You repeatedly introduce statistics that are either theoretical or are based upon comparing data that would be available only after the war and each sides archives became available, some of which many years after the war do to secrecy restrictions. The very definition of hindsight. Yes some of the data would be known in real time, but only that generated by that side and much would be deeply flawed. "Kill" claim's on both sides were wildly inflated, and if fully credited, Germany lost more subs than they built and the Allies lost more merchantmen than they could build. You acknowledge neither the Fog of War nor the Friction of War What is even more deeply flawed in your reasoning is the single mindedness with which you attempt to reduce every event to a mathematical equation. X minus Y inevitably leads to Z. Always, immutably, incontrovertibly. For you the human factor is always irrelevant and inconsequential despite the little issue that war is a human act. If numbers alone determined the outcome of human events The US and Israel would not exist, nor would there have been a British Empire. War is not a tabletop game where people who fight and command do what someone in a easy chair tells them to do regardless of the cost. Wars are won as much in the mind as it is on the ground. With respect to ENIGMA only you seem determined to put forth the red herring that it was the sole decisive factor in winning the Battle of the Atlantic, or the war itself, by falsely claiming it is our view. I do not believe any of us has made that claim, only that it played a important role, as did more escort's, better training, new weapons and tactic's, more long range aircraft and aircraft deployed on escort carrier's. I can not quantify how merchant hulls were not sunk because of RDF, K-Guns, Hedgehogs, Hunter-Killer groups or ENIGMA, but whatever the number they were saved by these things, winning the war faster and at considerably lower cost in lives and treasure. Irrelevant to you it may be, but not to those who actually went into harm's way. Unlike most Allied technical innovations ENIGMA offered value beyond one battlespace or segment of the conflict as it offered tactical intelligence from the entire ETO/MTO and even some on the Eastern Front. It didn't win battles in itself, but it offered the Allies the chance to get inside the decision making circle of the Axis. Again I can not quantify how many lives were saved, but some were and many of us here today would not be otherwise. Tactical intelligence helps win skirmishes at lower cost, win enough skirmishes and you win battles, win enough battles and you win campaigns, win enough campaigns you win the war. It isn't pretty and the math is fuzzy, but is none the less real, as real as counting bayonets.