Time for Some Math!

Great Ax or Maul, that is the Question!

 D&DNext has the following Critical Hit rules:

Critical HitsWhen you score a critical hit against a target, the attack deals its maximum damage to it. This means you don’t roll the attack’s damage dice; you instead take the highest rolls that each of those dice could produce and then apply any modifiers.
In addition, the target takes extra damage. Roll one of the attack’s damage dice, and add it to the damage. For example, if your attack normally deals 2d6 + 2 piercing damage, you would roll one extra d6 and add it to the damage of a critical hit
If the attack has different damage dice, you choose which die to roll. For example, if the attack deals 1d6 piercing damage and 1d8 bludgeoning damage, you can roll one extra d6 or d8.

So instead of double weapon damage, you get to roll one die again...A maul does 2d6. A great ax does 1d12. So on a normal hit a Maul averages 7 and a Great Ax averages 6.5. 

Obvious.

Assuming that both critical on a natural 20 we have a 5% chance to score a critical with Maul & Great Ax. 

Critical with the maul is 3d6, averaging 9. Critical with the Great Ax is 2d12, averaging 12. 

Great Ax is better!

However, the average damage of the Maul is 7+.05(3.5) or 7.175 and the average damage of the Great Ax is 6.5 + .05(6.5) or 6.825.

Maul is better!

What am I doing wrong?