Asking players to do the best that they can do

So, I was thinking on something earlier, and I'd be curious to hear thoughts, and if applicable, experiences, with what I am about to talk about.

Several coaches who have won a lot, for example John Wooden, Nick Saban, etc, have used such approaches as "Don't look at the scoreboard", "The score will take care itself", "Success is doing the best you are capable of doing", etc.

Now, just so it is clear, I do not want to suggest that these are bad approaches. I think they are certainly better than the traditional winning-is-everything, Lombardi-esque approach. I am however thinking that there might be a still better approach.

It's a fairly simple idea, really. The idea is this: Forget talking about winning, forget talking about not focusing on the scoreboard, forget talking about success, instead simply ask your players to do the best that they can do, regardless of whether it's getting better at something, performance during a practice, performance during a game, etc.

The thinking here is that this sets this up as being about the player trying to do their best. This is opposed to setting up something as being about winning, or about succeeding. The potential problem I see with setting something up as being about winning, or about succeeding, even if a coach's definition of success isn't winning championships, ala John Wooden, is that the downside of winning is losing, and the downside of success is failure. Losing and failure are negative, unpleasant, undesirable, wanted to be avoided, and can make players worry and/or feel pressured, which can lead to mistakes.

Also, when you say "Don't look at the scoreboard", or "Don't worry about the score", you are still calling attention to the object or subject you don't want them to look at or worry about because of the words you are using. It's kind of like the classic "White Rabbit" idea. If you want people to stop thinking about something, talking about something, focusing on something, or worrying about something, then don't mention it. If you want something not to not be thought about, talked about, focused on, or worried about, then one of the worst things you can do is say "Don't think about/talk about/focus on/worry about X."

To me, the approach I am suggesting here is much more positive, and puts much less pressure on the individual, which hypothetically should free them up to just go out and do their thing the best they can.

A quick note to acknowledge a potential objection I can see to this:

Yes, some players actually thrive off of presssure, and from a coaching perspective, it makes sense to tailor your motivational tactics to each individual rather than having a one size fits all approach. That said, I think maybe you can make what I talked about above the approach for your program/culture overall, especially when dealing with the team as a group, and then on an individual level, with players who thrive on pressure, you can find ways to challenge them, put pressure on them, etc.