One of the most common questions people want to know about skills is how much trickle-down they can expect in a skill if they raise a particular core ability either by spending IP, implanting, or buffing that core ability.
First a brief explanation of what trickle-down is, if you are not familiar with it. Every skill your character can develop is dependent on one or more of the six core abilities of Strength, Agility, Stamina, Intelligence, Sense and Psychic. When those core abilities go up, you increase your skill in every area that depends on the core ability without even having to spend IP directly on that skill. For example, as you raise Intelligence, you automatically become a little better in Nanoprogramming even if you never use IP to train that skill. You can find what abilities a skill depends on by shift-left-clicking its name when your skill menu is open. You can also see a full table of them all at AO Stratics.
An overly simple way to consider the problem is that trickle-down happens at a ratio of 4:1. That is, for a skill that is 100% dependent on a core ability, 4 points in that core ability raise the dependent skill by 1. Here is a simplified formul to use when just figuring minimum trickle-down from a single source:
<Amount of Core Ability Increase> / 4 * <Dependency Factor> = Trickle-Down. Discard any fractional part.
For example, using Ranged Init, which depends 60% on Sense, you could expect the following from Sense Boost (General buff for +12) and Enhanced Senses (Agent buff for +15):
27 / 4 * 60% = 6.75 * 0.6 = 4.05.
Discard the fractional part to get the result of 4 points of trickle-down. In practice you will find that this is sometimes a point less than what you really get, because of either hitting a rounding boundary or because of the contribution from other abilities the skill depends on. The only thing that matters is what the final value of each of the contributing core abilities is, not how much is coming from any individual source to any individual core ability.
Note that using the general boosts for +12 to each of the abilities (which is now even easier in Shadowlands with the Composite Boost) a skill is dependent on will always get you exactly +3 to the skill, no more and no less. This is because the sum of the dependencies is 100%, which is equivalent to the situation of a skill dependent on a single ability.
Rearrange the forumula and you can find out what the interval is for how often a skill goes up when only one dependent ability is considered:
1 / <Dependency Factor> * 4 = <Core Ability Increase Interval>
The possible intervals are all listed in the following table. (Well, 90% isn't actually possible; no skill depends 90% on an ability.)
Thus, looking at Mechanical Engineering and its 50% Intelligence factor, you would get one more point in the skill for every 8 you put into Intelligence past the first rounding hump. Of course, you could need as few as one point in Intelligence to get over the rounding hump to that next point of trickle-down, but after that every additional point will need the full 8 more Intelligence.
The complete formula for taking all of the dependencies into account looks more like this:
Sum(<Core Ability> * <Dependency Factor>) for each dependent ability = <Sum> (<Sum> - 0.1) / 4 = Trickle-Down Discard any fractional part.
Your minimum innate skill in anything is 5, so trickle-down benefits start from there. Say you were a level 100 Nanomage with maxed Agility and Stamina at 303 each and mediocre Strength at 200, with none of them implanted or buffed. Your Piercing weapons skill depends 50%, 30% and 20% on those abilities, which would be the following if you never put any points into it:
303 * 0.5 + 303 * 0.3 + 200 * .2 = 282.4 (282.4 - 0.1) / 4 = 70.575 70 + 5 innate = 75 Piercing
Unlike with the simplified forumla, where you can just plug in the amount of change to a single ability, this method requires you to compute your starting point, then recompute your ending point. The extra effort rewards you with a more accurate number, though.
All in all, it would be easier just to get on the skill emulator, like AO Skill Emulator Ex or AO Skills Emulator to play with the numbers. (The former is a more recent and more fully feature program; the latter deserves credit as the first program that emulated skill and ability interaction.) At least when you do so, you'll know how trickle-down works.