A lot of players here are veterans of the game and have played the game dozens or hundreds of hours. In their playthroughs they have encountered many aspects of the game, amongst which is the leveling system. Perhaps players have tried to manually train skills from the lowest level (5) to the highest level (100) by actually using the skills instead of buying it from a trainer. In this post I’m trying to explain why leveling weapon skills can be difficult when you are at both low and high skill levels using mathematics.
First things first, how do skills level? Every hit of the enemy gives you one progress point towards your next level. How many progress points do you need to increase your skill level? ProgresPointsRequired = (1 + SkillLevel)*SkillGroupBonus*SpecializationBonus. Basically, every level you need ‘level+1’ progress points or in this case hits. What are the SkillGroupBonus and the SpecializationBonus? The SkillGroupBonus is whether the Skill is Major, Minor or Miscellaneous. Major corresponds to SkillGroupBonus 0.75, Minor to 1.0 and Miscellaneous to 1.25. Basically, major skills level 25% faster and misc skills level 25%(actually 20%) slower. The SpecializationBonus means that you have chosen the skill group as a specialization (out of Combat, Magic and Stealth) and is 0.8 if the skill is in the right group and 1.0 otherwise. This also gives a 5 point bonus to all skills in the group.
Since the skill we are trying to level starts at 5, we know it is both misc and not in the specialization group. This gives us the following formula. ProgresPointsRequired = 1.25*(1 + SkillLevel). This means that at skill level 5, we need 1.25*(1+5)=7.5(=7 rounded down) hits to advance to the next level will at skill level 99 we need 125 hits to connect. In total, we would need 6294 hits to level from 5 to level 100 with each level become 1.25 points/hits harder.
It looks like we’re done now, right? The problem is, we’ve forgotten to add in the hit chance, which makes leveling from lower skill levels an issue. How does hit chance work in Morrowind. It’s quite a simple idea as the hit chance is (Attacker's Hit Rate - Defender's Evasion)%. How are both stats calculated? With the following formulas: HitRate = (Weapon Skill + (Agility / 5) + (Luck / 10)) * (0.75 + 0.5 * Current Fatigue / Maximum Fatigue) + Fortify Attack Magnitude + Blind Magnitude and EvasionRate = ((Agility / 5) + (Luck / 10)) * (0.75 + 0.5 * Current Fatigue / Maximum Fatigue) + Sanctuary Magnitude. Let’s assume no special situations(Fortify Attack, Blind and Sanctuary are 0). We get the reduced HitRate = (Weapon Skill + (Agility / 5) + (Luck / 10)) * (0.75 + 0.5 * Current Fatigue / Maximum Fatigue) and EvasionRate = ((Agility / 5) + (Luck / 10)) * (0.75 + 0.5 * Current Fatigue / Maximum Fatigue). Let’s assume that both the player and the enemy NPC are about evenly matched and at full fatigue, we can get an actual hit chance HitChance = 1.25*(SkillLevel)/100%. This is a bit of a simplification as the player will later on be a lot more powerful and have much higher stats than a random enemy NPC but this will suffice for this explanation. We can see that at low skill levels, the chance to hit is often abysmal (e.g 6.25% at level 5). We now deduce the number of strikes on average to produce a hit. Using the expected value, we get StrikesRequiredForOneHit=1/HitChance=100/1.25*SkillLevel. Combining this into the final formula we get StrikesRequiredForOneLevel=(100/1.25*SkillLevel)*1.25(1+SkillLevel) which reduces to StrikesRequiredForOneLevel= 100 + (100/SkillLevel).
This implies what we may have noticed ourselves when playing, leveling a weapons skill actually becomes easier when we are at a high level since we miss less too. Note that after level 80, since you are guaranteed to hit, HitsRequired simply becomes ProgressPointsRequired again and leveling becomes harder as the player becomes more skillful.