Mr. Allred beat the incumbent, Representative Julie Johnson, and is now favored to win the general election in a heavily Democratic Dallas-based district.

All eyes will be on the Republican Senate runoff between the incumbent John Cornyn and Attorney General Ken Paxton. But Tuesday’s runoffs in Texas will feature other important contests.

As podcasts and talk radio blur the lines between sports and politics, professional athletes — many of whom have found encouragement from President Trump — are running in midterm elections.