I'm quite sure I'm not going to change your outlook, so the only thing I can suggest if you're looking for some truth is to call up some football coaches and see what they think of your stock market analogy...if they agree that taking risks is the key to winning in football. I bet most would love to share their philosophical perspective of the game.
Since you laid out your philosophy I'll lay out mine and you can see how they compare and contrast.
I think football is about gaining (and keeping) control (of the ball, score, clock) not taking chances and risking giving it up. The better players execute, the more control you'll gain.
Risk taking in football means taking progressively bigger chances because you're otherwise unable to gain and/or running out of opportunity to gain the control you must have to win. You don't leave control to chance if you can help it and unlike the stock market or gambling on card games, bigger risk doesn't equal bigger reward in football, even though bigger risks become progressively necessary for the team lacking control because there are limits to how much control can be acquired. There's only one ball, a touchdown is only worth 7 and there are sixty minutes max before a winner is declared. Greater risks, while necessary as the team with poorer execution becomes increasingly desparate for control, deliver diminishing returns not increasing due to the ceiling on the benefit that can be gained and the likelihood that a bigger cost will be incurred with poor execution.
Therefore, the essence of football is the quest to eliminate risk taking, not do more of it.