A way to answer the question of offensive 5th member vs defensive 5th member

We've had this question a few times with the stones handed out end-of-season as well as over the past week or two, so I thought I'd try to put down one solid answer. The fact is that there are multiple ways to approach the question and mine is only one of them.

Method: consider both lift gained on offense and lift lost on defense for both possibilities. Assume 7 scored battles on defense and for offense, see https://fireemblem.gamepress.gg/q-a/how-ar-uses-aether-consumption-manage-tiers-and-which-tier-youre-likely-sit

For example:
5th attacker: offense, let's say now you only lose a unit 1 in 5 battles. In 5 battles you would then get 480 lift, or 96 lift per battle. If you attack 14 times in total, that's 1344 lift, which is an impossible number but we're working with a mathematical model here so it's ok. It's meant to be an estimate. Defense, let's say you manage to take out 7 units in 7 battles, so 420 lift lost. 1344 - 420 = +922 lift
5th defender: maybe now you lose a unit 2 in 5 battles. In 5 battles you would then get 460 lift, which averages to 92 lift per battle. 14 x 92 = 1288. On defense let's say you now manage 10 kills in 7 battles, so 360 lift lost. 1288 - 360 = +928 lift. So in this example, it would be about the same, so we go to look at additional considerations.

That's just to show how the method works. You need to substitute in the correct numbers based on how confident you are in your own play, and beware of overconfidence and underconfidence.

Additional considerations:
- if you build bonus structures every week, it might be a few weeks before you can get the 5th member for the other side.
- if you're willing to do without a bonus structure on one end for a week at some point, you can probably afford the 5th member on the other side in two weeks. I think falling behind in offensive fortress level is extremely risky and easily loses a unit, so I likely won't do it.
- getting the 5th defense member paves the way to getting the 6th defense member if you think you can reach T19 (for whether you can, see https://fireemblem.gamepress.gg/q-a/how-ar-uses-aether-consumption-manage-tiers-and-which-tier-youre-likely-sit ) and if you're one of the first players to put 6 defenders up, you might cause some people some serious issues who went for 5 defenders 4 attackers and bonus structures. Maybe less of an issue for players with 5 attackers.
- if your fortress level is 2 full levels higher than the opponent's (i.e. you have 2+1 and they have 1+0), on offense you're probably going to stomp them even 4v6 and on defense their numerical advantage might not save them from losing 3+ units.
- some strategies (ex: spamming ward armour or healers on defense) may increase exponentially in power as numbers increase, more so than other strategies.
- Defense teams may find numerical advantage especially important if using some kind of war-of-attrition strategy (attempting to trade down the enemy army), especially when the raiding player might try to force into the position by striking first (ex: with a galeforcer)
- 5th attacker isn't good just for not losing units; it's good for trying to break aether structures within 7 turns, which can definitely make or break an attempt at tier promotion.
- cost of constructing 3 structures other than schools = cost of one extra slot