As some bloggers have shrewdly pointed out, Obama does best in areas that have either a large concentration of African-American voters or hardly any at all, but he struggles in places where the population is decidedly mixed.That has been the case throughout the campaign. After the Super Tuesday contests, the correlation between Obama's white support and the percentage of the voting electorate that is black by state was an inverse .35.
The trend has become more pronounced over time, currently standing at an inverse .43, with a p-value of less than .02. The actual relationship is stronger still, as blowout states for both candidates weaken the perceived correlation.
The black shares of the total electorate on the Democratic side in Illinois and Arkansas are similar (24% and 17%, respectively). Yet, as 'home' states for each of the candidates, they are anomalies. And not only in how lopsided the overall outcomes were (65%-33% and 70%-26%), but also with regards to how the influence the general trend that as black proportional representation increases, whites move away from Obama. Obama took 57% of the white vote in Illinois (his second best performance among whites) but only 16% in Arkansas (his worst performance among whites).
Dropping these two states propels the inverse correlation between the percentage of the electorate that is black and Obama's white voter share to a vigorous .52. Excepting DC*, the caucus states without exit polling data that Obama has dominated in all have very small black populations. So presumably the real relationship is even stronger still.
I expound further on this to make clear that there is not a U-shaped pattern of white support for Obama as the black population increases. Bai didn't make that erroneous assertion either, but I can see how people following at a distance might.
The overall results (not the white results) do reveal a sort of U-shaped curve from Obama's perspective as the percentage of the total electorate that is black increases, but that is a result of the black-white proportions of a state's total electorate, not of either group changing their behaviors in the middle (black percentage between 10%-25%) relative to the extremes (black percentage less than 10% or more than 25%).
The bottom line is this: As the black percentage of the population grows, whites increasingly back Hillary. Blacks reliably back Obama no matter what. With Arkansas and Illinois included, for every 1% increase in the total electorate that is black, Obama's support among whites drops by .64%. When those two states are removed, the corresponding drop in Obama's white support is .90% for every 1% increase in the total electorate that is black.
* Unless DC's blacks totally broke away from the national trend of their brethren who have overwhelmingly supported Obama, Hillary held her own among non-blacks in the capital, where she was crushed 75%-24% overall. With over 56% of the district's population being black (and an even greater percentage of the Democratic electorate being so), Hillary probably took Obama in the ~35%-40% or so of non-black voters by a margin of about 60%-40%. Thus DC is not an exception, but instead an example of why Obama's loss of white support is only relevant to the statewide outcome up to a certain black threshold--once black representation hits 30%, Obama is home-free.