And remember, "the war" was also being fought in the Pacific, also with a spectacular imbalance in cryptology strength between the Allies and the Axis.
The allied shooting down of Japan's commander in chief, Isoroku Yamamoto, was based on breaking the Japanese naval codes and attests to your point of view.
From his wikipedia article: He died during an inspection tour of forward positions in the Solomon Islands when his aircraft (a Mitsubishi G4M "Betty" bomber) was shot down during an ambush by American P-38 Lightning fighter planes. His death was a major blow to Japanese military morale during World War II.
Enigma didn't result in 750,000 casualties and 900 Aircraft losses. Stalingrad did.
Enigma didn't result in the loss of the Sixth Army. Stalingrad did.
Enigma didn't change the scenario from Germany controlling all of Europe and its resources to playing defense from two sides. Stalingrad did.
For all the bravery and blood shed by the red army, their winter is the thing that changed the outcome of the battle. The winter forced a halt in the German advance, allowed the Russians to regroup and was the number one casualty producer
for the nazi's.
I don't undervalue the contribution code breaking made to that war, but there was only one turning point, and it came , very clearly, in Russia.
Rejewski and Turing's Enigma cracking accomplishments were staggeringly significant, but they won nothing. If the Allies bombed every submarine that radioed a position, the Germans would have thrown the machines into the ocean. The Enigma let the Allies stack the overall war strategy in their favor, but it was far from over.
I do agree that brainpower won the war - our cryptology was stronger, resource management between the Pacific and European fronts was superb, and the Allies had a knack for picking battles and battlefields where they could excel
What decided the war in the Pacific was that the USA had vastly more industrial capability than Japan. Even if Japan's leaders had made all the right decisions, and America's leaders done everything wrong, America would still have won any protracted war between the two countries.
Even if Japan's leaders had made all the right decisions, and America's leaders done everything wrong
If America's leaders had done everything wrong, they would have ended the war without big territorial gains for their side, with a negotiated peace leaving Japan in control of Asia. (That, by the way, is exactly what Japan's leaders got wrong from the strategic point of view. They really believed before the war started that that was a likely outcome of the war. They didn't count on the Allies insisting upon unconditional surrender after the sneak attacks on Pearl Harbor and Singapore.)
US leaders did do almost everything wrong until well into the war.
They were saved from their mistakes by superior equipment (especially aircraft) and eventually better and more experience personnel. They didn't start tactically winning battles until well into the Pacific Campaign.
Not by cracking Enigma?
http://en.wikipedia.org/wiki/Cryptanalysis_of_the_Enigma
And remember, "the war" was also being fought in the Pacific, also with a spectacular imbalance in cryptology strength between the Allies and the Axis.
http://en.wikipedia.org/wiki/Japanese_naval_codes
http://en.wikipedia.org/wiki/Magic_%28cryptography%29
In general, code-breaking had a lot to do with the outcome of the war.
http://www.cs.virginia.edu/jillcrypto/