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Jesse, of BlueBird Banter, wrote an article about whether lineup protection does exist, but he took a different look at it. Instead of looking at protecting batters ahead of a player, Jesse attempted to see if a player can protect a batter behind him. You can read that here.
However, I decided to approach the question of lineup protection from a different angle. What about the effects that a good hitter might have on the hitters behind him? Can a player improve his lineup simply by getting on base? Is the average hitter better with runners on than with the bases empty? If so, how much? I used a sample of all Fangraphs "qualified batters" by splits for runners on, bases empty, and runners in scoring position, a total of 136 batters (there should be more but I realized Fangraphs had some players missing for some reason -- this should not be a worry unless the players who were missing differed from the overall population as a whole -- I don't think they did so this sample should be valid). Here are the results:
wRC+ with Bases Empty wRC+ with Runners On
Min. : 31.0 Min. : 57.00
1st Qu.: 87.0 1st Qu.: 99.75
Median :104.0 Median :118.00
Mean :107.1 Mean :117.03
3rd Qu.:126.0 3rd Qu.:131.25
Max. :183.0 Max. :175.00
Based on the sample it appears that hitters do in fact perform better when runners are base, as opposed to when the bases are empty.
The difference in the median wRC+ was 104 compared to 118, that equates to the 2012 season of Derek Jeter and the 2012 season of B.J. Upton. The mean difference was 107 compared to 117, which is the difference between 2012 A.J. Pierzynski and 2012 Michael Bourn.
In the end he concluded that having a better hitter in front of you can slightly improve a hitter's performance and would add one extra run over the course of one season.
Question for the community:
1) How would you improve this study?