The 1S hyperfine splitting in hydrogen is measured to an impressive ppt precision and will soon be measured to ppm precision in muonic hydrogen. The latter measurement will rely on theoretical predictions, which are limited by knowledge of the proton polarizability effect Δ_pol. Data-driven evaluations of Δ_pol have long been in significant tension with baryon chiral perturbation theory. Here we present improved results for Δ_pol driven by new spin structure data, reducing the long-standing tension between theory and experiment and halving the dominating uncertainty in hyperfine splitting calculations.