I calculated my World Series winning 2015 Seattle Mariners, and found some interesting results based on Avoid K's, Contact, Runs, and RBI for the players on my roster. It seems that when displaying the batting ratings, customizing the view to show PA, R, RBI, and K's, there is a marginally noticeable inverse correlation between Avoid K's and runs produced.
It seems that, at least in my wacky team, the better the avoid K rating was, the fewer runs that player produced, either in runs scored or RBI's. The contact rating followed closely the Avoid K rating though, so it also seems that my better contact hitters were less responsible in 2015 for producing runs. This may show a bias, when simming games, for power hitters over contact hitters, although I cannot be sure.
For example: My best avoid K player, Melky Cabrera, with a 60 Avoid K (20-80) struck out 71 times in 487 PA, for a .146 percentage. He also produced 70 RBI and scored 64 times (.144 and .131 respectively). My worst Avoid K player, Sung hwan-Chung, with a 35 Avoid K rating struck out 132 times in 584 PA, for a .226 percentage. He produced 101 RBI and scored 83 times (.173 and .142 respectively).
There was also a noticeable "dip" in production in the middle of my roster where the median Avoid K rating occurs. Both RBI and Runs scored dropped off. The best Avoid K players had decent runs produced numbers, the middle guys had poor numbers, and the worst Avoid K guys had the best runs produced numbers.
This does make some logical sense, since power hitters who strike out a lot more do hit more HR, and the best contact hitters do get on base more, and would be driven in by those power hitters.
Therefore, I am forced to recognize that the Avoid K rating may not be the rating I thought it was. However, I must also point out that any rating that's higher, rather than lower, would improve the player. So having more players in your organization with higher avoid K ratings should be an improvement.