Most analysts expect Democrats to maintain their current edge in the Senate after Tuesday's election, plus or minus a few seats. But that doesn't mean that the body won't change considerably.

Thanks to retirements and primary defeats, the ideological composition of both parties could change considerably. Wisconsin's Herb Kohl (D) will likely be replaced with the much more liberal Tammy Baldwin (D), Indiana's Richard Lugar (R) was beaten by the more conservative Richard Mourdock (R) in the primary, and so forth.

So what are the races with the most at stake? Boris Shor at the University of Chicago calculated "item response estimates" — which are quite similar to DW-NOMINATE scores, the standard academic measure of ideology — for every House and Senate candidate. He used their stated policy preferences as aggregated by Project Vote Smart. Usually, one would generate DW-NOMINATE scores from floor votes, but obviously non-incumbents wouldn't have cast any, so that's not really tenable here.

So what Senate races see the biggest ideological split between the two candidates? I went through 12 of the most competitive races to see. Here they are, from most difference in candidates to least. Scores between -1 and 0 indicate the candidate is liberal; scores between 0 and 1 indicate the candidate is conservative:

You can break up the races into ones where there's a divergence because the Republican is moderate and the Democrat is very liberal, and ones where there's a divergence because the Democrat is moderate and the Republican is very conservative. The best case of the former, perhaps, is Massachusetts, where Scott Brown gets a very moderate score (0.13) but Elizabeth Warren scores as among the most liberal candidates running in any state (-1.42).

A good example of the latter is Missouri. Claire McCaskill, the Democrat, is pretty moderate (-0.35) but Todd Akin, her challenger, is the second most conservative Senate candidate in the country (1.67, just behind Wyoming's John Barrasso at 1.70).

There are obvious limitations to the data, not least that candidates' platforms often differ from their behavior in office. But it does suggest that most competitive Senate races give voters a choice between two candidates who are quite far apart ideologically.