Republicans know that these abysmal figures constitute a huge head wind against any chance for Trump’s reelection. Blacks compose significant shares of the voting population in the key swing states of Florida, North Carolina, Michigan and Pennsylvania. Even Wisconsin’s small black population could be decisive given how finely balanced that state is. Increase Trump’s share of the black vote to even as low as 15 percent, and Democratic chances of winning the electoral college become very low.

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As a result, many Trump backers have seized on anecdotal or cherry-picked evidence to show such a surge is happening. They note that some polls show Trump’s job approval rating among blacks to be as high as 34 percent, while others contend Trump’s support from high-profile blacks such as Kanye West is helping him make inroads. A new book — “Coming Home: How Black Americans Will Re-Elect Trump” — making the conservative rounds argues that Trump received 21 percent of the black vote in Pennsylvania in 2016, and that he will receive 15 percent to 20 percent of that vote in 2020. Conservatives desperately want to believe this is true, and thus all too credulously accept these claims as fact.

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Here’s what the facts really show: Trump’s job approval rating among blacks averages a mere 13.3 percent in three of the most recent polls that release breakdowns by race. Trump received an average of only 9 percent of the black vote against Joe Biden in surveys in four key swing states conducted by the New York Times and Siena College in November. And a recent Washington Post/Ipsos poll of blacks found Trump’s position to be even worse. This poll is the only recent public poll that interviewed only black voters, and thus has a lower margin of error for them than the other polls mentioned above. It found Trump had only a 7 percent job approval rating and gave him only 4 percent of the vote against Biden.

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Trump supporters should also review some facts about polling methodology. A poll’s margin of error is based on the number of people polled as compared with the number of people in the population being sampled. The margin of error for an entire poll, however, does not apply to the totals for any subgroup data within that poll. The margins of error for subgroups are much higher than for the overall poll because the number of people being sampled, as compared with the subgroup’s population, is much smaller. Thus, a poll that has an overall margin of error of plus or minus 5 percent will have a significantly higher margin of error for any data reported about the black population.

These error margins can be extremely high when you look at the actual numbers of blacks sampled in any given poll. Only 186 blacks were included in one poll that gave Trump a 34 percent job approval rating among blacks. The margin of error for that sample size is between 7 percent and 8 percent, and even that is only within a 95 percent confidence level. The subtotal figure will likely be wrong 5 percent of the time even if the poll was conducted perfectly.

That likely explains why the Pennsylvania poll cited in the book “Coming Home” was off. That poll had an overall margin of error of 1.89 percent, but the margin of error for the black subpopulation of about 320 respondents was closer to 6 percent. The Pennsylvania exit poll gave Trump only 7 percent of their votes. That figure is amply supported by a review of precinct data from heavily black areas, which show Trump receiving extremely low shares of the vote. The book’s authors, Verne Robinson III and Bruce Eberle, argue that most black voters don’t live in these areas. But even middle-class black areas such as Cheltenham Township in the Philadelphia suburbs gave Trump much less than 21 percent, and usually less than 5 percent, of the vote.

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The Trump campaign’s efforts to highlight the strong economy and his important criminal-justice reform are worthwhile and could make an impact. Even small increases in his black vote share could be decisive in an extremely close election. A campaign as flush with money as his can afford to fight for every conceivable vote. Republicans nonetheless need to accept Trump is unlikely to bring them so quickly to the promised land.