Did Fred McGriff make a
difference in the average
number of runs scored per
game?
Background:
Did Fred McGriff make a difference in the number of runs scored by the Atlanta Braves? Did
the Braves score significantly less runs when Fred McGriff did not play? Atlanta fans were
concerned when Fred McGriff was acquired for 3 younger and cheaper players. He was a highpriced veteran from San Diego and the fans were unsure if the price tag was worth it. Statistics
were recorded and collected for the season.
Methodology:
The number of runs scored by the Atlanta Braves was recorded throughout the entire 1993
season. The first 94 games were without Fred McGriff and the final 68 games had Fred McGriff
on the roster. This data can be found in figure 1.
Results:
A quick check of the box-whisker plots showed that there appear to be differences in the medians
of the runs scored with and without McGriff (Fig. 2). This preliminary observation must be
tested statistically. Because the sample size of the games played for each type is large (more
than thirty) a large sample, two independent groups, z-test was used to determine if the runs
scored with and without McGriff are statistically significant. We do not need to check for
normality since both sample sizes are more than 30.
The statistics for the two groups (Fig. 3) shows that the means are very different (3.99 without
McGriff and 5.78 with McGriff), as well as differences in the standard deviations (3.07 without
and 3.81 with McGriff). The z-test for the two groups shows there is a difference between the
runs scored with and without McGriff. The runs scored without McGriff is significantly fewer
than the runs scored with him (z = -3.19, p = .0018) (Fig. 4)
The confidence intervals (Fig. 5 & 6) shows that there is no overlap between the intervals with
and without McGriff, so there is a difference in runs scored. We are 95% confident that the
average runs scored with McGriff is between 3.36 and 4.62 and the average runs scored without
is between 4.86 and 6.7.
Conclusion and Discussion:
The average runs scored with McGriff are higher than the average runs scored without him
(p=.0018). Based solely on run production, Fred McGriff had an impact on the Atlanta Braves
team throughout the 1993 season. Further studies can look into the number of wins the Braves
had with and without McGriff because more run support does not always mean more wins.
Fig. 1
Fig. 2
With McGriff
8
14
7
6
11
13
12
10
3
0
4
4
3
3
9
4
2
3
3
3
4
8
14
4
1
3
5
5
3
6
4
5
6
9
7
6
8
8
2
5
7
3
3
1
1
8
1
3
13
4
10
7
3
2
2
11
18
1
6
0
9
7
2
6
8
7
10
5
Box Plot
Collection 1
With_McGriff
9
4
2
5
1
4
5
8
3
3
8
6
0
6
3
4
2
11
4
9
4
1
1
5
2
6
4
3
3
2
0
Without_McGriff
Without McGriff
1
8
0
12
5
2
6
5
2
5
1
10
3
5
1
4
3
5
0
0
1
1
0
4
2
1
12
2
5
5
7
0
3
4
3
7
11
3
3
3
3
2
2
1
1
5
5
4
3
4
3
1
4
2
3
4
1
4
13
1
13
6
7
0
2
4
6
8
10
12
14
16
18
20
Fig. 3
Collection 1
Without_McGriff With_McGriff
3.98936
5.77941
94
68
3.07433
3.81609
S1 = mean
S2 = count
S3 = stdDev
Fig. 4
Test of Collection 1
Compare Means
First attribute (numeric): Without_McGriff
Second attribute (numeric or categorical): With_McGriff
Sample count of Without_McGriff: 94
Sample count of With_McGriff: 68
Sample mean of Without_McGriff: 3.98936
Sample mean of With_McGriff: 5.77941
Standard deviation of Without_McGriff:
3.07433
Standard deviation of With_McGriff: 3.81609
Standard error of the mean of
Without_McGriff: 0.317093
Standard error of the mean of With_McGriff:
0.462769
Alternative hypothesis: The population mean of
Without_McGriff is not equal to that of
With_McGriff
The test statistic, Student's t, using unpooled
variances , is -3.191. There are 124.855
degrees of freedom.
If it w ere true that the population mean of
Without_McGriff w ere equal to that of
With_McGriff (the null hypothesis), and the
sampling process w ere performed repeatedly,
the probability of getting a value for Student's t
w ith an absolute value this great or
greater w ould be 0.0018.
Fig. 5
Estimate of Collection 1
Fig. 6
Estimate Mean
Attribute (numeric): With_McGriff
Estimate of Collection 1
Estimate Mean
Attribute (numeric): Without_McGriff
Interval estimate for population mean of
With_McGriff
Interval estimate for population mean of
Without_McGriff
Sample count: 68
Sample mean: 5.77941
Standard deviation: 3.81609
Standard error: 0.462769
Sample count: 94
Sample mean: 3.98936
Standard deviation: 3.07433
Standard error: 0.317093
Based on the sample, the 95.0 % confidence
interval for the population mean of
With_McGriff is 5.77941 plus or minus
0.923691, ranging from 4.85572 to 6.7031.
Based on the sample, the 95.0 % confidence
interval for the population mean of
Without_McGriff is 3.98936 plus or minus
0.629683, ranging from 3.35968 to 4.61905.
If the sampling process w ere performed
repeatedly, the confidence intervals generated
w ould capture the population mean 95.0 % of
the time.
If the sampling process w ere performed
repeatedly, the confidence intervals generated
w ould capture the population mean 95.0 % of
the time.