Really, the issue of protection is yet another baseball anomaly. That is, it makes perfect sense in reality, but not on paper. For instance, you have a runner on 2nd, Braun up. Normally the pitcher would think, "I'll go after the hitter, but giving him nothing fat. That way, if I walk him, it sets up the double play. But maybe I'll get him to fish for something." But when Prince is the guy on deck, that has to change the thought process a bit. Now the pitcher has to go after Braun with some meatier pitches, trying to entice an out. He no longer is willing to risk nibbling and walking Braun. So on a micro-level, protection exists, just as batting order can be significant. But on a macro level, the variances are so minute that they cannot be proven as statistically significant