Brown says he is relishing the opportunity to make an impact in the latter stages of games, such as his outstanding second-half performance in the win over Toulouse last month.
"I think you see the way that the game in world rugby is going at Test level and at club level, South Africa probably hit headlines for it with their bomb squad, their ability to roll off six, seven world-class forwards off the bench to see out a game," Brown told BBC Sport Scotland .
"That's coming to the game more. Traditionally it was probably best players starting, then a second team coming on.
"I do genuinely think that the game is shifting. Those last 20-30 minutes are really important.
"It's something that I take pride in. It would be easy for someone to be upset they're not starting and kick your heels, but I've definitely felt as much a part of the wins in the past few weeks as I was starting and I think you have such an important role to play coming off the bench."