# Impact of One Additional Substitution on Player Load and Coaching Tactics in Elite Football
## 3 Results  
### Evaluation of TOS  
For an overview, all the results are presented in Table 1. Our analysis showed that the overall average TOS of the matches with three substitutions (\(M_{\text{TOS}}\) = 71.25, \(SD\) = 14.85) was significantly higher than in matches with four substitutions (\(M_{\text{TOS}}\) = 67.03, \(SD\) = 15.94), \(U\) = 1,326,910.00, \(Z\) = \(-\)7.486, \(p\) < 0.001, \(\eta^{2}\) = 0.018. The average TOS of the first three substitutions in matches with a substitution contingent of three (\(M_{\text{TOS}}\) = 71.25, \(SD\) = 14.85) was significantly higher than in matches with a substitution contingent of four (\(M_{\text{TOS}}\) = 63.66, \(SD\) = 15.57), \(U\) = 652,170.00, \(Z\) = \(-\)13.037, \(p\) < 0.001, \(\eta^{2}\) = 0.061. Additionally, each substitution was made significantly earlier in matches with four substitutions with an increasing effect size. The first substitution in matches with a substitution contingent of four (\(M_{TOS1}=51.78\), \(SD=14.61\)) was significantly earlier than in matches with three substitutions (\(M_{TOS1}=56.45\), \(SD=14.31\)) with a small effect size, \(U=77\),220.50, \(Z=-7.866\), \(p<0.001\), \(\eta^{2}=0.064\). The second substitution in matches with a substitution contingent of four (\(M_{TOS2}=65.86\), \(SD=11.73\)) was significantly earlier than in matches with three substitutions (\(M_{TOS2}=72.96\), \(SD=10.73\)) with a small effect size, \(U=70\),440.00, \(Z=-9.152\), \(p<0.001\), \(\eta^{2}=0.089\). The third substitution in matches with a substitution contingent of four (\(M_{TOS3}=74.19\), \(SD=10.93\)) was significantly earlier than in matches with three substitutions (\(M_{TOS3}=83.02\), \(SD=7.08\)) with a moderate effect size, \(U=45\),162.00, \(Z=-12.270\), \(p<0.001\), \(\eta^{2}=0.173\). The overall utilisation rate of the matches with three substitutions (\(M_{UR}=95.37\%\), \(SD=21.02\%\)) was significantly higher than in matches with four substitutions (\(M_{UR}=89.90\%\), \(SD=30.14\%\)), \(U=1,263\),542.00, \(Z=-6.085\), \(p<0.001\), \(\eta^{2}=0.011\). The utilisation rate of the first three substitutions did not differ between matches with a substitution contingent of three (\(M_{UR}=95.37\%\), \(SD=21.02\%\)) and matches with a substitution contingent of four (\(M_{UR}=96.52\%\), \(SD=18.34\%\)), \(U=990\),930.00, \(Z=-1.500\), \(p=0.134\), \(\eta^{2}=0.002\). The resulting average number of substitutions was 2.86 in Bundesliga and 3.60 in U-19 Bundesliga matches. The \(rISC\) was calculated at 25.87% Equation (8) and is higher than the actual share of the added substitution in the substitution contingent (25%). Therefore, the additional substitution in regular time was assessed as beneficial towards the tactical influence of coaches on the match. The results of the utilisation rate per substitution showed no differences between matches with a substitution contingent of three and four. Nearly all (99.84%, 611/612) of the first substitutions, 98.37% (602/612) of the second substitutions, and 87.91% (538/612) of the third substitutions were used in matches with substitution contingent of three. Nearly all (99.18%, 361/364) of the first and the second substitutions, 91.71% (332/364) of the third substitutions, and 70.05% (255/364) of the fourth substitutions were used in matches with a substitution contingent of four. The relative load reduction per substitution was calculated at 2.37% in Equation (2), resulting in the relative load reduction of 6.79% in Equation (3) for every match with three substitutions. For matches with a substitution contingent of four, the relative load reduction per substitution was 2.82%, resulting in the relative load reduction of 10.15% per match. In comparison, the calculated increase in load reduction in Equation (7) indicated an increase of 49.63% with the additional substitution in regular time, which is higher than the calculated relative increase of the substitution contingent of 25.87%. Therefore, the additional substitution in regular time was assessed as beneficial towards load reduction.