When recovering game state after reconnect/refresh, the old code:
1. Only looked at the last play overall (regardless of team)
2. Used that play's batting order for the currently batting team
3. Reset the non-batting team's index to 0
This caused the wrong batter to appear after inning changes - e.g.,
batter #1 showing instead of #5 in top of 2nd after bottom of 1st ended.
Fix: Now recovers each team's batter index separately by filtering
plays by half ("top" = away team, "bottom" = home team) and finding
each team's last at-bat independently.
🤖 Generated with [Claude Code](https://claude.com/claude-code)
Co-Authored-By: Claude <noreply@anthropic.com>
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