That may seem like "common sense", but the results don't bear it out.
I could've sworn that "The Book" had a section on protection, but I can't seem to find it. At any rate,
Baseball Between the Numbers does, in the chapter dealing with lineup order titled "Was Billy Martin Crazy?"
They first show a graph of the performance of all players in 2004 that hit ahead of low-quality hitters, medium-low quality hitters, medium quality hitters, medium-high quality hitters, and high quality hitters. They show average, on-base percentage, slugging percentage, walk rate, and intentional walk rate, but for simplicity's sake, I'll just show the OPS:
Hitting in front of ___ quality hitters;
Low: .728
Med-low: .744
Med: .764
Med-high: .777
High: .796
At first glance, this would "confirm" the existence of protection. However, as the book goes on to note, there's serious problems with such a study. Lineups tend to be grouped by ability. The best hitters bat at the top or in the middle, and the worst hitters bat at the bottom. Therefore, players who bat in front of high quality hitters are more likely to be high quality hitters themselves. So, when you look at the performance of ALL players depending on who hit behind them, you're going to see a higher quality of performance from players ahead of high quality hitters simply because the methods of lineup construction will more often than not place high quality hitters in front of high quality hitters.
They correct for this, however, by comparing those numbers to what we'd expect the batters to do based on their overall season numbers. After doing that, rather than a steady upward progression, there's little chance in performance. Below is a chart of the change in OPS depending on the quality of the next hitter in the order.
Low: .008
Med-low: -.002
Med: -.002
Med-high: .010
High: -.013
There's no pattern at all here, and very little change in OPS depending on the next batter. As the chapter concludes on the protection issue:
"Protection is overrated. There's no evidence that having a superior batter behind another batter provides the initial batter with better pitches to hit; if it does, those batters see no improvement in performance as a result."
There's numerous other studies all over the internet that you can turn up with simple Google searches. If you're interested, I'd be happy to link to further ones.