DDB gave you a good answer on this one. Here is a good primer on how to do this calculation:

https://en.wikipedia.org/wiki/Checking_whether_a_coin_is_fair
Unfortunately, you continue to miss the point in your response to DDB, by presuming that "the answer" must necessarily consist of observing real-world data. I have already shown you that we know from a priori considerations that winning the coin flip still confers at least a net advantage of 5% win probability.

I think I speak for most skeptics of the current system when I say that fairness, per se, is not the issue - rather, it is the fact that there is a win probability swing associated with a completely exogenous event. See the blog post that I linked earlier for more on that. Extending the fourth quarter, or even performing the OT flip at half-time, are good ways to resolve this objection, even if they are not strictly "fair".

I certainly don't know how to do the calculation, but I honestly suspect that no one knows how to do the calculation for what the real-world probability is of one team winning the game by getting the ball first in overtime. We aren't flipping fair coins, as has been pointed out numerous times. There are so many factors that go into it. If you're the Patriots, would you rather have the ball first in overtime if:

1. Your offense is on a roll and playing a crappy defense in Foxboro?

2. Your defense has allowed just 3 points to a terrible offense and there's a 30 mph wind blowing in one direction?

3. Your offense is playing well but you've suffered injuries to Gronk and Edelman, and the opposing starting QB went down on the last play of regulation?

I mean, these are all things that factor in. Where you're playing, who you're playing, the health of your team, which team has the momentum, the quality of the offenses and defenses involved, etc. None of which is anything remotely like a random toss of a fair coin.

So honestly, how in the world can you calculate the probability of the Patriots scoring a winning TD on the opening drive of overtime? As others have pointed out, looking to regulation drive results won't do it, because overtime drives are a different animal. Health is a factor. The likelihood of the Pats scoring a TD if Gronk and Edelman are out is vastly different than if they're in but, say, Watt and Clowney are out for the Texans' D (who they may happen to be playing that day).

How do you calculate the probability of this? You're going by estimations based on regulation data, which may have very little to do with realities in overtime.

I totally totally totally get that you know more about this stuff than I do. So I'm not trying to be a dink. I'm just questioning the veracity of your process.