The $H_0$ world cup. II. A comprehensive competition between proposed Hubble tension solutions

Cosmology stands at a crossroads. The Hubble tension has reached a nominal significance above $7\sigma$, while analyses combining DESI BAO and Type Ia supernova data show emerging hints of departures from $\Lambda$CDM. Meanwhile, high-precision CMB measurements from ACT and SPT enable a timely and more stringent reassessment of proposed solutions to the tension. In this paper, we revisit the $H_0$ Olympics, a systematic contest comparing proposed alternatives to $\Lambda$CDM using common datasets, likelihoods, and statistical criteria. In this updated edition, the $H_0$ World Cup, we subject fourteen representative solutions to a common analysis of current CMB, BAO, and SN data. The contenders span four broad mechanisms: late-time modifications of the expansion history, modified recombination, additional pre-recombination radiation, and early non-radiative energy injection. Relative to the original analysis, the present competition includes models and mechanisms proposed in the intervening years and evaluates all contenders using both Bayesian and Frequentist tests of tension and model performance, letting the neutrino mass sum vary. We further test if late-time extensions through curvature or the Chevallier-Polarski-Linder (CPL) dark energy parametrization can aid the success of the models. Finally, we subject the leading contenders to dedicated robustness tests involving alternative CMB likelihoods and multipole cuts, supernova samples, large-scale-structure information, and big-bang nucleosynthesis constraints. This framework assesses both the ability of each mechanism to ease the Hubble tension and the robustness of our conclusions to datasets and analysis choices.