Was John Adams more consistent his Junior or Senior
year of High School Wrestling?
An investigation into my Dad’s high school Wrestling Career
Amanda Adams
Period 1
Statistical Reasoning in Sports
December 16, 2013
Was Dad more consistent at scoring team points Senior Year than Junior Year?
2
Table of Contents
Introduction.......................................................................................................................................................3
Data tables..........................................................................................................................................................5
Dotplots...............................................................................................................................................................6
Raw Data................................................................................................................................................6
Deviations...............................................................................................................................................6
Mean Absolute Deviation...................................................................................................................................7
Standard Deviation.............................................................................................................................................8
Test Statistc......................................................................................................................................................9
Simulation...........................................................................................................................................................10
Dotplot..................................................................................................................................................10
Conclusion...........................................................................................................................................................11
Work Cited..........................................................................................................................................................13
Was Dad more consistent at scoring team points Senior Year than Junior Year?
3
Introduction
All my life, I’ve grown up knowing that my dad was a wrestler, and that he’d been a really good
wrestler. As I grew up, and my older brother grew up and started to wrestle, we all go to see just h0w
much he’d loved the sport. He coached my brother as early as he could start, from when my brother was in
7th grade. Through the 6 years that my brother wrestled we all got to hear the stories of Dad’s wresting
days and meet all the dads of wrestlers that had come back to the same tournaments. For this
investigation, I chose to look into my dad’s wrestling career, but he only has his stats from high school, so
unfortunately I could not continue the investigation into his college career.
We always knew dad was good, we remembered the story of his undefeated senior year, losing only
one match, his very last one, at league finals and taking second, unable to advance to CIF. He lost 2-3 to the
same guy who had beaten him his junior year.
I’ve always admired my dad for his dedication to everything he did. He didn’t have an easy life
growing up, but he was completely self motivated to excel at wrestling. He worked harder to achieve more
than anyone in high school that I know today and he taught us that same desire for success and hard work.
I got my stats from our attic, dad was more than happy to get them down for me and go ever
every single match, all the tournament brackets and all the opponents that he remembered -- a surprising
amount actually. He had all the stats from his junior and senior years of wrestling at Rowland High School,
with the exception of Masters his junior year. Junior year, he advanced all the way to masters, but
unfortunately, he had his only loss for senior year in the last match of league finals and took second the
Was Dad more consistent at scoring team points Senior Year than Junior Year?
4
year that the CIF rules changed to only allow first place to advance. It was a sad end to his high school
career to say the least.
He went on to wrestle in college, and again one more time at an open tournament that my brother
wrestled in (well after my dad was already 50) and decided he was done for good after breaking his finger in
the first period.
I chose to compare the varsity points (team Points) that he earned because it is the only
measurement that gives a numerical value to a pin, rather than using points that he scored or points scored
on him because that makes it so that there is no numerical value for a pin.
Null Hypothesis: Dad had the same true Standard deviation of team points scored his junior and
sophomore years of wrestling in high school.
Alternative Hypothesis: Dad had a smaller true Standard deviation of team points scored his senior
year than his junior year.
Was Dad more consistent at scoring team points Senior Year than Junior Year?
5
Data Table
Junior Year (1974-1975)
Date
Score
Dec 3, 1974
Dec 5, 1974
Dec 9, 1974
Dec 20-21, 1974
Dec 20-21, 1974
Dec 20-21, 1974
Dec 20-21, 1974
Jan 9, 1975
Jan 16, 1975
Jan 21, 1975
Jan 23, 1975
Jan 30, 1975
Feb 6, 1975
Feb 13, 1975 League Finals (1st Place)
Feb 13, 1975
Feb 13, 1975
Feb 15, 1975 CIF (4th Place)
Feb 15, 1975
Feb 15, 1975
Feb 15, 1975
Feb 15, 1975
Feb 15, 1975
:14 Pin
10-2
8-5
6-8
5-0
Pin
0-4
5-11
9-3
1:05 Pin
:30 Pin
0-2
5-3
3-0
11-0
11-0
5:45 Pin
3:09 Pin
10-2
2:30 Pin
9-1
5-4
Senior Year (1975-1976)
Varsity
Points
6
3
3
1
3
6
1
1
3
6
6
1
3
3
4
4
6
0
3
6
3
1
Date
Score
Nov 26, 1975
Dec 4, 1975
Dec 8, 1975
Dec 11, 1975
Dec 19-20, 1975 Tournament (1st)
Dec 19-20, 1975
Dec 19-20, 1975
Dec 19-20, 1975
Dec 19-20, 1975
Jan 8, 1976
Jan 15, 1976
Jan 20, 1976
Jan 29, 1976
Feb 5, 1976
Feb 10, 1976
Feb 17, 1976 League Finals (2nd)
Feb 17, 1976
Feb 17, 1976
16-0
4:30 Pin
16-8
5-5
14-1
7-0
10-6
Pin
2-1
1:45 Pin
4:35 Pin
13-0
:44 Pin
11-0
5-3
9-1
12-4
2-3
Varsity
Points
5
6
4
2
5
3
3
6
3
6
6
5
6
1
1
8
8
2
Was Dad more consistent at scoring team points Senior Year than Junior Year?
6
Dotplots
Raw Data
Team Points Scored
Senior Year
Mean
Median
Junior Year
0
1
2
3
4
5
6
7
8
9
Deviations
Deviations (Data - Mean)
Senior Year
Mean
Median
Junior Year
-4.00
-3.00
-2.00
-1.00
0.00
1.00
2.00
3.00
4.00
The raw data dotplot shows an uneven distribution of points between the scores. The data is not skewed
either direction, but not quite symmetrical. The senior year mean and median are higher than the junior year
mean and median and there are no outliers for either distribution. Both have the same range, but the senior
year distribution is higher than the junior year one. For the deviations graph, both distributions are similar
in that they have a peak, but most of the data is evenly spread out making it difficult to determine how
many peaks it has. The positive values on the deviation dotplot mean that he performed higher than the
average and the negative values mean that he performed lower than the average.
Was Dad more consistent at scoring team points Senior Year than Junior Year?
7
Mean Absolute Deviation
Junior Year
Mean: 3.32
Deviations:
6-3.32= 2.68
3-3.32= -0.32
3-3.32= -0.32
1-3.32= -2.32
Absolute Value
2.68
0.32
0.32
2.32
3-3.32=
6-3.32=
1-3.32=
1-3.32=
-0.32
2.68
-2.32
-2.32
0.32
2.68
2.32
2.32
3-3.32=
6-3.32=
6-3.32=
1-3.32=
-0.32
2.68
2.68
-2.32
0.32
2.68
2.68
2.32
3-3.32=
3-3.32=
4-3.32=
4-3.32=
-0.32
-0.32
0.68
0.68
0.32
0.32
0.68
0.68
6-3.32=
0-3.32=
3-3.32=
6-3.32=
2.68
2.68
-0.32
2.68
3-3.32= -0.32
1-3.32= -2.32
2.68
3.32
0.32
2.68
0.32
2.32
Mean Absolute deviation: 1.527
Senior Year
Mean: 4.35
Deviations:
5-4.35= 0.65
6-4.35= 1.65
4-4.35= -0.35
2-4.35= -2.35
Absolute Value
0.65
1.65
0.35
2.35
5-4.35=
3-4.35=
3-4.35=
6-4.35=
0.65
1.35
1.35
1.65
Mean Absolute Deviation: 1.862
0.65
-1.35
-1.35
1.65
3-4.35=
6-4.35=
5-4.35=
6-4.35=
1.35
1.65
0.65
1.65
-1.35
1.65
0.65
1.65
1-4.35=
1-4.35=
8-4.35=
8-4.35=
3.35
3.35
3.65
3.65
-3.35
-3.35
3.65
3.65
2-4.35= -2.35
2.35
Was Dad more consistent at scoring team points Senior Year than Junior Year?
8
Standard Deviation
Junior Year
Mean: 3.32
Deviations:
6-3.32= 2.68
3-3.32=
3-3.32= -0.32 6-3.32=
3-3.32= -0.32 1-3.32=
1-3.32= -2.32
1-3.32=
Squared Deviations:
7.19
0.10
0.10
5.37
-0.32
2.68
-2.32
-2.32
0.10
7.19
5.37
5.37
3-3.32=
6-3.32=
6-3.32=
1-3.32=
-0.32
2.68
2.68
-2.32
0.10
7.19
7.19
5.37
3-3.32=
3-3.32=
4-3.32=
4-3.32=
-0.32
-0.32
0.68
0.68
0.10
0.10
0.46
0.46
6-3.32=
0-3.32=
3-3.32=
6-3.32=
2.68
2.68
-0.32
2.68
3-3.32= -0.32
1-3.32= -2.32
7.19
11.01
0.10
7.19
0.10
5.37
Standard Deviation: 1.985
Senior Year
Mean: 4.35
Deviations:
5-4.35= 0.65
6-4.35= 1.65
4-4.35= -0.35
2-4.35= -2.35
Squared Deviations:
0.42
2.71
0.12
5.54
5-4.35=
3-4.35=
3-4.35=
6-4.35=
0.42
1.83
1.83
2.71
Standard Deviation: 2.206
0.65
-1.35
-1.35
1.65
3-4.35=
6-4.35=
5-4.35=
6-4.35=
1.83
2.71
0.42
2.71
-1.35
1.65
0.65
1.65
1-4.35=
1-4.35=
8-4.35=
8-4.35=
11.24
11.24
13.30
13.30
-3.35
-3.35
3.65
3.65
2-4.35= -2.35
5.54
Was Dad more consistent at scoring team points Senior Year than Junior Year?
9
Test Statistic
Difference in Standard Deviations:
Senior year (2.206) - Junior Year (1.985) = 0.221
Test Statistic: 0.221
A positive test statistic means that senior year had a greater standard deviation than junior. To calculate
the test statistic I subtracted senior year’s standard deviation from junior year’s.
Notecard Simulation
With 42 notecards, label each with a point value, shuffle and deal into two piles, one with 18, one with 22 for
each year. Calculate the standard deviation of each pile and subtract senior year from junior year. Plot each
value on a dotplot and repeat 100 times for accuracy.
Was Dad more consistent at scoring team points Senior Year than Junior Year?
10
Simulation
Simulated Difference in Standard Deviation Senior - Junior Year
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
The dotplot is fairly symmetrical, definitely unimodal, with no outliers. It has a range of less than 2, and a
mean and median around zero. The P-value is 31%, with 31 trials of the simulation falling above the test
statistic of 0.221. This means that 31% of the time, the standard deviation of his performance will differ from
junior to senior year by 0.221 about 31% of the time. The positive values on the dotplot mean that his
standard deviation from junior year was larger than his senior. The minimum of the dotplot is -0.8 and the
maximum is 0.8 the mean is 0.0299 and the median is 0.
1
Was Dad more consistent at scoring team points Senior Year than Junior Year?
11
Conclusion
Because the p-value is so large, we cannot reject the null hypothesis. Therefore; we support the null
and thus it is plausible that dad’s true standard deviation Senior year was the same as Junior year. I believe
this is a type 2 error, because both my dad and I think that he performed better, and more consistently
senior year than junior. This may be due to the fact that scoring points in wrestling is not the best
measure of consistency. More realistically, I realized that my investigation probably would have been better if
I had treated the data as categorical instead of numerical, but I was curious to see what conclusion would
come of using point values as the measurement. The reason that this did not measure his 15-2-1 season as
more consistent than his 15-6-0 season is because there are more point values given for a pin than just a
win which offsets the data to count some wins as more than others, and some losses count as more than
others depending on how many points were scored.
I chose to use the team points scored as my testing variable because it was the only one that gave
numerical value to a pin, but it turned out to not work as well as I had hoped. Another error that may have
caused junior year to be more consistent than senior is that one of the scores on the old paper that I was
copying the statistics from was odd in that the dates were out of order, and it was another loss when
dad’s record was only one loss his senior year. I later asked him why the match was there and he couldn’t
remember why the loss was recorded so I left it where it was in the investigation since it was written on
the paper, but it’s still kind of a mystery match.
One last reason that the point values were not an accurate measure is because at the end of senior
year in league finals, one of the varsity wrestlers realized that he didn’t have and wasn’t able to get enough
Was Dad more consistent at scoring team points Senior Year than Junior Year?
12
varsity points to earn his letter, but the coach really thought he deserved it so he inflated the point value
of a win to 8 points because it was league finals and this greatly threw off the consistency of all of dad’s
season. As an experiment, I changed the two 8 point values down to 3 for a win and re calculated the
standard deviation, as anticipated, this lowered his standard deviation to less than junior year. Rather than
changing my investigation to reflect this, I left it so that we could see the authentic result of the actual
points that he got.
Hopefully, since this investigation did not turn out as accurately as I had hoped, there will be a
future opportunity to investigate my dad’s wrestling career.
Was Dad more consistent at scoring team points Senior Year than Junior Year?
13
Work Cited
"Statistical Reasoning in Sports." Statistical Reasoning in Sports. W H Freeman & Company, n.d. Web. 19 Dec.
2013.