The stats that predict breakouts
Baseball: Exit velo, barrel rate, walk rate (early-career). Young hitters with elite exit velo on 40%+ barrels will hit. Look for guys with 95+ mph average EV as rookies.
Basketball: Assist-to-turnover ratio, 3-point volume on 35%+ shooting, defensive versatility. Playmakers with positive assist ratios in year 2-3 often explode in year 4-5.
Football: Target share, air yards per target (WR), yards after catch consistency. Receivers getting 20%+ of team targets in year 1 are breakout candidates.
Off-season signals
Contract extension (implies team believes in the player). Trade deadline activity (did a playoff team acquire them? Why?). Draft capital (first-round picks trend to breakout faster than 6th-rounders, controlling for position). Coach/system change (new OC or GM might unlock a player's value).
The rookie card window
Rookie cards peak in value 2-4 years after a player's breakout season. A guy who's elite year 1 might have already had his card appreciate 3-5x by year 2 (priced in). The real wins: players who were drafted as prospects, underrated year 1, then break out year 2-3 (rookie cards are still cheap, now the performance justifies the price).
Wildcard strategy: the value stack
Buy rookie boxes of players you think will break out, 6-12 months before consensus catches on. Open the boxes, sell the non-rookie hits, hold the rookie auto. If you're right on the player, you're holding a $50-100 card that might be $300-500 in 2 years. Miss and you're -20%. But the ratio is favorable enough to make it a +EV play if you're even slightly better than market at evaluating talent.