Having managed to defeat my Davion lance with my Liao one, I decided to rotate the table and see whether I could beat the Liao missile nightmare with the Davion Banshee and its lancemates, using the same map as last time.
Battle 1
The first attempt ended ... badly. Round one saw LRMs blasting both ways across the battlefield, hitting nothing. Round two saw some hits, but all were glancing blows, reflecting the range. Round three, and it was all about the head hits. The Scorpion scored a hit on the Phoenix Hawk's head, with the Pixie being saved by it being another glancing blow. More impressively, the Rifleman made a direct hit on the Banshee's head with one of the autocannon. Shaken, but not stirred. And then, in round four, it all fell apart. The Longbow managed to score a crit on the Banshee's left leg, but the Rifleman followed that with a large laser to the Banshee's head, and it was lights out for the Banshee, with the pilot killed during ejection. At that point, the Griffin, Scorpion, and Assassin, although only having taken light damage between them, decided discretion was the better part of a long-range duel against a Longbow, Archer, and Rifleman, and fled the field, which at least meant none of them were lost (although they took some more damage in the retreat, including yet another head hit (Pixie's medium laser on the Griffin as a leaving present)).
Battle 2
So I fired things up again, and had another go. Same forces, same map, but this time I kept the Banshee moving faster, rather than trying a firing advance, putting the priority on closing (which I should have done the first time). That worked better. In round two, the Scorpion managed a PPC hit on the Archer's head, burning through the armour to cause a critical on the cockpit, taking it out of the battle nice and early. In round three, the Banshee crits the Rifleman's gyro, causing it to fall. Heavy damage to the Phoenix Hawk from the Griffin and Scorpion causes that to topple, too. The Rifleman, as is traditional, fails to stand in the next round, but the Longbow hits the Banshee with 20 LRMs ... which it soaks. Round five, the Rifleman falls again and the pilot blacks out. Round six, and the Griffin takes the Pixie's left arm, while the Banshee starts scouring the Longbow at short range. Round seven, and the Banshee has got up close and personal on the Longbow, hitting it with the autocannon, four medium lasers, and all six SRMs, while the Scorpion managed to crit the 'bow's leg, causing that to fall. Round eight, the Longbow falls while trying to stand, doing more damage to the leg. The Banshee, close up, followed with a pair of gyro crits to the Longbow, catching the Pixie's jump jets a critical as a bonus. Round nine, and both the Longbow and Rifleman pilots eject from their fallen machines, leaving the Pixie to lose the left torso to the Banshee, and take three more crits from the Assassin, then falling before losing a leg to a kick from the Banshee, ending the battle, although by that point the Banshee had itself started to take meaningful leg damage itself.
Summary
Lucky headshots were definitely important in both these battles - taking out the Banshee in the first, and the Archer in the second, before they could do much in the fight. I might still have won the second without that hit, but it would definitely have been a lot more of a struggle.