When a settlement attack is triggered (and the quest objective appears) and the player character is away from the targeted settlement, there is a chance it will be able to defend itself without the player character's interference, completing the quest objective.This chance is determined by comparing the defense strength (defense rating + population) + a random number between 1 and 100 and the attack strength ((food + water in the settlement) +/-50%) + a random number between 1 and 100. The defense strength is capped at 100, so it's not useful to have more than (100 - population) defense when not responding to settlement attacks. The amount of food + water and the attack strength are also capped at 100, so the maximum attack strength is 50-100 (100 +/-50% = 50-150, capped at 100). When the random numbers are added to the attack strength and defense strength, the total attack value is capped at 150 but not the defense which can go up to 200. This means that high defense is more likely to win, but even when it's maxed out there is still a fair (30.6%, roughly 1/3) chance to lose to an attack on a "rich" settlement.
Therefore, to maximize a settlement's chances of defensive victory while away (without sacrificing settlement happiness), the settlement's defense rating should be equal to (or greater than) 100 minus the total population of the settlement, and there should only be enough food and water (each equal to the total population) and no more. For example, if a settlement has a population of 13, it should have at least 87 defense, exactly 13 food, and exactly 13 water.

Results of a settlement attack simulation using Bethesda's algorithm (sample of 10M simulated attacks for each case):

Food + Water Defense + Population Attackers win %
0 1 48.5
0 25 27.7
0 50 12.2
0 75 3.0
0 100+ 0


Food + Water Defense + Population Attackers win %
50 1 85.7
50 25 70.4
50 50 49.5
50 75 28.3
50 100+ 12.8


Food + Water Defense + Population Attackers win %
100+ 1 97.7
100+ 25 91.4
100+ 50 78.4
100+ 75 53.7
100+ 100+ 30.6