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Lt. Commander
Join Date: Dec 2007
Posts: 120
This thread is to show the effectiveness of shields arrays and can serve as a guide to why you might want to use a particular shield over an alternative shields.

This research is mostly based on "theorycrafting" and mathematics - It is based on the numbers that define a shield and give insight about a shield's performance over the course of a battle, but a typical space battle is dynamic and there are many factors that my analysis cannot account for.

During the discussion on the new set items there was a lot of talk about how no one would want a shield array that isn't a covariant shield with the highest number of [CAP] modifiers. The Borg set was particularly criticized for offering "only" Regenerative Shields.
People like their shield capacity, and it seems no one really cares much about regeneration.

An assumption I had when making my my shield comparisons was that the longer you can stay in battle and keep regenerating your shields, the more impact a higher regeneration will have, and the less its base capacity has. I was basically calculating at what point this would occur.

Some basic mechanics behind shields:

Shield Regeneration
Shields apply their regeneration value to all shield facings every 6 seconds. "Overheals" (for example when a shield isn't damaged at all) are lost. That's why it is good to distribute shield power to equalize the facings so that every shield gets some healing. (This won't do much if you are already under attack from all side.)

The regeneration value is modified by your shield power. At 50 shield power, you have the number listed in a shield's description. For every point above 50, you shield regeneration value increases by 4 %, and for every below, it reduces by 4 %.
Formula: (1 + (Power Level - 50) / 25) x Base Regeneration at 50. Note that this formula doesn't really apply below 25 power - you would normally get a negative regeneration then, but this is not applied to your ship. Otherwise, you would lose shields at Full Impulse. Only if you are using an ability that brings your shield power to 0 do you lose shield capacity.

Shield Damage Reduction
Shield Power also grants your shields damage reduction. This damage reduction is Shield Power / 500.
Other powers also grant your shields damage reduction. There is a hard cap at 75 %.
Note that shield damage reduction does work differently from resistance modifiers for hull. It directly reduces all damage to shields, while there is a special formula for diminishing returns with hull resistance modifiers.
It can be handy to calculate your "effective" shield points with the damage reduction values. Your effective shield points are determined as follows: Shield Capacity x (1 / (1 - Damage Reduction)). If you could get 100 % shield resistance, the value for Resistance would be 1.0 and the formula would lead us to a infinite value - of course, if you take no damage at all, your shields are effectively infinite.

While this is handy to know, it is not really that crucial for comparing covariant and regenerative shields in my calculations. Since the resistance value is also applied to the shield points that get generated over time, the results don't really change. The consideration is still the same as before - can I live long enough for the regeneration to matter?

Effective Shield Points Over Time
Your effective Shield Points over time (in seconds), based on your base shield capacity, your regeneration value, and shield power and with an optional additional damage reduction value is as follows:

(Shield Capacity + ((1 + (Power Level - 50) / 25) x Base Regeneration) * (Time/6) ) x (1 / (1- Power Level/500 + Optional Additional Damage Reduction))

Visualization
Any lame (or decent?) mathematician would now use this formula with the values of two different shields at the same power level and no additional damage reduction, equate them, and resolve for time. Sounds boring, right?

Well, what I did was creating a chart in Excel and resolve the formula for different shields, different times and different power levels and check what would happen.
What I was looking for was the same as the mathematician - at what point in time would the effective shield capacity regenerated over time be higher for a shield slanted for regeneration over a shield slanted for capacity?

I made the following charts from those numbers to help visualize the results:

The following charts are based on my Tactical Vice Admiral Tactical Escort Retrofit Captain mostly.
She is trained in the Tier 3 and Tier 4 skills to about 5 ranks, fully trained in his Tier 5 skill, and at about 7 at the Tier 1 and Tier 2 ship command skills. I took a all these values from the values listed by vendors when I was in Earth Space Dock on Tribble.
The Tier 1 shield data actually comes from the stowiki.

The chart might look somewhat different for players with different skill selections, and for different ships. A Science Vessel for example has a bigger shield capacity then the Tactical Escort. Generally, the more bonuses you get for your shield capacity, the more shields with a high innate value benefit.

Below are the charts for all bog standard Mark I shields.
Below are charts for rare Mark X shields. I used rare Mark X since I could easily get their statistics from the Exploration vendors. The above charts have an additional annotation. Since it gets a little dense with data points and lines, I marked the major points where shields "catch up".

Observations
For Mark I shields, you will notice that the resilient shield seems to suck for a long time - well, my math above is unfair. I didn't really account for the fact that is has 5 % additional damage reduction that bring its bleedhtrough down to a 5 %. Oops. The problem here is that it's hard to evaluate what that reduced bleedthrough means in the shield comparison.

For just considering shield capacity alone, well, bleedthrough is non-damage. Having less of it makes no difference for the shields. But I suppose that everyone that remembers dying from bleedthrough under a Reverse Shield Polarity will feel differently about that. Let's leave this for another discussion.

For the Mark I shields, you can see that at 100 shield power, it takes about 48 seconds until a Regenerative Shield catches up to a Covariant shields. At 50 Shield Power, it takes about 144 seconds instead.

For the rare Mark X shields, it takes about 54 seconds at 100 shield power for the Regenerative [Reg]x2 shield to catch up with the Covariant [Cap] x2 shields. It takes about 42 seconds to catch on with the Covariant [Reg]x2 shield.
At 50 shield power, it needs 156 seconds and 120 seconds respectively.

What does that mean for the shield comparison? Which one should you take?
When discussing whether you want capacity or regenerative - go all the way. Either focus fully on capacity, or focus fully on regeneration. Covariant shields with Reg mods are quickly surpassed by regenerative shields, and Regenerative shields with capacity bonuses are quickly surpassed by regenerative shields with regeneration bonuses.

Whatever shields you are currently using, think about how long you last in combat when under fire. How long does it take for your shields to fall and you getting into trouble? You run at 100 shield power most of the time (be it with buffs or just because that's how you set shield levels).
Does it take less then 50-60 seconds? Get the best Covariant Shields with the most Cap mods you can get.
Do you last more then 50-60 seconds? Get the Regenerative Shields with the most Reg mods you can get.
You run at 50 shield power? Same question and answes, but with 156 minutes (2 1/2 minutes)).

When thinking about your shield power and regeneration, consider these aspects, too:
• When you cloak a lot, your shield power is often 0.
• If you expect to get a lot of shield heals, innate regeneration becomes less valuable.
• If you're already dead, you won't benefit from the shield regeneration, just from the respawn.

Of course, this is still a little too easy. 2 more things to consider:
• Distributing Shield Power. Your effective regeneration might be 4 times higher, which would mean the numbers above are inflated and could be about as 1/4 as long. Unfortunately, this is ignoring one thing - you are also distributing the already existing shield capacity. So you also have to multiply your shield capacity with a factor of 4, too, in all the calculations. This inflates the numbers of shield capacity (now describing the full capacity of your shields across all 4 facings), but it won't change the times.
• Shield Heals. There are tons of this flying around in this game. The reason you survive your covariant shields for 50 seconds might actually be due to the generous application of shield heals. And these ones clearly benefit covariant shields. You are more likely to not waste any shield points on covariant points, and the healing values tend to vastly exceed the amount of healing from regeneration.

All in all, I see why people prefer to go Covariant. And I am afraid I will have to say good bye to my Regenerative Shield Arrays, too. 50 seconds is a lot of time in PvP,and I have a lot of heals on my ship(s)... I might still take the Borg Shield Array, though - assuming I have a full set and get the bonus heals.

From a game design perspective, I think Cryptic will have to reevaluate a few aspects on shields if they want to make them more competitive.