I think you are a bit off base. Didn't the NFL change the rules because statistics showed that winning the coin toss resulted in a clear advantage?
I quickly tried looking up some percentages on the web and found the from wiki answers (there are likely better ones out there but this is what i got on short notice)
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The NFL has had 325 overtime games since the rule was adopted in 1974. The results:
Both teams have had possession 235 times (72.3%).
The team that has won the toss has won 169 times (52.0%).
The team that has lost the toss has won 141 times (43.4%).
223 games were decided by a field goal (68.6%).
86 games were decided by a TD (26.5%).
One game was decided by a safety (0.3%).
There have been 15 ties (4.6%).
Source: NFL
*It seems fair but these numbers are somewhat misleading because in 1994 a rule changed moved the kickoff back 5 yards to the 30 yard line (those numbers were based on data from 1973-2003). Since then, it's been about 60%. Prior to the rule change, the coin toss had no predictive value for deciding who would eventually win the game. Since 1994, the coin flip winner has a clear advantage.
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