There has been a great deal of research on the effects of variance in determining game strategies. Brian wrote a post a few years back about how underdogs need to use high variance strategies and Dean Oliver discussed the underlying statistical concepts in basketball terms. The main point is this: Below average teams must use riskier strategies to win. If a team's performance is below league average, then consistency is a flaw.
That brings us back to Orton v. Tebow. If the Broncos were a league average team or better, Orton would indeed give them a better chance to win. Yet, the fact that the Broncos are dismal should be more of a reason for Tebow to play. Picture Orton and Tebow as follows:
This is a rough sketch, portraying a Denver offense run by Orton (green) and Tebow (blue) versus the league average (red). Notice that Tebow's curve is wider, meaning he has a higher variability, and as a result, the area under the blue curve that intersects with the normal curve is greater than the comparable area under Orton's curve.
I tried looking at standard deviations in EPA/P from last year, which supports this notion (Tebow = 1.54 > 1.45 = Orton), but it is not convincing. More importantly, I don't feel comfortable using these numbers due to small sample sizes (Tebow had less than 100 passing plays). Yet, if we add in the running game, it is clear that Tebow presents a much wider range of opportunities for the Broncos. Tebow regularly has the potential to add numbers to the running game of which Orton could only dream.
The Broncos win this week over the Dolphins is a perfect parallel. Tebow played like pure garbage for three and a half quarters, much worse - I imagine - than Orton would have in similar situations. Then, Tebow prayed a little and showed off the upper portion of his blue curve, turning on Tebow Time and showing his high risk/high reward potential.
In any one game, Tebow gives the Broncos the best chance to win. That being said, every win is a loss in the Andrew Luck sweepstakes and a step toward perpetual mediocrity.