Combinations For Fantasy Football Roster

phrontister · 2021-04-22 02:19:26

Hi Mitch,

Some things in your last post puzzle me:

1. The WRs don't appear in the combinations parameter, but they appear
(a) in the minimum/maximum list, and
(b) in the list of 34 combinations.
2. The PKs only feature in the combinations parameter.

Is there some info missing from what you gave?

But very likely I'm not understanding this fully!

mathland · 2021-04-22 11:17:26

Nice question. Great replies. I also will be posting statistics and probability questions in the near future.

phrontister · 2021-04-23 03:35:57

Hi Mitch,

I got 56 combos:

Done by hand, with rows in descending order & columns ranked from left to right (governed by previous row's content).

Done with Mathematica formulas, giving the same result as Excel's.
I don't know how to display M's output like my E's, but copy/paste from M to E, + some manipulation in E, would fix that.

I proceeded with the exercise by assuming that maybe you meant 'WRs' instead of 'PKs' where you said "Made up of a combination of QBs, RBs, TEs & PKs"...because PKs appears nowhere else.

Happy to redo my list if I made a false assumption.

Btw, some WRs in your list are below their minimum of 2.

Last edited by phrontister (2021-04-23 16:43:20)

UCanCallMeMitch · 2021-04-23 20:39:50

"Stupid is as stupid does" (Name the movie / character)

I corrected my post (#49) to reflect the correct lineup parameters and align the headers of the columns with the entries (looks like it was creating confusion).

Thanks everyone for your responses, let me address each individually

Bob (post #50) - It looks like you are correct, 5-3-3-1 is a valid roster combination. When I have time I'll redo my spreadsheet.

phrontister (post #51 & 53) - As I mentioned above I corrected my original post. It should clear things up and the TEs minimums / maximums are 1 - 7. I'm sure that this will increase the number of combinations in your calculations.

mathland (post #52) - Thanks

-- Mitch

UCanCallMeMitch · 2021-04-23 23:45:28

Okay, I found the time to recalculate the number of combinations with the following parameters

Max on Roster = 12
Made up of a combination of QBs, RBs, WRs, & TEs
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

This time I came up with 80 combinations (no repeat, order doesn't matter) as shown in the below list.

Did I get it correct this time?

# QB RB WR TE TOT
01 1 8 2 1 12
02 1 7 3 1 12
03 1 7 2 2 12
04 1 6 3 2 12
05 1 6 2 3 12
06 1 5 4 2 12
07 1 5 3 3 12
08 1 5 2 4 12
09 1 4 5 2 12
10 1 4 4 3 12
11 1 4 3 4 12
12 1 4 2 5 12
13 1 3 7 1 12
14 1 3 6 2 12
15 1 3 5 3 12
16 1 3 4 4 12
17 1 3 3 5 12
18 1 3 2 6 12
19 1 2 8 1 12
20 1 2 7 2 12
21 1 2 6 3 12
22 1 2 5 4 12
23 1 2 4 5 12
24 1 2 3 6 12
25 1 2 2 7 12
26 2 7 2 1 12
27 2 6 3 1 12
28 2 6 2 2 12
29 2 5 4 1 12
30 2 5 3 2 12
31 2 5 2 3 12
32 2 4 5 1 12
33 2 4 4 2 12
34 2 4 3 3 12
35 2 4 2 4 12
36 2 3 6 1 12
37 2 3 5 2 12
38 2 3 4 3 12
39 2 3 3 4 12
40 2 3 2 5 12
41 2 2 7 1 12
42 2 2 6 2 12
43 2 2 5 3 12
44 2 2 4 4 12
45 2 2 3 5 12
46 2 2 2 6 12
47 3 6 2 1 12
48 3 5 3 1 12
49 3 5 2 2 12
50 3 4 3 2 12
51 3 4 2 3 12
52 3 3 5 1 12
53 3 3 4 2 12
54 3 3 3 3 12
55 3 3 2 4 12
56 3 2 6 1 12
57 3 2 5 2 12
58 3 2 4 3 12
59 3 2 3 4 12
60 3 2 2 5 12
61 4 5 2 1 12
62 4 4 3 1 12
63 4 4 2 2 12
64 4 3 4 1 12
65 4 3 3 2 12
66 4 3 2 3 12
67 4 2 5 1 12
68 4 2 4 2 12
69 4 2 3 3 12
70 4 2 2 4 12
71 5 4 2 1 12
72 5 3 3 1 12
73 5 3 2 2 12
74 5 2 4 1 12
75 5 2 3 2 12
76 5 2 2 3 12
77 6 3 2 1 12
78 6 2 3 1 12
79 6 2 2 2 12
80 7 2 2 1 12

phrontister · 2021-04-24 01:11:48

Hi Mitch,

I got 84 for the corrected version.

Mine are the same as yours, but I've got these 4 extras:

1,6,4,1
1,5,5,1
1,4,6,1
3,4,4,1

UCanCallMeMitch · 2021-04-24 02:45:19

Good catch. Thanks again.

phrontister · 2021-04-25 02:59:49

I tried MIF's Combinations and Permutations Calculator for the first time (understanding Cs & Ps has never been on my 'to do' list), and got it to work on the 2 scenarios I tried it on...with some issues (see end of post).

But at least they confirmed the total numbers of combinations mentioned in earlier posts, and spot checks I did on actual combo compositions were accurate.

These are my settings and outputs for the Post #1 and Post #55 scenarios:

In the 'List Them' entry, the first element in each scenario is the group comprising the fixed minimum number of players that must appear in each combo.

Without this 'trick' of reducing the number of elements, I failed in both scenarios:
Post #1: My 'has 3' rule was rejected (the limit is 2, as Mitch said in post #13).
Post #55: "List too large" error (MIF's max combinations is 10,000,000, which is well under the 86,493,225 for this scenario).

I copied MIF's output for post #55 and pasted it into Excel via the Text Import Wizard. That gave a single row/multiple column layout that I converted to multiple rows/multiple columns via Paste/Transpose. Player counts were then obtained by formula, producing the following:

To help explain some things, here's a screen image of my Excel worksheet:

Last edited by phrontister (2021-05-01 01:42:48)

phrontister · 2021-04-25 03:12:40

Here's a little program in BASIC that works for this latest scenario (post #55), and should work in other scenarios too...with some customising.

The code can be run online (free) here: YABASIC

I pasted the above code into YABASIC, and below is their output. The combos are in descending order, as per my code (which I changed to agree with MIF's calculator's order).

For comparison (to help in making custom tweaks for other scenarios), here's the code and YABASIC output for the Post #1 scenario.

The output can be copied from YABASIC via left-click in their output screen, followed by Ctrl+A and then Ctrl+C. Ctrl+V pastes it where you want.

I pasted it into Excel, but had to use the Text Import Wizard to place the data into their respective columns (instead of just a single column).

Edit: I changed the code so the output is in descending order (same as MIF's Combinations Calculator output).

Last edited by phrontister (2021-04-29 11:13:26)

UCanCallMeMitch · 2021-04-26 12:37:36

Thanks, I'll take a closer look at the YABASIC program and see if I can figure it out.

phrontister · 2021-04-26 12:48:45

Hi Mitch,

I've just edited my post #58 and added a screen image of my Excel worksheet to show how I used MIF's Combinations Calculator output in Excel.

So you won't necessarily need to look at the YABASIC option...but it is interesting, and a totally different approach!

Btw, the idea for the YABASIC method came from the way I go about doing this longhand.

Last edited by phrontister (2021-04-26 18:44:51)

Math Is Fun Forum

#51 2021-04-22 02:19:26

Re: Combinations For Fantasy Football Roster

#52 2021-04-22 11:17:26

Re: Combinations For Fantasy Football Roster

#53 2021-04-23 03:35:57

Re: Combinations For Fantasy Football Roster

#54 2021-04-23 20:39:50

Re: Combinations For Fantasy Football Roster

#55 2021-04-23 23:45:28

Re: Combinations For Fantasy Football Roster

#56 2021-04-24 01:11:48

Re: Combinations For Fantasy Football Roster

#57 2021-04-24 02:45:19

Re: Combinations For Fantasy Football Roster

#58 2021-04-25 02:59:49

Re: Combinations For Fantasy Football Roster

#59 2021-04-25 03:12:40

Re: Combinations For Fantasy Football Roster

#60 2021-04-26 12:37:36

Re: Combinations For Fantasy Football Roster

#61 2021-04-26 12:48:45

Re: Combinations For Fantasy Football Roster

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