Table 11 – Statistical Analysis of the Baseball Models
Measure
|
Model
|
SD
|
SD = 0.067 + 0.018ET* + 0.009YT* - 0.006LT + 0.008RS
|
NSD
|
NS = 1.704 + 0.463ET* + 0.219YT* - 0.163LT + 0.191RS
|
GC
|
GC = 0.074 + 0.019ET* + 0.009YT* - 0.008LT + 0.010RS
|
HHI
|
HH = 0.042 + 0.000ET + 0.003YT + 0.001LT - 0.009RS*
|
FCCR
|
FC = 0.241 + 0.008ET + 0.018YT + 0.002LT - 0.044RS*
|
Table 12 – Baseball Models
Key:
ET – Expansion Team
YT – Young Team
LT – Luxury Tax
RS – Revenue Sharing
Using the measures SD, NSD and GC the existence of the Luxury Tax is the only variable that has a negative sign. This suggests that the Luxury Tax initiative does improve CB in Baseball although the significance level of the Luxury tax variable is low. The other variables all have positive signs suggesting that they have an adverse effect on CB. That is to say that when an expansion occurs or just after an expansion occurs CB is reduced. The anomaly is the Revenue Sharing variable which has a positive sign and therefore appears to reduce CB.
However, using the HHI or the FCCR measures it is the revenue sharing variable that has the negative sign and therefore appears to improve CB whereas the other variables have positive signs, albeit with low absolute values for the HHI model and low absolute values for the FCCR model excluding the existence of a Young Team.
In the models using the measures SD, NSD and GC the constant and the two variables relating to the existence of an expansion team or a young team are all significant. This is in contrast to the models using the HHI or the FCCR where only the constant and the variable relating to the existence of the revenue sharing agreement are significant.
The collinearity of the variables was examined via the tolerance measure statistic as described in section 3.9. In all cases the tolerance values were well above the 0.1 threshold, mainly in the range 0.3-0.5. This was repeated for all models across all sports and as such will not be mentioned again in this study since it is clear that the variables are not collinear.
4.4.2 NBA (Basketball)
Dependent_Variable___Mean___Standard_Deviation'>Dependent Variable
|
Mean
|
Standard Deviation
|
SD
|
0.152
|
0.023
|
NSD
|
2.752
|
0.419
|
GC
|
0.167
|
0.026
|
HHI
|
0.057
|
0.027
|
FCCR
|
0.350
|
0.142
|
Table 13 – Dependent Variables used in Basketball Models
Explanatory Variable
|
Mean
|
Expansion Team
|
0.23
|
Young Team
|
0.40
|
Low Salary Cap
|
0.23
|
Medium Salary Cap
|
0.11
|
High Salary Cap
|
0.17
|
Table 14 – Explanatory Variables used in Basketball Models
Dependent
|
Explanatory
|
Coefficient
|
t-Statistic
|
Significance
|
SD
|
Constant
|
0.137 *
|
22.079
|
.000
|
Expansion Team
|
0.012
|
1.595
|
.118
|
Young Team
|
0.009
|
1.422
|
.163
|
Low Salary Cap
|
0.017 *
|
2.118
|
.040
|
Medium Salary Cap
|
0.031 *
|
2.882
|
.006
|
High Salary Cap
|
0.007
|
0.749
|
.458
|
NSD
|
Constant
|
2.473 *
|
22.193
|
.000
|
Expansion Team
|
0.218
|
1.615
|
.114
|
Young Team
|
0.173
|
1.459
|
.152
|
Low Salary Cap
|
0.320 *
|
2.202
|
.033
|
Medium Salary Cap
|
0.565 *
|
2.955
|
.005
|
High Salary Cap
|
0.133
|
0.813
|
.421
|
GC
|
Constant
|
0.149 *
|
21.707
|
.000
|
Expansion Team
|
0.011
|
1.313
|
.196
|
Young Team
|
0.011
|
1.529
|
.134
|
Low Salary Cap
|
0.023 *
|
2.544
|
.015
|
Medium Salary Cap
|
0.039 *
|
3.276
|
.002
|
High Salary Cap
|
0.012
|
1.181
|
.244
|
HHI
|
Constant
|
0.074 *
|
11.798
|
.000
|
Expansion Team
|
0.006
|
0.752
|
.456
|
Young Team
|
-0.001
|
-0.195
|
.847
|
Low Salary Cap
|
-0.031 *
|
-3.787
|
.000
|
Medium Salary Cap
|
-0.036 *
|
-3.338
|
.002
|
High Salary Cap
|
-0.037 *
|
-4.084
|
.000
|
FCCR
|
Constant
|
0.434 *
|
13.295
|
.000
|
Expansion Team
|
0.031
|
0.784
|
.437
|
Young Team
|
-0.002
|
-0.045
|
.965
|
Low Salary Cap
|
-0.159 *
|
-3.740
|
.001
|
Medium Salary Cap
|
-0.189 *
|
-3.378
|
.002
|
High Salary Cap
|
-0.198 *
|
-4.133
|
.000
|
Table 15 – Statistical Analysis of Basketball Models
Again there is consistency between the models for the SD, NSD and GC measures. In each the Low and Medium salary cap variables are significant while the other variables are not significant.
The coefficients of all the variables are positive suggesting that they have an adverse effect on CB. This is intuitively correct for the Expansion and Young team variables but counter intuitive for the variables that relate to league measures introduced to improve CB.
There is also consistency between the models for the HHI and FFCR measures. All three salary cap variables are significant and have negative signs. The Young team variable has a negative sign in both but is not statistically significant. The Expansion team variable is the only one with a positive sign but that isn’t significant either.
As can be seen there are significant differences between the HHI, FCCR measures and the other three. Different variables are significant and have different signs.
4.4.3 NFL (American Football)
Dependent Variable
|
Mean
|
Standard Deviation
|
SD
|
0.197
|
0.023
|
NSD
|
1.552
|
0.161
|
GC
|
0.218
|
0.027
|
HHI
|
0.040
|
0.003
|
FCCR
|
0.269
|
0.022
|
Table 16 – Dependent Variables in American Football Models
Explanatory Variable
|
Mean
|
Expansion Team
|
0.11
|
Young Team
|
0.24
|
Low Salary Cap
|
0.32
|
High Salary Cap
|
0.08
|
Free Agency Plan B
|
0.11
|
Free Agency Plan A
|
0.43
|
Balanced Schedule
|
0.30
|
Table 17 – Explanatory Variables used in American Football Models
Dependent
|
Explanatory
|
Coefficient
|
t-Statistic
|
Significance
|
SD
|
Constant
|
0.203 *
|
32.741
|
.000
|
Expansion Team
|
-0.003
|
-0.186
|
.854
|
Young Team
|
0.002
|
0.143
|
.887
|
Low Salary Cap
|
0.030
|
1.091
|
.284
|
High Salary Cap
|
0.042
|
1.356
|
.185
|
Free Agency Plan B
|
-0.001
|
-0.100
|
.921
|
Free Agency Plan A
|
-0.043
|
-1.753
|
.090
|
Balanced Schedule
|
-0.004
|
-0.261
|
.796
|
NSD
|
Constant
|
1.581 *
|
36.513
|
.000
|
Expansion Team
|
-0.049
|
-0.483
|
.633
|
Young Team
|
0.010
|
0.132
|
.896
|
Low Salary Cap
|
0.248
|
1.293
|
.206
|
High Salary Cap
|
0.335
|
1.556
|
.130
|
Free Agency Plan B
|
0.035
|
0.377
|
.709
|
Free Agency Plan A
|
-0.296
|
-1.743
|
.092
|
Balanced Schedule
|
-0.030
|
-0.299
|
.767
|
GC
|
Constant
|
0.225 *
|
31.033
|
.000
|
Expansion Team
|
-0.002
|
-0.144
|
.886
|
Young Team
|
0.003
|
0.264
|
.793
|
Low Salary Cap
|
0.030
|
0.941
|
.354
|
High Salary Cap
|
0.041
|
1.145
|
.261
|
Free Agency Plan B
|
-0.001
|
-0.093
|
.927
|
Free Agency Plan A
|
-0.046
|
-1.606
|
.119
|
Balanced Schedule
|
-0.003
|
-0.162
|
.873
|
HHI
|
Constant
|
0.043 *
|
74.408
|
.000
|
Expansion Team
|
-0.001
|
-0.682
|
.501
|
Young Team
|
-0.001
|
-0.596
|
.556
|
Low Salary Cap
|
-0.001
|
-0.376
|
.709
|
High Salary Cap
|
-0.002
|
-0.753
|
.457
|
Free Agency Plan B
|
-0.001
|
-1.175
|
.250
|
Free Agency Plan A
|
-0.004
|
-1.569
|
.128
|
Balanced Schedule
|
-0.001
|
-0.796
|
.433
|
FCCR
|
Constant
|
0.285 *
|
62.589
|
.000
|
Expansion Team
|
-0.008
|
-0.788
|
.437
|
Young Team
|
-0.003
|
-0.314
|
.756
|
Low Salary Cap
|
-0.000
|
-0.011
|
.991
|
High Salary Cap
|
-0.006
|
-0.282
|
.780
|
Free Agency Plan B
|
-0.010
|
-1.019
|
.316
|
Free Agency Plan A
|
-0.026
|
-1.432
|
.163
|
Balanced Schedule
|
-0.004
|
-0.365
|
.718
|
Table 18 – Statistical Analysis of American Football Models
There are no significant variables in any model. This suggests that all the initiatives and effects examined do not significantly influence the CB of the NFL. The strongest variable throughout is the Free Agency Plan A variable.
The HHI and FCCR models are very similar in that all coefficients are negative. The SD, NSD and GC models have the same signs for all their variables with the exception of Free Agency Plan B which is positive for the NSD model and negative (albeit very small) for the other two models.
4.4.4 NHL (Ice Hockey)
Dependent Variable
|
Mean
|
Standard Deviation
|
SD
|
0.115
|
0.026
|
NSD
|
2.062
|
0.451
|
GC
|
0.124
|
0.028
|
HHI
|
0.052
|
0.016
|
FCCR
|
0.313
|
0.094
|
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