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[LotharanAeron]

I apologize if this has been picked apart somewhere already.  While walking home I started adding up some rough numbers we are given in the game for the final battle and I think victory through conventional combat is certainly a possibility.

First off, the Reapers.  People have counted roughly 300 "Sovereign" class Reapers in the closing cinematic for ME2.  We know in ME3 that the little "destroyer" class Reapers are the most common, so for the sake of this post I'll double the dreadnaught Reapers since 300 seems a bit too low.  I've decided to give them 10x as many destroyers, putting Reaper forces at 600 Dreadnaughts and 6000 Destroyers with probably many thousands of those eyeballs.

Reaper survivability seems to vary greatly.  Sovereign took a pounding, but he also had a Geth fleet backing him up.  The Citadel probably made getting a clean shot on Sovereign difficult too.  Let's say it takes 1000 shots from a standard dreadnaught to kill a Reaper.  The little guys are significantly weaker, taking maybe 100 shots if their barriers are fully powered (or 1 if you hit the sweet spot).  Eyeballs go down with 1 shot from a fighter so they're kinda moot.  Also keep in mind Thanix cannons and missiles significantly increase Allied firepower against the Reapers so they may go down a lot faster than what is mentioned.

For allied forces I'll assume that every fleet possible if one goes full paragon has been assembled.  The Geth have at least 40,000 ships if I remember, as do the Quarians.  I'll assume 15,000 Quarian ships were left behind because they're barely armed civilian frigates.  That puts us at 65,000 ships already.  Alliance got the crap kicked out of them and we never really know how big their fleets are, but judging from how many are present in the final cinematics I'd say at least 3000 ships.  Turians, though getting hammered too, brought maybe 6000 ships.  The Salarian military, or at least whatof it that joins up, brings maybe 500 ships.  The Asari bring a lot less, maybe just a few hundred (400?) but they're friggin' huge and have massive firepower.  Add on to that the smaller groups we round up including Mercs, Batarians, Volus, Hanar, Elcor and anyone I forgot for maybe another 1000 ships. 

In total that puts the Allied fleet at probably a minimum of 75,000 ships.  Almost every one of those ships have Thanix cannons now and there are thousands of fighters as well.  The cinematic also shows the Allied fleet taking the opening shots of the battle, which is interesting because Reaper beams outrange Allied cannons.  Even if only 10,000 ships fired in the opening salvo that is still massive damage to the Reaper forces.  After even a couple minutes of fighting the Reapers would have started to incur significant losses.  As powerful as Reapers are, unless they have significantly more ships than it is indicated, as in the tens of thousands, the battle for Earth boils down to attrition and the Allies severely outnumber the Reapers.  While 600 may be a bit low, I don't see how giving them 2000 or even 3000 will make a huge difference in the long run, only tens of thousands.

Vigil said the Reaper's strategy is always to launch a surprise assault on the Citadel and shut off the relay network to anyone other than Reapers so a pitched battle never has to be fought.  Considering that it took the Reapers several centuries to finish off the Protheans, and it is taking them only a few months to finish off our cycle, even isolated the Prothean fleets gave the Reapers hell.  We are fighting the battle the Reapers did everything in their power for millenia to avoid.  We have enough ships to completely encircle the Reapers and have made advances in anti-Reaper techonology since Sovereign's attack. 

Maybe I'm way off and am just wasting my time, but it seems to me that even with only very, very rough calculations, that the Allies could win through conventional firepower alone IF the entire galaxy is united.  It would have been amusing for Hacket to come on the com channel while Shepard is talking to the Catalyst-kid and say "I don't know who you're talking to up there but the battle is over and we're just mopping up the stragglers now.  Want a shuttle to come pick you up?"