Obviously if a place has twice as many Obama opponents it's also going to have twice as many racist Obama opponents.

That doesn't follow. Suppose there are two states: Redstate and Raciststate. The two states have roughly the same population.

In Redstate, the normal political inclination in a year with two white men running is 60-40% Republican. 10% of the population is racist and won't vote for a black man no matter what. Let's assume these racists are equally divided by party.

In Raciststate, the normal political inclination is 50-50% split evenly between the parties. However, 30% of the population is racist and won't vote for a black man. Again, let's assume they're evenly divided by party.

So what happens when a black man runs as a Democrat? In Redstate, the Republican will pick up 4% (10% of the Democratic vote) to win 64%-36%. In Raciststate, he'll pick up 15% and win 65%-35%.

So even though the two states have roughly the same number of people voting Republican that year, you can tell Raciststate is more racist because of *Democrats* who voted based on race. What's more, if you took the ratio of racist voters relative to the Republican vote, rather than the whole population, you'd be get an inflated estimate of racism in the whole population in both states.