Combinations For Fantasy Football Roster

phrontister · 2020-03-21 12:00:34

Hi Bob,

bob bundy (post #12) wrote:

I put the two lists side by side and checked carefully. Definitely no repeats from my program and all possibilities are 'legit'...
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

Aren't 2 & 6 the same? Or are my cataracts playing up?

I thought it wouldn't hurt to have someone else check carefully, too.

Humble apologies. But I refer you to the third line of my signature

I'm onto you there!

I used Mitch's spreadsheet layout from post #4.

Couldn't get the right answer with MIF's calculator. Tried quite a few options that made sense to me, but not to the calc!

I got a bit further with Mathematica, but need Bobby to tidy up some things for me cos I just don't know enough!
Edit 24/4/2021: Got my Mathematica code to work, and it found & printed the 46...just not in the Excel format.

Edit 23/4/2021: I overlooked a combo in Excel (making 46 instead of 45), and have fixed the image.

Last edited by phrontister (2021-04-24 01:18:47)

UCanCallMeMitch · 2020-03-21 23:19:49

phrontister, Good catch. Fish and Pole

Because of the Lineup limitations, you are correct, only five configurations are possible for the lineup submission. I've corrected those posts erroneously showing six.

I rechecked my calculations (spreadsheets) and also what Bob posted here and in all cases it looks as though the calculations only allowed 2 TEs. So it seems everything is good in that regard.

Again, thanks for the heads-up.

++++++++++

Bob, it looks to me that the 86 combinations you came up with in post #19 is the number of different player combinations for the five lineup configurations. Here's the MIF calculation:

Combinations without repetition (n=10, r=7)
Using Items: rb1,rb2,rb3,rb4,wr1,wr2,wr3,wr4,te1,te2
Using Rule: has 2 of: rb1,rb2,rb3,rb4
Using Rule: has 2 of: wr1,wr2,wr3,wr1
Using Rule: has 1 of: te1,te2

List has 86 entries. [ Add 1 QB, 1 PK & 1 TM to each combination to come up with the 10-man lineup ]
rb1,rb2,rb3,rb4,wr1,wr2,te1
rb1,rb2,rb3,rb4,wr1,wr2,te2
rb1,rb2,rb3,rb4,wr1,wr3,te1
rb1,rb2,rb3,rb4,wr1,wr3,te2
rb1,rb2,rb3,rb4,wr2,wr3,te1
rb1,rb2,rb3,rb4,wr2,wr3,te2
rb1,rb2,rb3,wr1,wr2,wr3,te1
rb1,rb2,rb3,wr1,wr2,wr3,te2
rb1,rb2,rb3,wr1,wr2,wr4,te1
rb1,rb2,rb3,wr1,wr2,wr4,te2
rb1,rb2,rb3,wr1,wr2,te1,te2
rb1,rb2,rb3,wr1,wr3,wr4,te1
rb1,rb2,rb3,wr1,wr3,wr4,te2
rb1,rb2,rb3,wr1,wr3,te1,te2
rb1,rb2,rb3,wr2,wr3,wr4,te1
rb1,rb2,rb3,wr2,wr3,wr4,te2
rb1,rb2,rb3,wr2,wr3,te1,te2
rb1,rb2,rb4,wr1,wr2,wr3,te1
rb1,rb2,rb4,wr1,wr2,wr3,te2
rb1,rb2,rb4,wr1,wr2,wr4,te1
rb1,rb2,rb4,wr1,wr2,wr4,te2
rb1,rb2,rb4,wr1,wr2,te1,te2
rb1,rb2,rb4,wr1,wr3,wr4,te1
rb1,rb2,rb4,wr1,wr3,wr4,te2
rb1,rb2,rb4,wr1,wr3,te1,te2
rb1,rb2,rb4,wr2,wr3,wr4,te1
rb1,rb2,rb4,wr2,wr3,wr4,te2
rb1,rb2,rb4,wr2,wr3,te1,te2
rb1,rb2,wr1,wr2,wr3,wr4,te1
rb1,rb2,wr1,wr2,wr3,wr4,te2
rb1,rb2,wr1,wr2,wr3,te1,te2
rb1,rb2,wr1,wr2,wr4,te1,te2
rb1,rb2,wr1,wr3,wr4,te1,te2
rb1,rb2,wr2,wr3,wr4,te1,te2
rb1,rb3,rb4,wr1,wr2,wr3,te1
rb1,rb3,rb4,wr1,wr2,wr3,te2
rb1,rb3,rb4,wr1,wr2,wr4,te1
rb1,rb3,rb4,wr1,wr2,wr4,te2
rb1,rb3,rb4,wr1,wr2,te1,te2
rb1,rb3,rb4,wr1,wr3,wr4,te1
rb1,rb3,rb4,wr1,wr3,wr4,te2
rb1,rb3,rb4,wr1,wr3,te1,te2
rb1,rb3,rb4,wr2,wr3,wr4,te1
rb1,rb3,rb4,wr2,wr3,wr4,te2
rb1,rb3,rb4,wr2,wr3,te1,te2
rb1,rb3,wr1,wr2,wr3,wr4,te1
rb1,rb3,wr1,wr2,wr3,wr4,te2
rb1,rb3,wr1,wr2,wr3,te1,te2
rb1,rb3,wr1,wr2,wr4,te1,te2
rb1,rb3,wr1,wr3,wr4,te1,te2
rb1,rb3,wr2,wr3,wr4,te1,te2
rb1,rb4,wr1,wr2,wr3,wr4,te1
rb1,rb4,wr1,wr2,wr3,wr4,te2
rb1,rb4,wr1,wr2,wr3,te1,te2
rb1,rb4,wr1,wr2,wr4,te1,te2
rb1,rb4,wr1,wr3,wr4,te1,te2
rb1,rb4,wr2,wr3,wr4,te1,te2
rb2,rb3,rb4,wr1,wr2,wr3,te1
rb2,rb3,rb4,wr1,wr2,wr3,te2
rb2,rb3,rb4,wr1,wr2,wr4,te1
rb2,rb3,rb4,wr1,wr2,wr4,te2
rb2,rb3,rb4,wr1,wr2,te1,te2
rb2,rb3,rb4,wr1,wr3,wr4,te1
rb2,rb3,rb4,wr1,wr3,wr4,te2
rb2,rb3,rb4,wr1,wr3,te1,te2
rb2,rb3,rb4,wr2,wr3,wr4,te1
rb2,rb3,rb4,wr2,wr3,wr4,te2
rb2,rb3,rb4,wr2,wr3,te1,te2
rb2,rb3,wr1,wr2,wr3,wr4,te1
rb2,rb3,wr1,wr2,wr3,wr4,te2
rb2,rb3,wr1,wr2,wr3,te1,te2
rb2,rb3,wr1,wr2,wr4,te1,te2
rb2,rb3,wr1,wr3,wr4,te1,te2
rb2,rb3,wr2,wr3,wr4,te1,te2
rb2,rb4,wr1,wr2,wr3,wr4,te1
rb2,rb4,wr1,wr2,wr3,wr4,te2
rb2,rb4,wr1,wr2,wr3,te1,te2
rb2,rb4,wr1,wr2,wr4,te1,te2
rb2,rb4,wr1,wr3,wr4,te1,te2
rb2,rb4,wr2,wr3,wr4,te1,te2
rb3,rb4,wr1,wr2,wr3,wr4,te1
rb3,rb4,wr1,wr2,wr3,wr4,te2
rb3,rb4,wr1,wr2,wr3,te1,te2
rb3,rb4,wr1,wr2,wr4,te1,te2
rb3,rb4,wr1,wr3,wr4,te1,te2
rb3,rb4,wr2,wr3,wr4,te1,te2

Also, since #2 & #6, as phrontister pointed out, are the same does that mean there are only 45 combinations or is there a typo? FOLLOW-UP. I checked and I'm pretty sure it's a typo.

++++++++++

Food for thought: Would it help if I tried to consolidate all these 26 posts into one cohesive post to make sure we are all on the same page? Or are we good?

-- Mitch

Last edited by UCanCallMeMitch (2020-03-21 23:53:07)

Bob · 2020-03-21 23:55:28

hi Phro,

Thanks for your input. Hope you are keeping well, and you, Mitch, in these crazy times.

hi Mitch,

The error Phro found was a typo. I have now worked out how to store the program output as a text file (rather than 'hand' copying it) and re-run the roster check. I still get 46 (phew) but number 6 should have been QB RB WR WR. There may be more typos because of this. I can re-post my list if you want.

Once you have chosen a roster the rules say pick 10 for a team with these constraints

QB =1, RB = 2, WR = 2, TE = 1, PK = 1, TM = 1, FLEX = 2 (RBs WRs, TEs)

So 8 out of 10 are determined. Just 2 to choose from 14-8 = 6

6C2 = 15. So there cannot be more than 15 choices and less if you eliminate 'repeats'. My program finds 15 and after eliminations is down to 11. That's small enough to check manually, so I have, with the same result.

So I am mystified where 56 comes from. What is that working out?

I think I'm still missing something here.

Please keep the posts unconsolidated as I 'know' my way round them as they are.

Bob

UCanCallMeMitch · 2020-03-22 01:18:21

The 56 combinations comes from the number of player lineup combos possible with the following Roster configuration:

2 QBs, 3 RBs, 4 WRs, 2 TEs, 2 PKs and 1 TM (or any of the others in 'Combo Group E' (E01 - E08)

as shown in My Spreadsheet For Roster Configuration #38

-- Mitch Masked

Last edited by UCanCallMeMitch (2020-03-22 01:19:13)

Bob · 2020-03-22 02:36:46

??? So why isn't it:

QB RB RB WR WR TE PK TM + QB RB
QB RB RB WR WR TE PK TM + QB WR
QB RB RB WR WR TE PK TM + QB TE
QB RB RB WR WR TE PK TM + QB PK
QB RB RB WR WR TE PK TM + RB WR
QB RB RB WR WR TE PK TM + RB TE
QB RB RB WR WR TE PK TM + RB PK
QB RB RB WR WR TE PK TM + WR WR
QB RB RB WR WR TE PK TM + WR TE
QB RB RB WR WR TE PK TM + WR PK
QB RB RB WR WR TE PK TM + TE PK

Bob

UCanCallMeMitch · 2020-03-22 05:32:25

The most obvious reason to me is that you have 2 QBs & 2 PKs in the starting lineup. (lines 1 thru 4 & lines 4, 7, 10 & 11 respectively)

Remember, only 1 QB, 1 PK & 1 TM can be in the starting lineup.

Additionally, don't forget that we are looking for all the 10-men combinations that can be had using the 14-man Roster configuration of:

2 QBs (QB1 & QB2)
3 RBs, (RB1, RB2 & RB3)
4 WRs, (WR1, WR2, WR3 & WR4)
2 TEs (TE1 & TE2)
2 PKs (PK1 & PK2)
1 TM (TM1)

-- Mitch

Bob · 2020-03-22 06:08:42

My mistake. I missed that on the rules page. Amended result:

QB RB RB WR WR TE PK TM + WR WR = 1
QB RB RB WR WR TE PK TM + RB WR = 2

QB RB RB WR WR TE PK TM + RB TE = 4
QB RB RB WR WR TE PK TM + WR TE = 5

I got these in a different order but I've re-arranged them to fit the stated options on the rules page. Notice = 3 is missing because you haven't got 4 RBs in this roster. So far so good.

But I still don't get the spreadsheet. What does 56 measure then? I thought it was measuring the above. But obviously not. Pretend I'm really thick (easy to do in the current situation) and explain what 56 is a measure of.

Thanks,

Bob

UCanCallMeMitch · 2020-03-22 09:43:46

From Post #29

UCanCallMeMitch wrote:

The 56 combinations comes from the number of player lineup combos possible with the following Roster configuration:
2 QBs, 3 RBs, 4 WRs, 2 TEs, 2 PKs and 1 TM (or any of the others in 'Combo Group E' (E01 - E08)
as shown in My Spreadsheet For Roster Configuration #38
-- Mitch https://luckydogsports.net/images/smilies/masked-transp_25x25.png

UCanCallMeMitch · 2020-03-22 15:11:33

Maybe this will help -

In the 'Configuration Spreadsheet" you''ll see a list (I2 thru I9) of 8 Entries [sic combinations) of a Roster that can comprise the lineup.

The 1st Combination (QB1, TE1, PK1) is utilized Group 1; the 2nd Combination (QB1, TE, PK2) is shown in Group 2 and so forth.

One takes the original configuration , multiply by 8 (# of possible combinations of QB1, QB2,TE1, TE2, PK1, PK2 which is 7) to come up with a possible 56 different configuration for the Roster settings.

Make more sense?

UCanCallMeMitch · 2020-03-29 20:12:48

Bob,

Throwing In The Towel Throwing in the towel?

-- Mitch

Last edited by UCanCallMeMitch (2020-03-29 20:22:17)

Bob · 2020-03-29 21:16:26

No. In my head is a part program, part spreadsheet, solution to the whole problem. But lots has been happening so it has gone on the back burner. Give me a few days. It's taken me a while to fully get to grips with this. I couldn't understand what was wanted. This is what I think I'm aiming for:

(1) Find all possible rosters using the allowable position rules. (Done this … it's 46)

(2) For each identify the (up to 5) possible line ups and bench player alternatives.

(3) Now assume you've picked your players (14 for each of the above) label them WR1 WR2 etc.

(4) Work out how many alternative line ups that allows.

Bob

UCanCallMeMitch · 2020-03-29 21:42:13

Sounds like a plan.

-- Mitch

Bob · 2020-03-30 01:08:33

I want to go back to the basic rules to make sure I'm not getting anything wrong. Odd? I cannot find the post where you gave the rules link. I can get to the 'invitational' but no rules there. I'm sure it's lurking there somewhere. It's the line up possibilities I need. Please re-post the link for me. Thanks,

Bob

UCanCallMeMitch · 2020-03-30 03:57:11

That site is currently down for revisions so the link in Post #16 is currently broken, but you can find the RULES HERE at my test site.

--Mitch

Last edited by UCanCallMeMitch (2020-03-30 03:57:41)

Bob · 2020-04-02 22:53:05

hi Mitch and Phro,

After a couple of mammoth sessions I think I've cracked it and got a spreadsheet that contains:

roster number
possible rosters
lineup1
bench for lineup1
and same for lineups 2, 3, 4 and 5.

Some cases are impossible because the available players in a roster don't fit with the lineup requirements. These are shown as 'impossible'.

So there are potentially 460 cells of data. I have checked a few at random and all worked out ok … that is to say I could pick a lineup from the roster and have 4 bench players except when there wasn't enough players to fulfil the lineup and got an 'impossible' message.

I've not tried this before so I don't know if I've done it properly, but I have uploaded the sheet to my google drive and shared it with each of you. Please let me know if that has worked and then see if you can find any errors. (Fingers crossed!)

The key to calculating the number of possibilities lies with the bench player options. eg. If the lineup has a QR and there's a second QR on the bench then you have x2 possibilities for who to play. Or if the lineup has 3 WRs and they're all in the team then there are x1 possibilities as you've got no extra WRs you can swap in. I'll start working on a quick way to calculate them all.

In the UK all sporting fixtures have been cancelled so I'm guessing your league won't have any matches at the present. What a disaster!!! Let's hope things can get back to normal soon.

Best wishes, stay healthy,

Bob

UCanCallMeMitch · 2020-04-05 21:48:44

Sorry for my absence - been working on another project.

How do I get to your spreadsheet (never used Google Drive) so I can compare your results with mine?

-- Mitch

Bob · 2020-04-05 23:12:02

When you joined MIF forum you gave an email address. Google drive software has emailed the sheet to you at that address.

Bob

phrontister · 2020-04-06 00:52:43

Hi Bob;

I received my Excel file ok, thx.

Only had time to have a quick look at it, and all I did was check for duplications in the columns by using the UNIQUE function that's part of the new Excel Dynamic Arrays family.

Example: Entering '=COUNTA(UNIQUE(B2:B47))' in B48 returns '46' there, confirming that your 46 column B entries are unique. Similarly with Column G.

I'll have to take a closer look at earlier posts to try and understand this thread before examining further. Previously I've only skimmed through the posts.

Might take me a bit of time, though!

UCanCallMeMitch · 2020-04-06 11:40:12

Unfortunately, I can't find where I received a copy of the SS. I checked junk, trash, etc. and a no show.

Can you send again?

Sorry for the trouble.

Last edited by UCanCallMeMitch (2020-04-06 11:40:33)

UCanCallMeMitch · 2020-04-08 22:20:22

Bob - Received the SS; reviewing it and will get back to you (et al).

UCanCallMeMitch · 2020-04-09 05:52:58

Ok Bob, I looked at your Spreadsheet and it seem that you just calculated the number of roster configurations possible with the limitation of the lineups. And I'm not sure what "impossible" refers to.

Correct me if I'm wrong, but I thought you were going to figure-out the player possibilities as you stated in #2 of Post #36 and as I outlined in Posts #29, #31 & 33.

Am I confused on what I'm seeing? (could be)

Bob · 2020-04-09 06:13:39

hi Mitch,

I'm glad you've got the sheet.

Step 1 was to find all the rosters. I got 46 and I think that's correct. Phro has checked there's no repeats.

Step 2. There are only 5 possible lineups so I inserted those onto the sheet. But some lineups are not possible with some rosters.

eg. With the first roster there are 3 WRs, but the lineup wants 4. So it cannot be done, hence the impossible label. What I did was to run each lineup through each roster, trying to make the lineup and working out what's left on the bench. If there wasn't enough of a position I recorded 'impossible; otherwise I recorded the bench.

You're right that there is one more step to do. I wanted you to cast an eye over my progress so far, in case I'm still missing something in the rules. I suggest you pick a few rosters and think whether the sheet row shows the lineup/bench possibilities. If you cannot find anything wrong I'll do the final step. The code is in my head; so I've just got to implement it.

What I'll do is add another column, after each bench column, that gives the number of player combinations for that lineup/bench. Then it will just be a case of summing up the columns to get the grand total.

Hope that clarifies what I've sent and my plan for the last step.

Bob

Bob · 2020-04-11 01:42:10

hi Mitch,

Spreadsheet completed showing 6824 possibilities in total. I'll email it to you.

For each lineup/bench possibility I have calculated the number of ways the bench players can be shuffled into the lineup by swapping one player for another of the same positional type. I'll give you one example of how it works:

Look at the sheet row 13. Here's the roster, 3rd lineup bench and calculation:

Roster number 12 = QB QB RB RB RB RB WR WR WR TE PK PK TM TM

Lineup 3 = QB RB RB RB RB WR WR TE PK TM

Bench 3 = QB WR PK TM

Calcs = 24

QB 2 altogether(including the bench), lineup needs 1, so choose 1 from 2 = 2 choices
Four RB, all used so 1 choice
WR 3 altogether, lineup needs 2, so choose 2 from 3 = 3 choices
TE just 1 choice
PK 2 altogether, lineup needs 1, so choose 1 from 2 = 2 choices
TM 2 altogether, lineup needs 1, so choose 1 from 2 = 2 choices

Altogether 2 x 1 x 3 x 1 x 2 x 2 = 24

I have checked a couple dozen entries to make sure the calcs went ok.

Then I totalled the five calcs columns, and then totalled these five to get the final total in cell T49.

Hope that is all ok and I can move on now. Please don't change the rules.

Bob

UCanCallMeMitch · 2021-04-21 22:57:03

I'm baaaack!

First, you are correct phrontister. Sorry it took so long to reply. And I've corrected the post.

But I have another combination of football positions that I would appreciate it if someone would verify my final number of combinations that can make up a fantasy football roster

The parameters are:

Max on Roster = 12
Made up of a combination of QBs, RBs, WRs, & TEs CORRECTED
Each position has a minimum and maximum allowed as shown below

QBs (Min = 1, Max = 7)
RBs (Min = 2, Max = 8
WRs (Min = 2, Max =8)
TEs (Min = 1, Max = 7) CORRECTED

I came up with 34 combinations (no repeat, order doesn't matter) as shown in the below list.

Am I correct in my count of 34 different combinations?

QB RB WR TE TOT
7 2 2 1 12
6 3 2 1 12
6 2 3 1 12
6 2 2 2 12
5 4 2 1 12
5 2 4 1 12
5 2 2 3 12
4 5 2 1 12
4 2 5 1 12
4 2 2 4 12
3 6 2 1 12
3 2 6 1 12
3 2 2 5 12
2 7 2 1 12
2 2 7 1 12
2 2 2 6 12
1 8 2 1 12
1 7 3 1 12
1 7 2 2 12
1 6 4 1 12
1 6 2 3 12
1 5 5 1 12
1 5 2 4 12
1 4 6 1 12
1 4 2 5 12
1 3 7 1 12
1 3 2 6 12
1 2 8 1 12
1 2 7 2 12
1 2 6 3 12
1 2 5 4 12
1 2 4 5 12
1 2 3 6 12
1 2 2 7 12

Total = 34

Thanks - Mitch

Last edited by UCanCallMeMitch (2021-04-23 19:49:52)

Bob · 2021-04-22 00:30:40

hi Mitch,

I think there may be more, such as 5 3 3 1

I haven't looked for all cases yet.

Bob

Math Is Fun Forum

#26 2020-03-21 12:00:34

Re: Combinations For Fantasy Football Roster

#27 2020-03-21 23:19:49

Re: Combinations For Fantasy Football Roster

#28 2020-03-21 23:55:28

Re: Combinations For Fantasy Football Roster

#29 2020-03-22 01:18:21

Re: Combinations For Fantasy Football Roster

#30 2020-03-22 02:36:46

Re: Combinations For Fantasy Football Roster

#31 2020-03-22 05:32:25

Re: Combinations For Fantasy Football Roster

#32 2020-03-22 06:08:42

Re: Combinations For Fantasy Football Roster

#33 2020-03-22 09:43:46

Re: Combinations For Fantasy Football Roster

#34 2020-03-22 15:11:33

Re: Combinations For Fantasy Football Roster

#35 2020-03-29 20:12:48

Re: Combinations For Fantasy Football Roster

#36 2020-03-29 21:16:26

Re: Combinations For Fantasy Football Roster

#37 2020-03-29 21:42:13

Re: Combinations For Fantasy Football Roster

#38 2020-03-30 01:08:33

Re: Combinations For Fantasy Football Roster

#39 2020-03-30 03:57:11

Re: Combinations For Fantasy Football Roster

#40 2020-04-02 22:53:05

Re: Combinations For Fantasy Football Roster

#41 2020-04-05 21:48:44

Re: Combinations For Fantasy Football Roster

#42 2020-04-05 23:12:02

Re: Combinations For Fantasy Football Roster

#43 2020-04-06 00:52:43

Re: Combinations For Fantasy Football Roster

#44 2020-04-06 11:40:12

Re: Combinations For Fantasy Football Roster

#45 2020-04-08 22:20:22

Re: Combinations For Fantasy Football Roster

#46 2020-04-09 05:52:58

Re: Combinations For Fantasy Football Roster

#47 2020-04-09 06:13:39

Re: Combinations For Fantasy Football Roster

#48 2020-04-11 01:42:10

Re: Combinations For Fantasy Football Roster

#49 2021-04-21 22:57:03

Re: Combinations For Fantasy Football Roster

#50 2021-04-22 00:30:40

Re: Combinations For Fantasy Football Roster

Board footer