So, inspired by the Z95 thread of TL or Focus (and a slow day at work), I decided to run the numbers that I must have run a long time ago, but completely forgot now, as to whether or not to spend a TL or wait for later for a TL+F shot.

For starters, I'll look at a 3 dice attack, and I'll look at both against 0 agi and 3 agi.

Against 0 agility, if you didn't stack actions, you'd roll 2.25 + 2.25 hits = 4.5 hits. If you did stack them, you'd roll 1.5 + 2.81 = 4.31 hits. So math says it's better to normally spend the TL. But you're not actually going to roll 1.5 hits, you're going to roll a discrete 0, 1, 2, or 3 hits. And obviously you don't want to spend it at 3, and you would at 0, but what about 1 and 2?

Rolling 1 hit, the spending the TL would net you an average of 1 hit for a total of 2 on the first attack, and an expected 2.25 on the second, for 4.25 expected damage. If you did not spend it though, you'd have 1 hit + 2.81 = 3.81 expected damage. You're better of spending the TL if you only roll one hit naturally.

If you roll 2 hits, spending the TL would net you .5 extra. And the next attack would have a projected 2.25 for 4.75 total expected damage. Not spending it nets you 2 + 2.81 = 4.81 expected damage. Therefore, on a 3 dice attack against 0 agility, if you roll 2 natural evades, you're better off NOT spending the TL to try for the 3rd hit.

Does this change though if you're expecting to line up a R1 shot the next turn? If you naturally rolled 1 hit, Spending the TL = 1 hit + 1 expected reroll + 3 expected next attack = 5 damage. Not spending the TL = 1 hit + 3.75 expected next attack = 4.75. You're still better off rerolling those two dice, though it's not as big of a difference.

Rolling 2 hits, Spending the TL = 2 hit + .5 expected reroll + 3 expected next attack = 5.5 damage. Not spending the TL = 2 hit + 3.75 expected next attack = 5.75 damage. In this case, go figure, it's still better to not spend the TL.

So this is all good and whatnot, but what about against an agile target - that one hit is unlikely to do damage by itself, but is it better to give up on the first attack to make the second even stronger? I'm going to assume the defender has a Focus token.

3TL vs. 3F expected damage is only .64. If you only naturally roll 1 hit, spending the TL gives you .47 + .64 = 1.11 damage. Not spending the TL = .05 + .93 = .98 damage. So, you're STILL better spending the TL on the first attack.

If you naturally roll 2 hits, Spending TL = .735 + .64 = 1.375. Not spending the TL = .36 + .93 = 1.29. Unlike the against 0 agility, you're actually better off spending the TL to try and get that 3rd hit on the first attack.

As for following it up with a R1 the following turn, 1 hit naturally, spending the TL = .47 + 1.23 = 1.7. Not spending the TL = .05 + 1.64 = 1.69. Rerolling with 1 hit is essentially a toss up at that point. I suppose it comes down to how confident you are that you'll have a R1 shot, and if you can perhaps take the next shot without the defender having a focus token.

2 natural hits, Spending the TL = .735 + 1.23 = 1.965. Not spending the TL = .36 + 1.64 = 2. Once again, this is essentially a toss up as to whether or not to spend the TL.

So, I hope this is useful to someone out there. It pretty much confirms what I already instinctively knew, but I found it interesting to run the numbers with the R1 follow up - I was surprised that it essentially doesn't matter regardless of the hits you roll.

Well there are a few other scenarios. For instance, you might be 100% that you won't get a shot next turn, so then you of course spend.

There is also the case (with X-wings, the initial TL ship, I remember thinking about this after playing the core set for the first time) that you shoot, and the next turn you K-turn, so you won't have an action. This is further incentive to not spend if you have 2 hits out of 3 dice, since you are now at 2dmg + 0.5 + 1.5 = 4 expected damage over two turns if you spend, as opposed to 2 + 2.25 = 4.25 if you don't.

But all of these evaporate once you're up against medium-to-high agility targets.

Correct, this is not a full scenario of when to do what, and there's no guarantee that you'll get a second shot - you could fail to have arc, bump, kill the ship beforehand, get killed beforehand... But I figured I'd give a general guideline on the most common (well, "common") scenarios.

Well it wasn't meant as a criticism, I was just adding some scenarios.

This resembles the question "Should I use a focus token if I have only one and I am attacked by X ships?", in that you'd think that not spending is clever in some scenarios but it actually isn't.

There's always the fact that the value of damage reduces as the game goes on. Inflicting that additional hit this turn may mean the enemy fighter is destroyed later that turn denying it the opportunity to fire again. I generally would only keep a TL if 1) I have no viable target that round and I'm pretty safe so don't need focus for defence or I smash a 100% hits on the target. Other than those scenarios, I'd think the value of upfront damage outweighs any potential extra sustained damage over subsequent rounds.

(Edit: typo)