Let's look at how this mirrors today.
Democrat candidate (Wilson/Clinton) faces Socialist challenger (Debs/Sanders).
Faces Conservative challenger (Taft/Most of Republican field) who should be a shoe-in. Uses loud mouth candidate promising everything (Roosevelt/Trump) to anger and split the party- big issues, trade and immigration.
Loud mouth 'denied' nomination, splits to make his own party (Progressive Party, AKA Bull Moose).
Republicans split, hands Wilson nomination.