I'll never agree. I disagree completely with your larger sample size averages evening out.
2006 playoffs Spurs Vs Mavs - Brent Barry didn't want to shoot the ball at times in games where we needed him to. He wanted nothing to do with it (even though he's one of the best shooters in the NBA), he didn't want to shoot the ball. I wanted him traded because of him not shooting the ball. He looked scared to at times. Usually, that was in big games.
2011 NBA finals. Lebron James pissed his pants in the 4th quarters of pretty much all those games. Lebron James also looked scared for quite a few years in Cleveland during crunch time and didn't want to shoot the ball with the game on the line numerous times over the years. It's taken him years to improve on that and get over it. Flip that over to Kobe Bryant. The guy never showed any fear taking big shots from the get go with the game on the line. He might not have made many of them, but he shot them with no fear at all since day one of him being in the NBA.
2013 NBA finals. I hate saying this one, but where is that picture of Kawhi? Does he not look scared before shooting those free throws?