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I think this is going to be a more involved answer than requested, but I'll give it anyway.
I tend to avoid finding ways that could give me an unfair advantage in some way. This is akin to essentially setting house rules. I think by cutting your scouting budget to zero (because you know you are playing stats only), you could be potentially giving yourself an advantage over the AI teams because the other AI teams are spending on scouting budget while you have more money to reapportion to other things. Some of the purpose of these budgets is to have realistic expendures in the game other than just salaries. If you subvert this by not using them, then you are working slightly against the intent of the game.
Of course, you could also argue this is just a management style and that would be fine too. I'm not really saying one way is right or wrong, just my opinion. My recommendation would be to just spend the average and leave it at that.
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