM} … 2 ways

(10) TE RB RB and 1 from {PK TM} … 2 ways

(11) TE RB WR and 1 from {PK TM} … 2 ways

(12) TE WR WR and 1 from {PK TM} … 2 ways

(13) TE RB RB RB  … 1 way

(14) TE WR WR WR … 1 way

(15) {PK RB RB  WR}  {PK RB WR WR} {PK RB RB RB} {PK RB RB RB} {PK WR WR WR} each have 1 way so that's 5 ways altogether.

(16) Starting with TM:

{TM RB RB  WR}  {TM RB WR WR} {TM RB RB RB} {TM RB RB RB} {TM WR WR WR} each have 1 way so that's 5 ways altogether.

Then ways that have none from QR   TE  PK  TM

(16) {RB RB RB WR} {RB RB WR WR} {RB WR WR WR} 3 ways altogether.

I think that's everything and I seem to have written out all the possibilities in doing this.

I'll post this then have a break, then check that I haven't left out any ways or counted any more than once.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

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## #3 2020-02-28 23:29:30

Bob
Registered: 2010-06-20
Posts: 8,930

### Re: Combinations For Fantasy Football Roster

I think this is a complete list of the 4 where you have a choice:

QR  TE  PK  TM
QR  RB  TE  PK
QR  RB  TE TM
QR  RB  PK TM
QR WR TE  PK
QR WR  TE TM
QR WR  PK  TM
QR  RB  RB  TE
QR  RB  RB  PK
QR  RB  RB TM
QR WR  WR  TE
QR  WR  WR   PK
QR WR WR TM
QR RB  WR  TE
QR  RB  WR  PK
QR RB  WR  TM
QR  RB  RB  RB
QR  WR  WR  WR
TE  RB  PK  TM
TE  WR PK  TM
TE RB  RB    PK
TE  RB  RB   TM
TE  WR  WR  PK
TE  WR  WR  TM
TE  RB  WR   PK
TE  RB  WR  TM
TE  RB  RB  RB
TE  WR  WR  WR
PK  RB  RB  TM
PK  WR  WR TM
PK  RB   WR  TM
TM  RB  RB  RB
TM RB  RB  WR
TM  RB  WR  WR
TM  WR  WR  WR
RB  RB  RB  WR
RB  RB  WR  WR
RB WR  WR  WR

I make that 38 choices.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

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## #4 2020-02-29 02:40:34

UCanCallMeMitch
Member
Registered: 2020-02-28
Posts: 24

### Re: Combinations For Fantasy Football Roster

Thanks Bob,

I was surprised that you calculated the combinations manually.  I was expecting a formula.

I was doing something similar, but your way makes more sense.

I've taken your list of 38 and put it in an Excel Spreadsheet.  Take a look.

Again, thanks,

-- Mitch

Last edited by UCanCallMeMitch (2020-03-01 12:00:19)

"The more you explain it, the more I don't understand it."
-- Mark Twain

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## #5 2020-03-01 01:44:51

Bob
Registered: 2010-06-20
Posts: 8,930

### Re: Combinations For Fantasy Football Roster

hi Mitch,

I did start by using combination techniques but the explanation was getting increasingly complicated because of the repeated elements.  Also in your first post you say these are beyond your reach so that would have made the explanations even longer.  I realised that there aren't very many possibilities and so a systematic 'number crunching' technique seemed to be appropriate.  It also fits my style; at school I could never be bothered to learn a load of formulas; preferring to work out what I needed from basic principles each time.  My exam papers were full of margin scribbles as I derived what I needed.  But, when asked to prove something, like the quadratic formula,  I was totally at home as that's what I did all the time.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

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## #6 2020-03-02 00:35:09

UCanCallMeMitch
Member
Registered: 2020-02-28
Posts: 24

### Re: Combinations For Fantasy Football Roster

Alrighty then, can we take this to the next level?

We now know that there are 38 combinations based on the roster limitations of:

QB:  Min = 1; Max = 2
RB:  Min = 3; Max = 6
WR: Min = 3; Max = 6
TE:  Min = 1; Max = 2
PK:  Min = 1; Max = 2
TM:  Min = 1; Max = 2

The starters' configurations for a fantasy lineup is:

QB:  Min = 1; Max 1
RB:  Min =2; Max = 4
WR:  Min =2; Max = 4
TE:  Min =1; Max = 2
PK:  Min =1; Max = 1
TM:  Min =1; Max = 1

Can't start 0 at any position.

What would be the number of total individual starter player combinations for each roster combo?  I know that the there are only 6 5 starter configurations possible as listed below:

1 QB, 2 RBs, 2 WRs, 3 TEs, 1 PK, 1 TM
1 QB, 2 RBs, 3 WRs, 2 TEs, 1 PK, 1 TM
1 QB, 2 RBs, 4 WRs, 1 TE, 1 PK, 1 TM
1 QB, 3 RBs, 3 WRs, 1 TE, 1 PK, 1 TM
1 QB, 3 RBs, 2 WRs, 2 TEs, 1 PK, 1 TM
1 QB, 4 RBs, 2 WRs, 1 TE, 1 PK, 1 TM

For instance - some of the combinations for a different individual player starter configuration based on the roster makeup of:

QB = 2, RB = 6, WR = 3, TE = 1, PK = 1, TM = 1

Would be (Exchanged Player Red for Player Blue):

QB1
RB1, RB2, RB3, RB4
WR1, WR2
TE1
PK1
TM1

or

QB2
RB1, RB2, RB3, RB4
WR1, WR2
TE1
PK1
TM1

or

QB1
RB1, RB2, RB3, RB4
WR1, WR2
TE1
PK1
TM1

or

QB2
RB1, RB2, RB3, RB5
WR1, WR2
TE1
PK1
TM1

and more . . .

The question - how many total different individual player combinations will there be for all the roster configurations with the starter limitations in place?  I'm thinking hundreds at least, possibly in the thousands?

Make sense?

Last edited by UCanCallMeMitch (2020-03-21 21:27:52)

"The more you explain it, the more I don't understand it."
-- Mark Twain

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## #7 2020-03-08 20:41:46

UCanCallMeMitch
Member
Registered: 2020-02-28
Posts: 24

### Re: Combinations For Fantasy Football Roster

???

"The more you explain it, the more I don't understand it."
-- Mark Twain

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## #8 2020-03-09 03:06:06

Bob
Registered: 2010-06-20
Posts: 8,930

### Re: Combinations For Fantasy Football Roster

hi Mitch,

I thought I'd try to produce a general method and set it aside for a long think.  Hhmm! Maybe too long; sorry.

I don't play the fantasy game so I'm not up with the rules.  You said 14 players but your second example :

QB:  Min = 1; Max 1
RB:  Min =2; Max = 4
WR:  Min =2; Max = 4
TE:  Min =1; Max = 2
PK:  Min =1; Max = 1
TM:  Min =1; Max = 1

Has a maximum of 13.  I tried looking up the rules, but that didn't help as I found one site that said 16 players and another that said 15.

So we need to clear that up first.  What is your team size please?

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

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## #9 2020-03-10 05:13:49

UCanCallMeMitch
Member
Registered: 2020-02-28
Posts: 24

### Re: Combinations For Fantasy Football Roster

Roster is made up of the following (38 Combinations - Post #3):

QB:  Min = 1; Max = 2
RB:  Min = 3; Max = 6
WR: Min = 3; Max = 6
TE:  Min = 1; Max = 2
PK:  Min = 1; Max = 2
TM:  Min = 1; Max = 2

From the one of the configurations an owner would start a combination of 10 player consisting of:

QB - 1
RB - 2 (Max of 4)
WR - 2 (Max of 4)
TE - 1 (Max of 2)
PK -1
TM - 1
Flex Players - 2 (Either RBs, WRs, or TEs); there are six five combinations:  [ Because of the lineup limitations only 2 TEs can be started ]

1 QB, 2 RBs, 2 WRs, 3 TEs, 1 PK, 1 TM
1 QB, 2 RBs, 3 WRs, 2 TEs, 1 PK, 1 TM
1 QB, 2 RBs, 4 WRs, 1 TE, 1 PK, 1 TM
1 QB, 3 RBs, 2 WRs, 2 TEs, 1 PK, 1 TM
1 QB, 3 RBs, 3 WRs, 1, TE, 1 PK, 1 TM
1 QB, 4 RBs, 2 WRs, 1 TE, 1 PK, 1 TM

Which brings me back to the question "How many total different individual player combinations will there be for all the roster configurations with the starter limitations in place?  I'm thinking hundreds at least, possibly in the thousands?

For instance - some of the combinations for a different individual player starter configuration based on the roster makeup of: (Post #6)

QB = 2, RB = 6, WR = 3, TE = 1, PK = 1, TM = 1

For instance - some of the combinations for a different individual player starter configuration based on the roster makeup of:

QB = 2, RB = 6, WR = 3, TE = 1, PK = 1, TM = 1

Would be (Exchanged Player Red for Player Blue):

QB1
RB1, RB2, RB3, RB4
WR1, WR2
TE1
PK1
TM1

or

QB2
RB1, RB2, RB3, RB4
WR1, WR2
TE1
PK1
TM1

or

QB1
RB1, RB2, RB3, RB4
WR1, WR2
TE1
PK1
TM1

or

QB2
RB1, RB2, RB3, RB5
WR1, WR2
TE1
PK1
TM1

and more . . .

Make more sense Bob?

Thanks for your interest - Mitch

Follow-Up:  I'm thinking that to calculate the number of total combinations of Rosters vs. Lineups one would do what you did to calculate the number of Roster combinations, but do it for each of the different Roster configurations. But, what do I know?

Last edited by UCanCallMeMitch (2020-03-21 22:06:50)

"The more you explain it, the more I don't understand it."
-- Mark Twain

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## #10 2020-03-11 01:37:09

UCanCallMeMitch
Member
Registered: 2020-02-28
Posts: 24

### Re: Combinations For Fantasy Football Roster

Me again.

I'm not sure I can use your combinations calculator at https://www.mathsisfun.com/combinatorics/combinations-permutations-calculator.html to compute the number of lineup combinations for each of the roster configuration.

If so, what / how what are the parameters I would use so using the "rules" of has and / or no?

I tried the following:

Combinations without repetition (n=14, r=10)
Using Items: QB1,QB2,RB1,RB2,RB3,RB4,RB5,RB6,WR1,WR2,WR3,TE1,PK1,TM1
Using Rule: has 1 of: QB1,QB2

And I get two QBs when only one QB is allowed in a lineup. i.e,

{QB1,QB2,RB1,RB2,RB3,RB4,RB5,RB6,WR1,WR2}  --> (you will notice that there isn't a PK or TM in the lineup either)

Inquiring minds want to know.

"The more you explain it, the more I don't understand it."
-- Mark Twain

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## #11 2020-03-11 21:32:45

Bob
Registered: 2010-06-20
Posts: 8,930

### Re: Combinations For Fantasy Football Roster

hi Mitch,

Those pages were made by MIF himself, not me.  I haven't tried that utility before.  Try using the 'no' rule … maybe in combination with the 'has' rule.

I have been trying to come up with a formula but it eludes me.  Too many variables to pin something down.  So I thought I'd write a computer program.  Barely started when I got your latest post so it looks like MIF has beaten me to it.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

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## #12 2020-03-14 23:48:30

Bob
Registered: 2010-06-20
Posts: 8,930

### Re: Combinations For Fantasy Football Roster

Progress report.

The 'glitch' you describe above is because it allocates one compulsory element and then makes up the rest from the remainder.  This means that the alternative compulsory element now gets a chance to show too.  Maybe the 'no' rules will stop this.

I've been working on a computer program to generate all the possibilities.  To use it I first need the compulsory positions to be assigned so there is only a smaller set to choose between.  First it finds them all regardless of repeats then it makes a new list with the repeats left out.

Having tested it with some simple cases I thought I would go back to post 1 and re-work it using the program.  Whoops! The program found 46 cases not the 38 I had claimed.  I put the two lists side by side and checked carefully.  Definitely no repeats from my program and all possibilities are 'legit' so it looks like I was very careless back at the start.  Humble apologies.  But I refer you to the third line of my signature

Anyway here they are:

1.  QR  RB  RB  RB             2. QR  RB  RB  WR extra
3.  QR  RB  RB  TE             4. QR  RB  RB  PK
5.  QR  RB  RB  TM             6. QR  RB  RB  WR extra
7.  QR  RB  WR  TE             8. QR  RB  WR  PK
9.  QR  RB  WR  TM           10. QR  RB  TE  PK
11. QR  RB  TE  TM            12. QR  RB  PK  TM
13. QR  WR  WR  WR         14. QR  WR  WR  TE
15. QR  WR  WR  PK          16. QR  WR  WR  TM
17. QR  WR  TE  PK           18. QR  WR  TE  TM
19. QR  WR  PK  TM           20. QR  TE  PK  TM
21. RB  RB  RB  WR           22. RB  RB  RB  TE
23. RB  RB  RB  PK extra    24. RB  RB  RB  TM
25. RB  RB  WR  WR           26. RB  RB  WR  TE extra
27. RB  RB  WR  PK extra    28. RB  RB  WR  TM
29. RB  RB  TE  PK             30. RB  RB  TE  TM
31. RB  RB  PK  TM             32. RB  WR  WR  WR
33. RB  WR  WR  TE extra    34. RB  WR  WR  PK extra
35. RB  WR  WR  TM            36. RB  WR  TE  PK
37. RB  WR  TE  TM             38. RB  WR  PK  TM
39. RB  TE  PK  TM              40. WR  WR  WR  TE
41. WR  WR  WR  PK extra    42. WR  WR  WR  TM
43. WR  WR  TE  PK             44. WR  WR  TE  TM
45. WR  WR  PK  TM             46. WR  TE  PK  TM

If you want me to put another set up through the program I need the possible positions as a single string like this:

QRRBRBRBWRWRWRTEPKTM

It is essential that repeats are put together.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

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## #13 2020-03-15 21:44:39

UCanCallMeMitch
Member
Registered: 2020-02-28
Posts: 24

### Re: Combinations For Fantasy Football Roster

Yo Bob,

Thanks for your continued interest in my problem.

Now pull up a chair, take a deep breath, light up a cigarette, because what follows is quite lengthy.

++++++++++

Here's what I've been up to:

I've been manipulating the MIF combinations calculator to see if I could come up with a total for all the player lineup possibilities for each of the roster configurations - now at 46 with your last update.

Example 1 - Using the 14-man/position Roster Configuration of: 2 QB, 5 RBs, 3 WRs, 2 TEs, 1 PK, 1 TM

First, I calculated the number of different non-repetitive combinations when using qb1,qb2,te1,te2 which is 4.  [qb1,te1; qb1,te2; qb2,te1; qb2, te2)

Second, I then set up the MIF combinations calculator with the following:

Combinations without repetition (n=12, r=10)
Using Items: qb1,rb1,rb2,rb3,rb4,rb5,wr1,wr2,wr3,te1,pk1,tm1
Using Rule: has 2 of: rb1,rb2,rb3,rb4,rb5
Using Rule: has 2 of: wr1,wr2,wr3
Using Rule: has 1 of: qb1
Using Rule: has 1 of: pk1
Using Rule: has 1 of: tm1

And came up with the below 33 combinations:

List has 33 entries.
qb1,rb1,rb2,rb3,rb4,rb5,wr1,wr2,pk1,tm1
qb1,rb1,rb2,rb3,rb4,rb5,wr1,wr3,pk1,tm1
qb1,rb1,rb2,rb3,rb4,rb5,wr2,wr3,pk1,tm1
qb1,rb1,rb2,rb3,rb4,wr1,wr2,wr3,pk1,tm1
qb1,rb1,rb2,rb3,rb4,wr1,wr2,te1,pk1,tm1
qb1,rb1,rb2,rb3,rb4,wr1,wr3,te1,pk1,tm1
qb1,rb1,rb2,rb3,rb4,wr2,wr3,te1,pk1,tm1
qb1,rb1,rb2,rb3,rb5,wr1,wr2,wr3,pk1,tm1
qb1,rb1,rb2,rb3,rb5,wr1,wr2,te1,pk1,tm1
qb1,rb1,rb2,rb3,rb5,wr1,wr3,te1,pk1,tm1
qb1,rb1,rb2,rb3,rb5,wr2,wr3,te1,pk1,tm1
qb1,rb1,rb2,rb3,wr1,wr2,wr3,te1,pk1,tm1
qb1,rb1,rb2,rb4,rb5,wr1,wr2,wr3,pk1,tm1
qb1,rb1,rb2,rb4,rb5,wr1,wr2,te1,pk1,tm1
qb1,rb1,rb2,rb4,rb5,wr1,wr3,te1,pk1,tm1
qb1,rb1,rb2,rb4,rb5,wr2,wr3,te1,pk1,tm1
qb1,rb1,rb2,rb4,wr1,wr2,wr3,te1,pk1,tm1
qb1,rb1,rb2,rb5,wr1,wr2,wr3,te1,pk1,tm1
qb1,rb1,rb3,rb4,rb5,wr1,wr2,wr3,pk1,tm1
qb1,rb1,rb3,rb4,rb5,wr1,wr2,te1,pk1,tm1
qb1,rb1,rb3,rb4,rb5,wr1,wr3,te1,pk1,tm1
qb1,rb1,rb3,rb4,rb5,wr2,wr3,te1,pk1,tm1
qb1,rb1,rb3,rb4,wr1,wr2,wr3,te1,pk1,tm1
qb1,rb1,rb3,rb5,wr1,wr2,wr3,te1,pk1,tm1
qb1,rb1,rb4,rb5,wr1,wr2,wr3,te1,pk1,tm1
qb1,rb2,rb3,rb4,rb5,wr1,wr2,wr3,pk1,tm1
qb1,rb2,rb3,rb4,rb5,wr1,wr2,te1,pk1,tm1
qb1,rb2,rb3,rb4,rb5,wr1,wr3,te1,pk1,tm1
qb1,rb2,rb3,rb4,rb5,wr2,wr3,te1,pk1,tm1
qb1,rb2,rb3,rb4,wr1,wr2,wr3,te1,pk1,tm1
qb1,rb2,rb3,rb5,wr1,wr2,wr3,te1,pk1,tm1
qb1,rb2,rb4,rb5,wr1,wr2,wr3,te1,pk1,tm1
qb1,rb3,rb4,rb5,wr1,wr2,wr3,te1,pk1,tm1

Third, I multiplied the number of different combinations by 4 to come up with a grand total of 132 combinations (33 x 4)

++++++++++

Here's another example:

Example 2 - using the 14 man/position Roster Configuration of 2 QBs, 4 RBs, 3 WRs, 2 TEs, 2 PKs, 1 TM.

First, I calculated the number of different non-repetitive combinations when using qb1,qb2,te1,te2,pk1,pk2 which is 8. [ qb1,te1,pk1; qb1,te1,pk2; qb1,te2,pk1; qb1,te2,pk2; qb2,te1,pk1; qb2,te1,pk2; qb2,te2,pk1; qb2,te2,pk2 ]

Second, I then set up the MIF combinations calculator with the following:

Combinations without repetition (n=11, r=10)
Using Items: qb1,rb1,rb2,rb3,rb4,wr1,wr2,wr3,te1,pk1,tm1
Using Rule: has 1 of: qb1
Using Rule: has 2 of: rb1,rb2,rb3,rb4
Using Rule: has 2 of: wr1,wr2,wr3
Using Rule: has 1 of: te1
Using Rule: has 1 of: pk1
Using Rule: has 1 of: tm1

And came up with the following 7 combinations:

List has 7 entries.
qb1,rb1,rb2,rb3,rb4,wr1,wr2,te1,pk1,tm1
qb1,rb1,rb2,rb3,rb4,wr1,wr3,te1,pk1,tm1
qb1,rb1,rb2,rb3,rb4,wr2,wr3,te1,pk1,tm1
qb1,rb1,rb2,rb3,wr1,wr2,wr3,te1,pk1,tm1
qb1,rb1,rb2,rb4,wr1,wr2,wr3,te1,pk1,tm1
qb1,rb1,rb3,rb4,wr1,wr2,wr3,te1,pk1,tm1
qb1,rb2,rb3,rb4,wr1,wr2,wr3,te1,pk1,tm1

Third, I multiplied the number of the above different combinations to come up with a grand total of 56 combinations (7 x 8).

++++++++++

Notes:  The MIF calculator logic in its formula limits the number of 'has" and "no" rules to two or more.  It would have been a lot easier if it has a rule that required at 1 of 2 or more items.  i.e, 'must have, 1,qb1,qb2' Make sense?

I'm not sure your program is capable of the calculating above combinations without the additional steps that are involved with MIF's, but if it is, maybe, if you have the time and inclination, could you check my calculations to see if I'm on the right track / did it correctly?

Again thanks for all your input.

--Mitch

Last edited by UCanCallMeMitch (2020-03-15 23:09:14)

"The more you explain it, the more I don't understand it."
-- Mark Twain

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## #14 2020-03-16 01:33:50

UCanCallMeMitch
Member
Registered: 2020-02-28
Posts: 24

### Re: Combinations For Fantasy Football Roster

UPDATE:  I finished my calculations and came-up with 5,226 lineup combinations for all the roster combinations.

Here's the Spreadsheet I put together.

Tell me if I'm right or wrong.

"The more you explain it, the more I don't understand it."
-- Mark Twain

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## #15 2020-03-16 04:33:22

Bob
Registered: 2010-06-20
Posts: 8,930

### Re: Combinations For Fantasy Football Roster

hi Mitch,

Since post 6 I have to admit I've been confused and it seems to me you are no longer doing what you did in post 1.  Let's explain why I'm confused.

Firstly, I'm from the UK.  It looks like you are talking about what we call American football to distinguish it from what we call football, ie soccer.

So all those positions mean nothing to me.

But we do have a game here called football manager.  You make up a fantasy team from real players and score points each week depending how well your players do in the real matches.  I'm guessing your fantasy game is similar.  But problem two: I've never played football manager and only have a vague idea of the rules.

I looked up fantasy football using google and found that teams can consist of 15  or 16 players as well depending on the game site.  And some have 'bench' players which further confuses me. (third confusion)

So please can you treat me like a complete beginner and start with an outline of the rules and then what you are trying to compute.

Fourth confusion: it's very easy to confuse me anyway.

Thanks,

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

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## #16 2020-03-16 22:31:02

UCanCallMeMitch
Member
Registered: 2020-02-28
Posts: 24

### Re: Combinations For Fantasy Football Roster

NP.  Lets see if I can explain.

At its core fantasy football is a math-based game based on the real-life production of NFL players. Each week you fill out a lineup by "starting" players at the various positions from a Roster that is picked / drafted according to the league settings. The statistics your starting players accumulate on the field (yards, touchdowns, etc.) contribute to their point total for the week. The point totals of all of the players in your starting lineup are tallied into your weekly score, and if you have a higher total than your opponent (another member of your league) you win that week! Players who you do not start are considered on your "bench." They'll still score points like everyone else, but those points will not be counted toward your weekly total.

A Roster is made up of players made up of different positions - QuarterBacks (QB), RunningBacks (RB), WideReceivers (WR), TightEnds (TE), PlaceKickers (PK) and Defense/Special Teams (TM).

In the scenarios we have been working with the Roster is comprised of:

QBs - 1 to 2
RBs - 3 to 6
WRs - 3 to 6
TEs - 2 to 4
PKs - 1 to 2
TMs - 1 to 2

At no time can a Roster have less than the minimum or maximum at any one position, nor can the Roster have less than 10 players or more than 14 players.

You came up with 46 different Roster combinations using the above settings - Posts #3 & #11

From this Roster of 14 Players an 'Owner/Manager' will choose which 10 players to start each week from the Roster and in this particular league they consist of:

1 QB
2 RBs
2 WRs
1 TE
1 PK
1 TM
2 Flex Players (either RBs, WRs or a TE).

Those players that aren't started are called the bench players.

In my posts #13 & #14 I stated that I calculated the starting lineup combination/possibilities for several of the Roster configurations using MIF Calculator and the spreadsheet shows the final tally of the total number of starting lineup combinations for each of the 46 Roster Combos.

There's a lot of other rules/nuances when playing in a fantasy football league, but for the time-being our focus is on how many different combinations of "Starters/Lineups" for each Roster Combination there can be and what is the grand total of the number individual combinations? But if you want to learn more, go ahead and do a Google search for "A Beginner's Guide To Fantasy Football" and in my particular case, you can read the Rules For The Invitational

-- Mitch

Last edited by UCanCallMeMitch (2020-03-16 23:29:32)

"The more you explain it, the more I don't understand it."
-- Mark Twain

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## #17 2020-03-17 02:12:42

Bob
Registered: 2010-06-20
Posts: 8,930

### Re: Combinations For Fantasy Football Roster

hi Mitch

That's great!  I think I've got a handle on it now.  I'll try to summarise as a test.

You have 14 gamers and each one creates a roster of 14 'actual' players from the National league.  Each player has a 'position, QB etc. and you have to make sure your roster conforms to a set of minimum and maximum of each position type.  Using those rules  we think there are 46 roster configurations.  I notice the website also says 46.  Is that someone else's calculation or have you put that figure up ie. are you the commissioner?

Each week, before any real matches are played, a gamer must choose 10 players for that week's play.  Using the actual match stats a gamer's team scores points.  A team 'plays' against another from the league and the one with the highest points score 'wins' that week.  The next week another team of 10 and another opponent.

As you have chosen your 14 players and you know their positions you must pick your team from the roster; but, the team you field must have positions according to the lineup rule.  So, and now we come to the 'nub' of the problem, you want to know how many different configurations there are once you've got a roster of 14.  ie. how many configurations of 10 players will there be?

The program I've tried to create at the moment will allow any number of pre-roster positions and I have chosen to select 4 actual positions from that because in your first example 10 positions were compulsory so only 4 were left for choice.  Although it was 4 from the remaining 10, by luck the input at the start can be anything (over 4 of course).

So, if you have a chosen roster and you then want 10 from this, the easy way would be to choose which 4 to leave out and then subtract these from the 14, to leave the 10 you actually want.

If that's all correct, please specify a roster and I'll run it through the program and post back the results.

If not, please tell me where I'm going wrong and I'll have another go.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

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## #18 2020-03-17 08:01:56

UCanCallMeMitch
Member
Registered: 2020-02-28
Posts: 24

### Re: Combinations For Fantasy Football Roster

By golly I think you got it!

Yes, I'm the Commissioner and I inserted the number of Roster combinations in the rules.

Try this 14-man roster configuration to see how many different 10-man lineups you come up with based on the position minimums/maximums.  Lets see if you come up with the same number as I show for Config #38 in the spreadsheet.

QBQBRBRBRBWRWRWRWRTETEPKPKTM

--Mitch

"The more you explain it, the more I don't understand it."
-- Mark Twain

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## #19 2020-03-17 21:39:05

Bob
Registered: 2010-06-20
Posts: 8,930

### Re: Combinations For Fantasy Football Roster

hi Mitch,

Tried that and got 86.  Not sure if that's right.  At the moment my program shows which are NOT included so I've got to reverse that which will require an additional procedure.  Hope to get that later today and then I'll post them.  I cannot find that roster and number in your sheet.  Should I be looking at line 42 of the sheet?  That says 56.  There may be a bug in my program … I quickly adapted it this morning.  My brain works best in the evening so I might realise later why 86 isn't right.

If the 14 players are distinguished by referring to them as QB1 QB2 etc then there are 1001 combinations (14x13x12x11)/(4x3x2x1) and the program finds them all so that part is working ok.

More later.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

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## #20 2020-03-17 23:15:03

UCanCallMeMitch
Member
Registered: 2020-02-28
Posts: 24

### Re: Combinations For Fantasy Football Roster

The Configuration For Testing Location In The Spreadsheet:

Line #42
Configuration #38
Combo Group E04
Total Number of Combos - 56

I believe the 1001 combinations are all the possible combinations without any parameters.

We'll get there.

--Mitch

Last edited by UCanCallMeMitch (2020-03-17 23:15:47)

"The more you explain it, the more I don't understand it."
-- Mark Twain

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## #21 2020-03-18 21:56:53

Bob
Registered: 2010-06-20
Posts: 8,930

### Re: Combinations For Fantasy Football Roster

hi Mitch,

Program complete but had difficulty getting it past the Windows 10 operating system so as to get a text file.  Found a way this morning but still cannot get a numbered list.

RBWRWRWRWRTETEPKPKTM
RBRBWRWRWRTETEPKPKTM
RBRBWRWRWRWRTEPKPKTM
RBRBWRWRWRWRTETEPKTM
RBRBWRWRWRWRTETEPKPK
RBRBRBWRWRTETEPKPKTM
RBRBRBWRWRWRTEPKPKTM
RBRBRBWRWRWRTETEPKTM
RBRBRBWRWRWRTETEPKPK
RBRBRBWRWRWRWRPKPKTM
RBRBRBWRWRWRWRTEPKTM
RBRBRBWRWRWRWRTEPKPK
RBRBRBWRWRWRWRTETETM
RBRBRBWRWRWRWRTETEPK
QBWRWRWRWRTETEPKPKTM
QBRBWRWRWRTETEPKPKTM
QBRBWRWRWRWRTEPKPKTM
QBRBWRWRWRWRTETEPKTM
QBRBWRWRWRWRTETEPKPK
QBRBRBWRWRTETEPKPKTM
QBRBRBWRWRWRTEPKPKTM
QBRBRBWRWRWRTETEPKTM
QBRBRBWRWRWRTETEPKPK
QBRBRBWRWRWRWRPKPKTM
QBRBRBWRWRWRWRTEPKTM
QBRBRBWRWRWRWRTEPKPK
QBRBRBWRWRWRWRTETETM
QBRBRBWRWRWRWRTETEPK
QBRBRBRBWRTETEPKPKTM
QBRBRBRBWRWRTEPKPKTM
QBRBRBRBWRWRTETEPKTM
QBRBRBRBWRWRTETEPKPK
QBRBRBRBWRWRWRPKPKTM
QBRBRBRBWRWRWRTEPKTM
QBRBRBRBWRWRWRTEPKPK
QBRBRBRBWRWRWRTETETM
QBRBRBRBWRWRWRTETEPK
QBRBRBRBWRWRWRWRPKTM
QBRBRBRBWRWRWRWRPKPK
QBRBRBRBWRWRWRWRTETM
QBRBRBRBWRWRWRWRTEPK
QBRBRBRBWRWRWRWRTETE
QBQBWRWRWRTETEPKPKTM
QBQBWRWRWRWRTEPKPKTM
QBQBWRWRWRWRTETEPKTM
QBQBWRWRWRWRTETEPKPK
QBQBRBWRWRTETEPKPKTM
QBQBRBWRWRWRTEPKPKTM
QBQBRBWRWRWRTETEPKTM
QBQBRBWRWRWRTETEPKPK
QBQBRBWRWRWRWRPKPKTM
QBQBRBWRWRWRWRTEPKTM
QBQBRBWRWRWRWRTEPKPK
QBQBRBWRWRWRWRTETETM
QBQBRBWRWRWRWRTETEPK
QBQBRBRBWRTETEPKPKTM
QBQBRBRBWRWRTEPKPKTM
QBQBRBRBWRWRTETEPKTM
QBQBRBRBWRWRTETEPKPK
QBQBRBRBWRWRWRPKPKTM
QBQBRBRBWRWRWRTEPKTM
QBQBRBRBWRWRWRTEPKPK
QBQBRBRBWRWRWRTETETM
QBQBRBRBWRWRWRTETEPK
QBQBRBRBWRWRWRWRPKTM
QBQBRBRBWRWRWRWRPKPK
QBQBRBRBWRWRWRWRTETM
QBQBRBRBWRWRWRWRTEPK
QBQBRBRBWRWRWRWRTETE
QBQBRBRBRBTETEPKPKTM
QBQBRBRBRBWRTEPKPKTM
QBQBRBRBRBWRTETEPKTM
QBQBRBRBRBWRTETEPKPK
QBQBRBRBRBWRWRPKPKTM
QBQBRBRBRBWRWRTEPKTM
QBQBRBRBRBWRWRTEPKPK
QBQBRBRBRBWRWRTETETM
QBQBRBRBRBWRWRTETEPK
QBQBRBRBRBWRWRWRPKTM
QBQBRBRBRBWRWRWRPKPK
QBQBRBRBRBWRWRWRTETM
QBQBRBRBRBWRWRWRTEPK
QBQBRBRBRBWRWRWRTETE
QBQBRBRBRBWRWRWRWRTM
QBQBRBRBRBWRWRWRWRPK
QBQBRBRBRBWRWRWRWRTE

Could probably modify to insert numbers and spaces if you want.

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

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## #22 2020-03-18 23:42:40

UCanCallMeMitch
Member
Registered: 2020-02-28
Posts: 24

### Re: Combinations For Fantasy Football Roster

Thanks Bob, but its not right.

Remember, there are minimums / maximums for each starting lineup position.  For instance, in your list, you have 2 QBs or 0 QBs (min/max=1), 2 PKs (max=1), etc.

Take a look at My Spreadsheet For Roster Configuration #38 and you'll see all the combinations I came up with.  A total of 56. (8 groups of 7)

--Mitch

"The more you explain it, the more I don't understand it."
-- Mark Twain

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## #23 2020-03-19 21:00:30

Bob
Registered: 2010-06-20
Posts: 8,930

### Re: Combinations For Fantasy Football Roster

hi Mitch,

Oh silly me.  I said I'm easily confused.

But actually that makes it easier for me.  I think (haven't done it yet) that one program will handle both steps … 1. getting the roster possibilities and 2.  getting the team possibilities.

Later I'll modify the program and hopefully get 56 this time.

bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

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## #24 2020-03-19 23:16:55

Bob
Registered: 2010-06-20
Posts: 8,930

### Re: Combinations For Fantasy Football Roster

hi Mitch,

I thought I was getting it but only came up with 15 possibilities.

I'm still confused about the roster and min/max I'm supposed to be using

In post 13 you say: Example 2 - using the 14 man/position Roster Configuration of 2 QBs, 4 RBs, 3 WRs, 2 TEs, 2 PKs, 1 TM.

But in the spreadsheet: Roster Configuration: 2QBs, 3RBs, 4WRs, 2TEs, 2PKs, 1TM
Then:
RB = 2 / 6  (With The Above Roster Configuration The Max Is 3)

I'm ready to roll with a revised program but I need to be sure I'm putting in the right data.

(1) The 14 positions in the roster

(2) The min and max values to use for a team of 10. Are these the same for any other roster?

Thanks

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

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## #25 2020-03-21 11:59:30

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 4,653

### Re: Combinations For Fantasy Football Roster

Hi Mitch,

I've been casually following this thread and so haven't understood all that much.

However, I thought I'd check some of your workings and Bob's, and found what may be an error in post #9:

UCanCallMeMitch (post #9) wrote:

QB - 1
RB - 2 (Max of 4)
WR - 2 (Max of 4)
TE - 1 (Max of 2)
PK -1
TM - 1
Flex Players - 2 (Either RBs, WRs, or TEs); there are six combinations:

1 QB, 2 RBs, 2 WRs, 3 TEs, 1 PK, 1 TM
1 QB, 2 RBs, 3 WRs, 2 TEs, 1 PK, 1 TM
1 QB, 2 RBs, 4 WRs, 1 TE, 1 PK, 1 TM
1 QB, 3 RBs, 2 WRs, 2 TEs, 1 PK, 1 TM
1 QB, 3 RBs, 3 WRs, 1, TE, 1 PK, 1 TM
1 QB, 4 RBs, 2 WRs, 1 TE, 1 PK, 1 TM

Isn't the first combo invalid, as it exceeds the max number of TEs? If so, that would reduce the number of valid combinations to 5.

Or aren't Flex Players included in the Max count?

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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