Superbowl XLIV Pool Analysis

Gameday: February 7, 2010

South Florida

Questions: hiram@hellskitchen-ny.com

1

The Superbowl Numbers

There have been 43 Superbowl games played since 1967…

…this year’s game is #44 if you forgot your Roman numerals (XLIV)

This equates to…

– 172 quarters of football

– 172 pairs of scores

– 344 individual digits that have occurred

No overtime periods have ever been played in a Superbowl game

2

Since most scoring occurs in increments of 3 or 7 – a key hypothesis would be that 0, 3, 7 would be likely last digits at any point of a game…

…historical Superbowl scores by quarter validate this theory

There is a very significant

difference between the

five “have” numbers

(0,3,4,6,7) and the five

“have nots” (1,2,5,8,9) –

83% to 17%

64.5%

18.9%

16.6%

100.0%

0%

20%

40%

60%

80%

100%

0, 3, 7 4, 6 1, 2, 5, 8, 9 All

Frequency of Groups of Digits

Last year’s game had

4 different

combinations of

0-3-7

3

As far as individual digits from Superbowls go, “zero” is a hero in this game

Note: Based on quarterly scores of all previous Superbowl games (see appendix)

27.3%

20.9%

16.3%

10.8%

8.1%

4.7% 4.4%

2.6% 2.6% 2.3%

0.0%

5.0%

10.0%

15.0%

20.0%

25.0%

30.0%

0

10

20

30

40

50

60

70

80

90

100

0 7 3 4 6 1 9 8 2 5

% o

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ren

ces

# o

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ces

Digit

Frequency of Last Digits

Count %

4

Looking at digit combinations, there are 36* pairs (of 100) that have NEVER occurred as a quarter-ending score in a Superbowl

Although 4-6 would seem a good

combination, that pair occurred for

the FIRST time in the 2007 game.

Funny enough, the pair was good in

BOTH the first and second

quarters, even though additional

scoring occurred in the second

quarter!

Legend:

= Never occurred in Superbowl

= Occurrence > 5% in Superbowl

Note: * 36 pairs is composed of 18

combinations and their converses

(i.e., I have made a fundamental assumption

that 7-9 and 9-7 have the same probability)

Team 1

0 1 2 3 4 5 6 7 8 9

0 7.0% 1.7% 1.7% 9.9% 5.8% 2.3% 2.9% 11.6% 1.7% 2.9%

1 1.7% 0.0% 0.0% 0.6% 1.7% 1.7% 0.6% 1.7% 0.6% 0.6%

2 1.7% 0.0% 0.0% 0.0% 0.6% 0.0% 0.0% 1.7% 0.6% 0.6%

3 9.9% 0.6% 0.0% 3.5% 3.5% 0.0% 4.1% 7.6% 0.0% 0.0%

4 5.8% 1.7% 0.6% 3.5% 0.6% 0.0% 1.2% 6.4% 0.0% 1.2%

5 2.3% 1.7% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.6%

6 2.9% 0.6% 0.0% 4.1% 1.2% 0.0% 1.2% 2.9% 1.7% 0.6%

7 11.6% 1.7% 1.7% 7.6% 6.4% 0.0% 2.9% 4.1% 0.0% 1.7%

8 1.7% 0.6% 0.6% 0.0% 0.0% 0.0% 1.7% 0.0% 0.0% 0.6%

9 2.9% 0.6% 0.6% 0.0% 1.2% 0.6% 0.6% 1.7% 0.6% 0.0%

Tea

m 2

5

These 100 pairs are actually 55 unique combinations of scores (i.e., 9-5 and 5-9 would count as one pair), and of the 37 pairs that have occurred, 0-3-7 again dominate

11.6%

9.9%

7.6%

7.0%

5.8%

4.1%

3.5% 2.9%

2.3%

1.7% 1.2%

0.6%0.6%

0.0%

2.0%

4.0%

6.0%

8.0%

10.0%

12.0%

14.0%

0

5

10

15

20

25

0-7

0-3

3-7

0-0

4-7

0-4

7-7

3-6

3-4

3-3

0-6

0-9

6-7

0-5

0-2

0-8

1-5

1-7

6-8

1-4

0-1

2-7

7-9

6-6

4-9

4-6

2-9

1-3

1-6

1-9

2-4

2-8

5-9

6-9

8-9

1-8

% o

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# o

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ren

ces

Score Pair

Frequency of Score Pairs

Occurences %

The 2009 game benefitted

only people who had a good

shot of winning from the

start, since the winning pairs

were:

0-3, 7-7, 0-7, and 3-7

There was even a safety in

last year’s game but it is not

apparent from the end digits

6

At this point we are all trying to determine what combination of safeties, 2-point conversions, and missed extra points will yield our pairs – here is some additional data to help

There have been 1,954 total points scored through last year’s Superbowl…

…items to note:

– Safeties and 2-point conversions are very rare – 1.02% of scoring

– Touchdowns are followed by the single extra point 91.0% of the time – the single extra point is NOT really automatic because of misses and the newer 2 pt. conversion

– Field goals are not automatic either, with a 71.1% success ratio (thank you Scott Norwood)

– Touchdowns outpace field goals by a ratio of 2.2-to-1

* = “Extra Points” means the 1 pt. extra point kick, any 2 pt. conversions (attempted or made) would lower the maximum possible value of extra points

1,954

Total Points

233 212 108 6 4

Touchdowns Extra Points* Field Goals Safeties 2-Point Conv.

1,398 212 324 12 8

Points Points Points Points Points

7

The 2009 game had the first safety in 18 years; the first 2 pt. conversion occurred 13 years ago, and between them add a needed twist to pairs scoring

Game Year TD XP FG

FG

Attempt Safety 2-pt

2-pt

Attempt

Total

Points

I 1967 6 6 1 2 45

II 1968 5 5 4 5 47

III 1969 2 2 3 7 23

IV 1970 3 3 3 4 30

V 1971 3 2 3 4 29

VI 1972 3 3 2 3 27

VII 1973 3 3 2 21

VIII 1974 4 4 1 1 31

IX 1975 3 2 2 1 22

X 1976 4 3 3 5 1 38

XI 1977 6 4 2 3 46

XII 1978 4 4 3 6 37

XIII 1979 9 9 1 2 66

XIV 1980 6 5 3 3 50

XV 1981 4 4 3 5 37

XVI 1982 5 5 4 4 47

XVII 1983 5 5 3 3 44

XVIII 1984 6 5 2 3 47

XIX 1985 6 6 4 4 54

XX 1986 6 6 4 4 1 56

XXI 1987 7 6 3 5 1 59

XXII 1988 7 7 1 3 52

XXIII 1989 3 3 5 7 36

XXIV 1990 9 8 1 1 65

XXV 1991 4 4 3 4 1 39

XXVI 1992 7 7 4 4 61

XXVII 1993 9 9 2 2 69

XXVIII 1994 4 4 5 5 43

XXIX 1995 10 8 1 2 2 75

XXX 1996 5 5 3 3 44

XXXI 1997 7 6 2 2 1 56

XXXII 1998 7 7 2 2 55

XXXIII 1999 6 5 4 7 53

XXXIV 2000 4 3 4 7 39

XXXV 2001 5 5 2 3 41

XXXVI 2002 4 4 3 4 37

XXXVII 2003 9 6 3 3 69

XXXVIII 2004 8 5 2 4 1 61

XXXIX 2005 6 6 1 1 45

XL 2006 4 4 1 3 31

XLI 2007 5 4 4 5 46

XLII 2008 4 4 1 1 31

XLIII 2009 6 6 2 2 1 50

Number 233 212 108 152 6 4 TBD 1,954

Points 1,398 212 324 12 8 1,954

% of Scores 71.5% 10.8% 16.6% 0.6% 0.4% 100%

Success Rate 91.0% 71.1% TBD

8

Since Superbowls only represent a very small portion of games (and scoring), it would also help to use a full season of scores as a sample

For the 2002-2003 regular season, there were 32 NFL teams that played 16 games each…

– 256 games played

– 1,024 regulation quarters played plus 25 games went into overtime, for a grand total of 1,049 quarters played

In pool terms, this means…

– 1,049 pairs of scores

– 2,098 individual digits that occurred

The post-season was not included in the analysis

9

Single Digit Analysis revealed similar results to the Superbowls…

Frequency of Last Digits

27.9%

23.0%

15.5%

12.3%

6.5% 6.2%

2.8% 2.7%1.9%

1.2%

0

100

200

300

400

500

600

700

0 7 3 4 1 6 9 8 5 2

Digit

# o

f O

cc

ure

nc

es

(o

ut

of

2,0

98

)

0.0%

5.0%

10.0%

15.0%

20.0%

25.0%

30.0%

% o

f O

cc

ure

nc

es

Count %

Rank order for digits is

same as Superbowl

except for swap

of 1 and 6 &

5 and 2

10

…as did the Combination Analysis, with 0-3-7 displaying an even stronger tendency…

Frequency of Score Pairs

14.7%

8.9%

6.5%6.0%

5.6%

4.7%

3.6% 3.4%3.0%

2.4% 2.3% 2.3% 2.3% 2.2% 2.0%1.6% 1.5%

1.0% 1.0% 1.0% 1.0% 1.0%

9.8%

0

20

40

60

80

100

120

140

160

0-7

0-3

0-0

3-7

0-4

7-7

4-7

3-4

1-7

0-6

3-3

3-6

4-4

6-7

1-4

4-6

1-3

0-1

7-8

0-9

3-9

5-7

7-9

Score Pair

# o

f O

cc

ure

nc

es

(o

ut

of

1,0

49

)

0.0%

2.0%

4.0%

6.0%

8.0%

10.0%

12.0%

14.0%

% o

f O

cc

ure

nc

es

Occurences %

Pairs with a

probability of less

than 1% (9 or fewer

occurrences in 1,049

pairs) are not shown

on chart

11

…but the larger sample does prove that almost all pairs can really occur, albeit infrequently, and there are only a handful of “automatic losers”

0 1 2 3 4 5 6 7 8 9

0 8.9% 1.5% 0.6% 9.8% 6.0% 0.8% 3.0% 14.7% 0.9% 1.0%

1 1.5% 0.9% 0.3% 1.6% 2.2% 0.1% 0.7% 3.4% 0.8% 0.8%

2 0.6% 0.3% 0.0% 0.2% 0.4% 0.3% 0.1% 0.2% 0.0% 0.4%

3 9.8% 1.6% 0.2% 2.4% 3.6% 0.5% 2.3% 6.5% 0.8% 1.0%

4 6.0% 2.2% 0.4% 3.6% 2.3% 0.5% 2.0% 4.7% 0.6% 0.1%

5 0.8% 0.1% 0.3% 0.5% 0.5% 0.1% 0.1% 1.0% 0.2% 0.3%

6 3.0% 0.7% 0.1% 2.3% 2.0% 0.1% 0.6% 2.3% 0.3% 0.7%

7 14.7% 3.4% 0.2% 6.5% 4.7% 1.0% 2.3% 5.6% 1.0% 1.0%

8 0.9% 0.8% 0.0% 0.8% 0.6% 0.2% 0.3% 1.0% 0.4% 0.1%

9 1.0% 0.8% 0.4% 1.0% 0.1% 0.3% 0.7% 1.0% 0.1% 0.2%

Legend:

= Never occurred in 2002-03 Season Game

= Occurred 1 time in 2002-03 Season Game

= Occurrence > 5% in 2002-03

2-2, 2-8, and 8-2

are very bad draws

to say the least!

Note: Based on the 2002-2003 sample of over 1,000 pairs

12

Good Luck!

13

Appendix -- Superbowl Data 1967-present

# Date Team 1Q 2Q 3Q 4Q Final

XXVIII Jan. 30, 1994 Dallas 6 0 14 10 30

Buffalo 3 10 0 0 13

XXVII Jan. 31, 1993 Buffalo 7 3 7 0 17

Dallas 14 14 3 21 52

XXVI Jan. 26, 1992 Washington 0 17 14 6 37

Buffalo 0 0 10 14 24

XXV Jan. 27, 1991 Buffalo 3 9 0 7 19

Giants 3 7 7 3 20

XXIV Jan. 28, 1990 San Francisco 13 14 14 14 55

Denver 3 0 7 0 10

XXIII Jan. 22, 1989 Cincinnati 0 3 10 3 16

San Francisco 3 0 3 14 20

XXII Jan. 31, 1988 Washington 0 35 0 7 42

Denver 10 0 0 0 10

XXI Jan. 25, 1987 Denver 10 0 0 10 20

Giants 7 2 17 13 39

XX Jan. 26, 1986 Chicago 13 10 21 2 46

New England 3 0 0 7 10

XIX Jan. 20, 1985 Miami 10 6 0 0 16

San Francisco 7 21 10 0 38

XVIII Jan. 22, 1984 Washington 0 3 6 0 9

Raiders 7 14 14 3 38

XVII Jan. 30, 1983 Miami 7 10 0 0 17

Washington 0 10 3 14 27

XVI Jan. 24, 1982 San Francisco 7 13 0 6 26

Cincinnati 0 0 7 14 21

XV Jan. 25, 1981 Oakland 14 0 10 3 27

Philadelphia 0 3 0 7 10

# Date Team 1Q 2Q 3Q 4Q Final

XIV Jan. 20, 1980 Rams 7 6 6 0 19

Pittsburgh 3 7 7 14 31

XIII Jan. 21, 1979 Pittsburgh 7 14 0 14 35

Dallas 7 7 3 14 31

XII Jan. 15, 1978 Dallas 10 3 7 7 27

Denver 0 0 10 0 10

XI Jan. 9, 1977 Oakland 0 16 3 13 32

Minnesota 0 0 7 7 14

X Jan. 18, 1976 Dallas 7 3 0 7 17

Pittsburgh 7 0 0 14 21

IX Jan. 12, 1975 Pittsburgh 0 2 7 7 16

Minnesota 0 0 0 6 6

VIII Jan. 13, 1974 Minnesota 0 0 0 7 7

Miami 14 3 7 0 24

VII Jan. 14, 1973 Miami 7 7 0 0 14

Washington 0 0 0 7 7

VI Jan. 16, 1972 Dallas 3 7 7 7 24

Miami 0 3 0 0 3

V Jan. 17, 1971 Baltimore 0 6 0 10 16

Dallas 3 10 0 0 13

IV Jan. 11, 1970 Minnesota 0 0 7 0 7

KC 3 13 7 0 23

III Jan. 12, 1969 NY Jets 0 7 6 3 16

Baltimore 0 0 0 7 7

II Jan. 14, 1968 Green Bay 3 13 10 7 33

Oakland 0 7 0 7 14

I Jan. 15, 1967 KC 0 10 0 0 10

Green Bay 7 7 14 7 35

# Date Team 1Q 2Q 3Q 4Q Final

XLIII Feb. 1, 2009 Steelers 3 14 3 7 27

Cardinals 0 7 0 16 23

XLII Feb. 3, 2008 Giants 3 0 0 14 17

Patriots 0 7 0 7 14

XLI Feb. 4, 2007 Indianapolis 6 10 6 7 29

Chicago 14 0 3 0 17

XL Feb. 5, 2006 Seattle 3 0 7 0 10

Pittsburgh 0 7 7 7 21

XXXIX Feb. 6, 2005 New England 0 7 7 10 24

Philadelphia 0 7 7 7 21

XXXVIII Feb. 1, 2004 Carolina 0 10 0 19 29

New England 0 14 0 18 32

XXXVII Jan. 26, 2003 Oakland 3 0 6 12 21

Tampa Bay 3 17 14 14 48

XXXVI Feb. 3, 2002 St. Louis 3 0 0 14 17

New England 0 14 3 3 20

XXXV Jan. 28, 2001 Baltimore 7 3 14 10 34

NY Giants 0 0 7 0 7

XXXIV Jan. 30, 2000 St. Louis 3 6 7 7 23

Tennessee 0 0 6 10 16

XXXIII Jan. 31, 1999 Denver 7 10 0 17 34

Atlanta 3 3 0 13 19

XXXII Jan. 25, 1998 Green Bay 7 7 3 7 24

Denver 7 10 7 7 31

XXXI Jan. 26, 1997 New England 14 0 7 0 21

Green Bay 10 17 8 0 35

XXX Jan. 28, 1996 Dallas 10 3 7 7 27

Pittsburgh 0 7 0 10 17

XXIX Jan. 29, 1995 San Diego 7 3 8 8 26

San Francisco 14 14 14 7 49

14

All logos are property of the NFL and its member teams

15

All logos are property of the NFL and its member teams

16

All logos are property of the NFL and its member teams

17

All logos are property of the NFL and its member teams