In the early game, the main and arguably the only strength of having a thief in the party (no one would be stupid enough to put TWO thieves in the same party) is the facilitated running ability. I do not mean to suggest that a party without a thief should never run. Running is a crucial part of FF1. However, with a thief, one can reasonably expect that on average, the party can escape a battle one or two rounds earlier than it could without said thief. Depending on the exact battle one wishes to run from, this may or may not be important, and so it comes down to having a little bit of increased flexability in deciding which battles to fight, and which battles to run. Consequently, the party without a thief is forced to be more careful in these decisions.
In general, the more rounds a battle takes to win, the more one gains by choosing not to fight at all. If a battle can likely be won in 2-3 rounds, then by the time running is successful, the enemies may very well have been defeated anyway, with the added benefit of exp and gold. Thus, running does not save much damage, and is therefore not an optimal choice (assuming the party does not have a thief - if the party has a thief, things are not quite as strict because it is often possible to escape even before any damage is dealt). But if the battle is likely to last for more like 9 or 10 rounds, then even running by the 3rd or 4th round may prove to be a valuable conservation of damage. To illustrate this a little more clearly, let's take a look at some examples.
Party: Fighter, Red Mage, Black Belt, White Mage (a strong non-thief party)
Level: 6
Area: Marsh Cave
Battle 1: Crawl, Red Bone, and 3 Bones
This is a tough battle - arguably one of the toughest in the Marsh Cave (excluding bosses). Red Bones have a very strong physical attack. Stronger than a Muck even. Combine this with the fact that there's a good chance the fighter will be paralyzed by the Crawl without even getting a shot off, and it is easy to see the danger here. However, the nice thing is that Red Bones are vulnerable to FIRE and HARM magic. Taking this into consideration, it is possible to focus-fire and remove the Red Bone within the first couple rounds of play (HARM will get rid of the Bones as well). Once the Red Bone is gone, nothing else can inflict significant damage (Crawls usually only hit for 7 or so even against a light-armored character). Therefore, it should be easy to see that not much is gained from running here. Again, that is not to say one should never run from this battle, but on average, will not gain relatively as much from doing so.
Battle 2: 2 Crawls, and 3 Bones
While almost identical to Battle 1, the change from a Red Bone to an additional Crawl is huge in how it affects the dynamics of the battle. Even though the enemies will deal less damage per round, the battle is now expected to take longer, for two reasons. First, with two Crawls, the fighter is now going to be paralyzed about 75% of the time by the end of round 1, with other characters soon to follow. More paralysis means more time. Second, unlike Bones and Red Bones, Crawls are difficult to take out quickly. They aren't weak against any particular magic, and they have a higher physical evade than their undead allies. It follows that running is usually going to be a better decision here.
Battle 3: 2 Arachnids, 1 Spider, 1 Scum, and 1 Muck
Here we have an interesting battle that is not quite as difficult, chiefly because Mucks are not as strong as Red Bones, and there is no danger of paralysis. Mucks are weak against LIT, and due to their strong physical attack, should be taken out immediately. This can usually be done in the first round. The rest of the battle should flow smoothly. Poison is annoying, but one normally has an adequate supply of PURE before going into an area like this. This battle is almost always a must fight.
Battle 4: 4 Scum
Now we take a look at an example of the extreme opposite situation. Unless one can afford to blow 4 spells on a single battle, which is not usually the case, this battle will take a long time to win due to the high defense of the Scum - all characters will hit for 1 or 2 damage unless they get lucky with a critical. The exp and gold is not great, and the poison often ends up doing a fair amount of damage over the course of the entire battle. Running here is usually the right instinct.
