In this paper, we investigate how human egocentric videos can benefit robot policy learning without action supervision. Building on a pretrained VLM, we propose Shared Prediction on Action and Representation (SPAR), an MoT architecture in which future visual state prediction can provide independent and complementary learning signals alongside action prediction. We find that representations learned from egocentric videos improve downstream performance on out-of-distribution robot tasks, with further gains as video data scales. We also study the effects of objective choices and data curation, providing insights into how to leverage action-free videos for scalable robot learning.