A study by Bradley, Lago-Peñas and Rey entitled "Evaluation of the Match Performances of Substitution Players in Elite Soccer" was published in the International Journal of Sports Physiology and Performance in 2014.
It noted that substitutions were found to offer the benefit of enhancing the team's physical performance efficiency, thereby contributing to positive game outcomes.
It also noted that substitutions have positively affected the match outcome and goal difference in matches played.
In addition to the above, a study by Myers in 2012 entitled "A Proposed Decision Rule for the Timing of Soccer Substitutions" published in the Journal of Quantitative Analysis in Sports noted that substitutes also enhance the performance of players who have completed an entire match. Amongst other stats, substitutes were reported to exhibit a higher total distance covered and number of sprints relative to their playing time, allowing a team to sustain a higher level of physical output throughout an entire match.
Proof enough?