The Spartans tried to push forward immediately but the evasion skills of the peltasts, combined with totally ineffective spartan die rolls, led to few injuries.
The Spartans only managed to eliminate a few Athenians when they cornered them at the top side of the map.
Meanwhile, the peltasts managed to both inflict wounds with ranged shots and gain victory points by attacking (with the support of the leader) in close combat.
The Spartan cavalry never managed to enter the game (due to lack of cards) while the Athenian heavy infantry managed to get close enough to score a couple of victory points.
The final result (6-3 for the Athenians) underlines the great power of evasion.
I'm starting to think that the special rule for bringing in Spartan reinforcements is too stringent. Perhaps more activation cards could be added (or a specific entry turn could be established).