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This is a great point, and begs the question - who or what do you have around you to combat your biases? Who's someone on your coaching staff, in your circle of colleagues, or in your general life that will help point out your biases? If no one, then what statistical methods do you have to help you overcome your biases? I think it's a fair question to consider.
"When I hired, I made sure I looked outside at somebody who didn’t have the experience bias with my first, and maybe even one of the best hires I ever had was Paul DePodesta, who was a Harvard Econ major, didn’t play sports, and really, was able to come in and look at things with an eye that wasn’t biased."
The tricky part is that you have to figure out what your biases are in the first place. Not everyone's are the same. My bias used to be that drills taught fundamentals and I would over drill things. I was lucky enough to have a friend of mine, Art Errickson, coach with me for a year. He was able to help me cut through my biases and truly embrace a much more effective games based approach.
Also, we need people or methods to help us deconstruct biases about our team. We all have biases when it comes to our players. Maybe we see something in a certain player, so we play him a lot even though he's not producing. Who or what is going to tell you that you need to play that player less because there are other players who are more productive?
The obvious answers to this are assistant coaches and statistics. I think it's important to find assistant coaches who will back you 100%, but think differently than you. You want the guy who's going to make 100 suggestions, get told no 100 times, and still be willing to make that 101st suggestion. You also have to be willing to listen to your coaches when you know deep down they are correct.
I also think statistics can help eliminating biases. Instruments such as effective field goal percentage or true shooting percentage are simple, yet effective, ways to cut through to who your most efficient scorers are. Lineup efficiency is another great way to see who really plays well with each other. Using statistics eliminates your "eye test" which could be a good thing.
Lastly, I think eliminating biases revolves around focusing in on what you want to accomplish. In basketball it's simple - score more baskets than the other team. The biases come in when we think about HOW to get things done. So I would suggest taking some time to analyze your HOW and determine where your biases lie.