First, the gender gap can work both ways. Women voted for Democrat Tom Barrett while men voted for Walker. Indeed, Walker’s share of the vote among women was 12 points lower than his share among men. But he carried males by a landslide: 59 percent to 40 percent. Walker lost women much more narrowly, 52 percent to 47 percent. The lesson is that Republicans can survive a rather big gender gap as long as they win men overwhelmingly.

Second, Walker’s heavy early spending clearly helped him. The pre-election polls suggested that Barrett was closing in on Walker in the final days, and he clearly was. The exit poll found that eight percent of the voters said they decided how to vote in the last few days, and they went overwhelmingly for Barrett, 69 percent to 27 percent. The rest of the electorate that decided earlier went for Walker, 55 percent to 44 percent. It’s intriguing to imagine what Barrett might have done with more money that he could have spent earlier. Money matters.

Third, to win, Democrats need to overwhelm Republicans among moderates. Looking at the vote by ideology, you might imagine Barrett won: he carried liberals by 86 percent to 13 percent, and moderates by 54 percent to 46 percent. Walker carried only conservatives, by 86 percent to 14 percent. But the math added up for Walker because only 21 percent of Wisconsin’s voters called themselves liberals, while 36 percent were conservatives; 44 percent were moderates. Because of the advantage conservatives have over liberals, Democrats don’t just need to win moderates; they need to win them by very large margins. Victorious Democratic coalitions are inevitably an alliance of the center with the left.

That’s how President Obama managed to win a seven point lead over Mitt Romney in an electorate that was voting for Scott Walker. Roughly one Walker voter in six preferred Obama to Romney. Who were the Walker-Obama voters? An analysis by Jon Cohen, the Post’s polling director, found that this swing group was made up of more moderates than the electorate as a whole, and also more independents — not surprising for a swing group, but an important finding nonetheless. Turning out your own supporters is essential. But so is fighting for the pure swing voters.