I mean in OTL Teddy got 4.12M and Taft got 3.68M to Wilson’s 6.29M. I think it’s more than barely possible that Wilson loses in 1912 in this scenario since 7.8M voted for the two Republican candidates.
I am perfectly aware of the voting figures - and also of the fact that they mean nothing, as no single candidate could have held on to all of the Taft and TR votes. By the time the Conventions met, the Republicans' campaign had been long and bitter, far beyond any hope of reconciliation (even four years later they *still* weren't reunited enough to defeat Wilson) so that anyone conservative enough to hold all of Taft's vote would be likely to lose half of TR's, and anyone progressive enough to hold all of TR's vote could similarly expect to lose half of Taft's.
Nor have I ever denied the possibility that TR *might* - just possibly - hang on to enough of the Taft vote to scrape through to a narrow win - though, depending on just *how* narrow it is, he may face a Democratic Congress. However, he will need to guard his tongue about the war, since if he is even suspected of wanting to drag Americans into a sordid European squabble he will be virtually certain to lose in 1916, esp if (as is all too possible) he has already got the US into a messy "quagmire" in Mexico. It would be one of history's little jokes if a TR win in 1912 led to someone like Bryan getting elected four years later and keeping America out of the war altogether.