Has strength of schedule impacted James Shields' HR/FB%?

Much noise has been made about James Sh(Y)ields and his fellow rotation-mates propensity to give up the long ball this season. Facts are facts and the Rays rotation has allowed an American League worst 11.3% of fly-balls to leave the yard (AL Average 9.18%). Shields (13.5%) and Wade Davis (12.3%) have been the biggest offenders, but only David Price has been below the rotation average (7.3%). A key principal of sabermetrics is that pitchers have little control over the percentage of fly-balls that leave the yard, but do have some control over batted ball type. Fluctuations away from the mean for HR/FB are typically dismissed as luck, or as I prefer random variation, with little correlation year-over-year. Over the course of a season, one would think that the outliers made fewer or greater number of mistakes, but the greater influence is when those pitchers made the mistakes and if they were taken advantage of.  Over a period of multiple-seasons almost all pitchers fall within 1% of the mean. This is the reason why xFIP is such a useful true talent stat due its normalization of HR/FB rates.

While HR/FB% is not considered a pitching skill, it is indeed a hitting skill. This should be intuitive as we all have witnessed more of Carlos Pena's fly-balls turn into home runs, while Dioner Navarro's are as automatic an out as you can find. Even on a team level, the top team in terms of HR/FB%, the Blue Jays (13.3%) has more than double the rate fly-balls converted to home-runs than the bottom dwelling Mariners (6.0%).

Upon further examination, the top three offenses in terms of HR/FB% in the American League were our AL East brethren the Jays, Yankees, and Red Sox. It's no surprise the Rays are at the bottom of the leaderboard as they play a disproportionate amount of games against these slugging offenses in their respective band boxes. I wondered just what each starter's individual expected HR/FB rate would be based on his opponents faced. How much of James Shields' HR/FB rate could be explained by schedule versus random variation. Below is the table with each pitcher's HR/FB and xHR/FB% based on opponent's HR/FB%:

Indeed playing in the American League East as the Rays expected HR/FB% above the league average, but it seems as if its impact is minimized to about 1% either way. It is surprising to see James Shields and Wade Davis who have had the most home run issues face the easiest home run schedules on the team. It's also amusing that two pitchers on the same staff can have a 1.7% difference in xHR/FB% based on the way the series schedule falls out. I also took in one step further with Shields and weighted his opponents' HR/FB rates in terms of FB/PA using the formula (1-(K%+BB%) = ContactPA%. ContactPA%*FB%= FB/PA%. It produced a marginal difference of .1% so I decided against doing the leg work for the other pitchers.

In summary, the marginal difference between the league average HR/FB% and a pitchers xHR/FB% does not seem to produce any meaningful impact, but taking a look at a pitcher's division can serve as an eyeball test to expect a slightly above-average HR/FB% rate.