Initial Probabilities - AdvoCare Bowl eliminations.

We are finally here.  I was up half the night putting this together, but I was able to calculate the probabilities of winning any place in the pool.  For those that aren't familiar, here's the methodology:  I assume that every game is a coin flip (even though I know that's not technically true) and figure all the final scores of all the sheets in every one of the 65,536 possible outcomes.  I then figure out who would finish 1st, 2nd and 3rd in all of those scenarios (including ties).  Once I have that information, I can determine when a sheet is mathematically eliminated from contention.  Some of the data is a little surprising.  Often times, there are sheets that were at top of the points standings that can't win because every possible outcome yields a sheet with more points.  Often sheets with really low points still have a chance if they picked something bizarre that few other sheets picked.  Also, the variability of the assigned points makes a difference.  Many of you have the same picks, only for different points.  That makes a difference.

Sadly, there are 14 of the 89 sheets that are already mathematically eliminated from any contention.  Here they are:

Ally H.

Amos W.

Dave M.

DesGru

Howard S.

Hutch H. #1

James G. #1

Justin

Luis B. #1

Matt N.

Michelle R.

Miguel D.

Mike L. #1

Mike S.

Sorry to those 14 entries.  Maybe next year.  Some of them can still have respectable showings, but none of them can finish in the top 3.  Everyone is eligible for at least 1 place in the payouts.

There are 4 entries that can only win 3rd place:

BAD

Chad C.

Hutch H. #2

Mike L. #2

There are another 11 entries that can only win 2nd or 3rd, but not 1st:

Andy M.

Brent S. #2

Brett W.

Damien R. #1

Jackie S.

Karl K.

Larry G. #2

Luis B. #2

Michelle L. #2

Peter J. #2

Scott Her. #2

There are another 2 sheets that fall in the strange category where they can win 1st or 3rd, but not 2nd:

Mike W.

Marc R. #2

So that's who is eliminated from what so far.  Here are the probabilities of winning the pool:

1.: Carl B. (16.5907%)

2.: Larry G. #3 (12.8191%)

3.: Jay H. #3 (12.1259%)

4.: Adam E. (5.7579%)

5.: Bruce G. (5.5142%)

6.: Damien R. #2 (4.7462%)

7.: Brent E. #1 (4.3757%)

8.: Chris L. #2 (3.6355%)

9.: Daryl J. (3.3472%)

10.: Klei R. #2 (2.7633%)

11.: Brent E. #3 (2.5786%)

12.: Abel R. (2.2969%)

13.: Erica A. (2.1778%)

14.: Dre (2.1596%)

15.: Jim W. (1.7545%)

16.: Roth W. #2 (1.661%)

17.: Kansas C. (1.6381%)

18.: Brent S. #1 (1.5978%)

19.: James G. #2 (1.1375%)

20.: CJ (1.0847%)

21.: Jeff W. (0.9442%)

22.: Huki Julie (0.8532%)

23.: Sally R. (0.8092%)

24.: Roth W. #1 (0.6633%)

25.: Scott Has. (0.5956%)

26.: Kevin F. (0.5844%)

27.: Chad L. (0.5513%)

28.: Marc R. #1 (0.5424%)

29.: Michelle L. #1 (0.5015%)

30.: Brad R. (0.4842%)

31.: Klei R. #1 (0.4684%)

32.: Jay H. #1 (0.4302%)

33.: Chris L. #1 (0.3929%)

34.: Dennis R. (0.3156%)

35.: Sailor Dan (0.3097%)

36.: Mandi A. (0.2632%)

37.: Ben P. (0.2085%)

38.: Jay H. #2 (0.2085%)

39.: Bosun Ava (0.1841%)

40.: Max W. (0.1683%)

41.: Steve D. (0.163%)

42.: Brent E. #2 (0.1093%)

43.: Shawn S. (0.0928%)

44.: Peter J. #1 (0.089%)

45.: Becky H (0.074%)

46.: Ben W. (0.0465%)

47.: Greg F. (0.0427%)

48.: Matt J. (0.0419%)

49.: Tony S. (0.0198%)

50.: Tim N. (0.016%)

51.: Easten S. (0.0152%)

52.: Kevin W. (0.0142%)

53.: Scott Her. #1 (0.0114%)

54.: Larry G. #1 (0.0068%)

55.: Marc R. #3 (0.0045%)

56.: Jeff D. (0.003%)

56.: Marc R. #2 (0.003%)

58.: Mike W. (0.0015%)

58.: Sammie B. (0.0015%)

60.: Amy D. (0.0007%)

...and here are the probabilities of winning 2nd place: 

1.: Carl B. (11.3%)

2.: Larry G. #3 (8.257%)

3.: Adam E. (7.0688%)

4.: Damien R. #2 (5.344%)

5.: Chris L. #2 (5.315%)

6.: Brent E. #1 (4.5708%)

7.: Kansas C. (4.5376%)

8.: Bruce G. (4.3128%)

9.: Klei R. #2 (3.5154%)

10.: Brent S. #1 (3.4565%)

11.: Jay H. #3 (3.445%)

12.: CJ (2.6273%)

13.: Roth W. #2 (2.6124%)

14.: Jim W. (2.5868%)

15.: Erica A. (2.3375%)

16.: Daryl J. (2.1945%)

17.: Abel R. (2.189%)

18.: Dre (2.1353%)

19.: Roth W. #1 (1.7454%)

20.: Brent E. #3 (1.64%)

21.: James G. #2 (1.4067%)

22.: Sally R. (1.344%)

23.: Kevin F. (1.3065%)

24.: Chris L. #1 (1.1872%)

25.: Scott Has. (1.1056%)

26.: Chad L. (1.0297%)

27.: Michelle L. #1 (1.0208%)

28.: Jay H. #1 (0.9057%)

29.: Jeff W. (0.8761%)

30.: Brad R. (0.8516%)

31.: Klei R. #1 (0.8098%)

32.: Huki Julie (0.8088%)

33.: Dennis R. (0.6181%)

34.: Mandi A. (0.6017%)

35.: Brent E. #2 (0.5406%)

36.: Marc R. #1 (0.5228%)

37.: Jay H. #2 (0.4831%)

38.: Bosun Ava (0.4679%)

39.: Max W. (0.4074%)

40.: Sailor Dan (0.3878%)

41.: Ben P. (0.2638%)

42.: Shawn S. (0.2629%)

43.: Peter J. #1 (0.2499%)

44.: Steve D. (0.1904%)

45.: Greg F. (0.1815%)

46.: Matt J. (0.1416%)

47.: Kevin W. (0.1036%)

48.: Larry G. #1 (0.1001%)

49.: Easten S. (0.0923%)

50.: Becky H (0.0905%)

51.: Tim N. (0.0905%)

52.: Marc R. #3 (0.0698%)

53.: Karl K. (0.048%)

54.: Tony S. (0.047%)

55.: Ben W. (0.045%)

56.: Scott Her. #1 (0.0442%)

57.: Jeff D. (0.016%)

58.: Andy M. (0.0144%)

59.: Amy D. (0.0134%)

60.: Luis B. #2 (0.0122%)

61.: Damien R. #1 (0.0091%)

61.: Sammie B. (0.0091%)

63.: Jackie S. (0.0083%)

64.: Larry G. #2 (0.0061%)

65.: Scott Her. #2 (0.0053%)

66.: Brett W. (0.0038%)

67.: Brent S. #2 (0.003%)

68.: Peter J. #2 (0.0015%)

69.: Michelle L. #2 (0.0003%)

...and the probabilities of winning 3rd place:

1.: Carl B. (9.4036%)

2.: Larry G. #3 (6.228%)

3.: Kansas C. (6.2251%)

4.: Adam E. (6.0287%)

5.: Brent S. #1 (5.383%)

6.: Chris L. #2 (5.3106%)

7.: Damien R. #2 (4.6225%)

8.: Klei R. #2 (3.4361%)

9.: Bruce G. (3.3624%)

10.: Roth W. #1 (3.1661%)

11.: Roth W. #2 (3.1651%)

12.: CJ (2.7757%)

13.: Erica A. (2.7508%)

14.: Brent E. #1 (2.6701%)

15.: Jim W. (2.6386%)

16.: Jay H. #3 (2.3737%)

17.: Abel R. (2.082%)

18.: Dre (1.7762%)

19.: Chris L. #1 (1.677%)

20.: Scott Has. (1.5882%)

21.: Daryl J. (1.5548%)

22.: Brent E. #3 (1.5249%)

23.: James G. #2 (1.4859%)

24.: Kevin F. (1.4461%)

25.: Chad L. (1.3715%)

26.: Michelle L. #1 (1.2491%)

27.: Sally R. (1.0375%)

28.: Brad R. (1.0088%)

29.: Klei R. #1 (0.9886%)

30.: Jeff W. (0.9393%)

31.: Jay H. #1 (0.9237%)

32.: Huki Julie (0.8714%)

33.: Dennis R. (0.8136%)

34.: Mandi A. (0.7116%)

35.: Bosun Ava (0.6852%)

36.: Brent E. #2 (0.6168%)

37.: Marc R. #1 (0.6014%)

38.: Jay H. #2 (0.4676%)

39.: Peter J. #1 (0.4296%)

40.: Shawn S. (0.4224%)

41.: Max W. (0.4053%)

42.: Sailor Dan (0.3776%)

43.: Kevin W. (0.3174%)

44.: Ben P. (0.3025%)

45.: Matt J. (0.3021%)

46.: Tim N. (0.2941%)

47.: Greg F. (0.2899%)

48.: Larry G. #1 (0.2605%)

49.: Steve D. (0.26%)

50.: Easten S. (0.2217%)

51.: Marc R. #3 (0.2126%)

52.: Andy M. (0.129%)

53.: Karl K. (0.1258%)

54.: Becky H (0.1148%)

55.: Scott Her. #1 (0.0801%)

56.: Ben W. (0.0656%)

57.: Tony S. (0.0494%)

58.: Larry G. #2 (0.0493%)

59.: Sammie B. (0.0404%)

59.: Scott Her. #2 (0.0404%)

61.: Brett W. (0.0398%)

62.: Brent S. #2 (0.0345%)

63.: Luis B. #2 (0.032%)

64.: Damien R. #1 (0.0312%)

65.: Jeff D. (0.0305%)

66.: Amy D. (0.0251%)

67.: Jackie S. (0.0106%)

67.: Peter J. #2 (0.0106%)

69.: BAD (0.0081%)

70.: Hutch H. #2 (0.0061%)

70.: Marc R. #2 (0.0061%)

72.: Chad C. (0.0038%)

73.: Mike L. #2 (0.003%)

74.: Mike W. (0.0022%)

75.: Michelle L. #2 (0.0011%)

So, it looks like things are pretty good right now for Carl B., as he is the frontrunner to win every one of the three payouts.  Of course, the most he can win is one, but that's still a nice place to be.  I also have the average rank finish.  I think this statistic shows the general health of the sheet as it takes every scenario and averages where the sheet would finish over them:

1.: Carl B. (7.8285)

2.: Kansas C. (10.6389)

3.: Brent S. #1 (12.1231)

4.: Roth W. #1 (14.897)

5.: Larry G. #3 (16.774)

6.: Adam E. (17.8794)

7.: Erica A. (19.1854)

8.: Damien R. #2 (19.4864)

9.: Klei R. #2 (21.7928)

10.: Chris L. #2 (21.7941)

11.: Chris L. #1 (21.9786)

12.: BAD (22.4844)

13.: CJ (22.9189)

14.: Roth W. #2 (24.1894)

15.: Kevin W. (25.0466)

16.: Miguel D. (25.9549)

17.: Michelle L. #1 (26.2317)

18.: Andy M. (27.8792)

19.: Jim W. (28.2926)

20.: Bruce G. (28.808)

21.: Abel R. (29.7616)

22.: Mike L. #2 (30.7208)

23.: Scott Has. (31.9632)

24.: Brent S. #2 (32.7449)

25.: James G. #2 (32.9264)

26.: Hutch H. #1 (34.5036)

27.: Larry G. #1 (36.7018)

28.: Mike L. #1 (36.9515)

29.: Matt N. (37.7668)

30.: Brent E. #2 (38.1166)

31.: Matt J. (38.14)

32.: Marc R. #3 (38.7104)

33.: Kevin F. (39.0121)

34.: Klei R. #1 (39.0752)

35.: Brad R. (39.401)

36.: Chad L. (40.2141)

37.: Bosun Ava (40.641)

38.: Brent E. #1 (41.1036)

39.: Jay H. #1 (41.4839)

40.: Dre (42.4085)

41.: Scott Her. #2 (42.7177)

42.: Hutch H. #2 (42.9487)

43.: Jeff W. (43.8204)

44.: Jay H. #3 (44.1438)

45.: Brett W. (44.8465)

46.: Karl K. (45.3442)

47.: Brent E. #3 (45.4286)

48.: Tim N. (45.6498)

49.: Daryl J. (45.9834)

50.: Amos W. (46.5962)

51.: Mandi A. (46.7993)

52.: Greg F. (47.2975)

53.: Dave M. (47.7804)

54.: Shawn S. (47.8014)

55.: Scott Her. #1 (48.1926)

56.: Larry G. #2 (48.2287)

57.: Michelle L. #2 (49.038)

58.: Steve D. (50.393)

59.: Peter J. #1 (51.6777)

60.: Sally R. (52.6093)

61.: Huki Julie (53.0164)

62.: Damien R. #1 (53.7895)

63.: Ben P. (54.9492)

64.: Mike W. (55.2162)

65.: Marc R. #1 (56.3494)

66.: Jeff D. (58.2318)

67.: Amy D. (58.3597)

68.: Easten S. (60.5406)

69.: Jay H. #2 (60.7821)

70.: Sailor Dan (61.0319)

71.: Max W. (61.2457)

72.: Becky H (61.4516)

73.: Dennis R. (61.6933)

74.: Chad C. (62.6985)

75.: Mike S. (63.2648)

76.: Howard S. (63.4208)

77.: Peter J. #2 (63.9292)

78.: Marc R. #2 (65.7305)

79.: James G. #1 (66.3632)

80.: Luis B. #2 (66.8366)

81.: Luis B. #1 (67.7223)

82.: Tony S. (71.2932)

83.: Ben W. (71.4277)

84.: Sammie B. (72.393)

85.: Justin (74.5494)

86.: Jackie S. (77.6805)

87.: DesGru (78.0534)

88.: Michelle R. (78.6273)

89.: Ally H. (82.9133)

That was all fun, but there's a game going off pretty soon, so what about eliminations?  Here they are:

If Arizona wins:

Amy D. is eliminated from 1st place contention.  (Arizona for 11) Becky H is eliminated from 1st place contention.  (BC for 12) Ben W. is eliminated from 1st, 2nd & 3rd place contention.  (BC for 19) Chad C. is eliminated from 3rd place contention.  (Arizona for 12) Chad L. is eliminated from 1st place contention.  (BC for 18) Easten S. is eliminated from 1st, 2nd & 3rd place contention.  (BC for 14) Jackie S. is eliminated from 2nd & 3rd place contention.  (BC for 6) Jay H. #2 is eliminated from 1st place contention.  (BC for 20) Jeff D. is eliminated from 1st & 2nd place contention.  (Arizona for 6) Larry G. #1 is eliminated from 1st, 2nd & 3rd place contention.  (BC for 8) Larry G. #2 is eliminated from 2nd place contention.  (Arizona for 8) Luis B. #2 is eliminated from 2nd & 3rd place contention.  (BC for 14) Mandi A. is eliminated from 1st, 2nd & 3rd place contention.  (BC for 29) Marc R. #2 is eliminated from 1st & 3rd place contention.  (Arizona for 8) Mike L. #2 is eliminated from 3rd place contention.  (Arizona for 19) Mike W. is eliminated from 1st & 3rd place contention.  (BC for 19) Peter J. #2 is eliminated from 2nd & 3rd place contention.  (BC for 5) Sammie B. is eliminated from 1st & 2nd place contention.  (Arizona for 2) Scott Her. #1 is eliminated from 1st & 2nd place contention.  (BC for 4) Scott Her. #2 is eliminated from 2nd & 3rd place contention.  (Arizona for 10) Shawn S. is eliminated from 1st, 2nd & 3rd place contention.  (BC for 17) Tim N. is eliminated from 1st, 2nd & 3rd place contention.  (BC for 25)

If Boston College wins:

Andy M. is eliminated from 2nd place contention.  (Arizona for 24)

Brent S. #2 is eliminated from 2nd & 3rd place contention.  (Arizona for 29)

Brett W. is eliminated from 2nd place contention.  (Arizona for 25)

Damien R. #1 is eliminated from 2nd & 3rd place contention.  (Arizona for 25)

Hutch H. #2 is eliminated from 3rd place contention.  (Arizona for 25)

Marc R. #3 is eliminated from 1st & 2nd place contention.  (Arizona for 28)

Michelle L. #2 is eliminated from 2nd & 3rd place contention.  (Arizona for 24)

So you can see from the eliminations that even if you picked Arizona to win, you can still be eliminated if they do, in fact, win.  That's because you will lose ground to someone else that you can't recover from.  I think that little piece of knowledge is interesting.

I'll try to get to the eliminations for the 2nd game of the day later, but I am taking my cat to the hospital, so it may take some time.  I hope everyone enjoys the day.

Good luck!!!!!!