The Power Question

It is rather taken for granted that there are four primary batting attributes, Contact and Power versus left-handed and right-handed pitching. However I would contest that we don't really need that. This leads into a larger discussion about the way hitting systems are configured in general, but power seems to be the glaringly obvious problem.
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Power is generated from weight transfer and bat speed. It is a byproduct of the physical swing. A swing with good mechanics by a strong hitter will obviously deliver the most power.
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In video games, we see this power attribute applied versus both lefties and righties, as if by some bizarre magic hitters lose strength or bat speed when someone is pitching for and different angle.
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Below is a sample of some major league hitters. It displays how frequently they hit home runs versus lefties and versus righties per fangraphs.

Home Run Rates

Player Name	PA/HR (vs. RHP)	PA/HR (vs. LHP)	PA/H (vs. RHP)	PA/H (vs. LHP)	HR% (vs. RHP)	HR% (vs. LHP)
Albert Pujols	17.79	17.05	3.70	3.60	20.79%	21.11%
Joey Votto	24.35	26.29	3.80	3.95	15.61%	15.02%
Jose Bautista	21.33	18.58	4.70	4.41	22.03%	23.74%
Mark Teixeira	18.71	21.17	4.36	3.90	23.30%	18.42%
Victor Martinez	34.92	29.65	3.66	3.74	10.48%	12.61%
Jimmy Rollins	43.15	43.41	4.13	4.14	9.57%	9.53%
Mark Reynolds	19.08	20.41	4.95	5.10	25.94%	24.98%
Derek Jeter	60.72	35.68	3.79	3.35	6.24%	9.39%
Jose Reyes	57.90	60.89	3.75	3.72	6.47%	6.11%
Ryan Howard	15.30	18.63	4.08	4.99	26.66%	26.78%

It's admittedly a small sample size, but among them, there isn't anyone who has significantly different power depending on the pitcher. The two most interesting cases are Teixeira and Jeter. For Teixeira, being a switch hitter makes everything wonky. I'd be willing to go ahead and say that he likely has a different approach to the plate because he standing in a different batter's box depending on the handedness of the pitcher. 

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Of course, Jimmy Rollins is remarkably consistent despite also being a switch hitter. So perhaps my hypothesis needs more test subjects before we right off Tex's change to being a switch hitter.

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Getting back to Jeter, he is interesting because he has one of the most dramatic changes in not just homers, but in overall hitting between lefties and righties. He hits left handed pitchers more often and harder than righties, and has had a full career of taking advantage of pulling the ball down the left field line in Yankee Stadium, something exacerbated by a hanging breaking ball from a lefty. 

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However even in that case with Jeter, he is only hitting 103 homeruns against lefties for every 100 he hits against righties, everything else being equal. That's not exactly enough to really build a case on Jeter having more lefty power than righty power.

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The problem is that Jeter is (behind the switch hitting Teixeira) the best case that can be made for a discernible difference. For most of the above 10 hitters, it doesn't really appear that distance they are hitting the ball is at all based on the handedness of the pitcher.

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So why is it in games? Are we just catering to tradition, or something that makes the simulation give realistic results? Are there people who really think Ryan Howard is hitting the ball twice as hard when a righty is on the hill? The whole hitting approach needs to be reexamined from the catcher's view, see the ball, hit the ball, hope the attributes are lined up well model that has been around for almost 30 years now.