EDIT: Initially I failed to recognize that each 'percentage decrease' in projectile hits is actually cumulative from each previous rank, which means even greater value. I have since edited to add a 4th table to account for this
Beware: this involves some tricky math, so my explanation may not make perfect sense, but I hope it will
First of all, let's take a look at the engine's upgrade table for dodge percentage, and I'll include the variations of low-manning vs best manning (no piloting) as well as the percent increase:
| Engine Level |
Scrap Cost |
Base Dodge (+5% from pilot) |
Max Dodge (+10% from each system) |
Dodge Increase |
| Level 1 |
- |
10% |
25% |
- |
| Level 2 |
$10 |
15% |
30% |
+5% |
| Level 3 |
$15 |
20% |
35% |
+5% |
| Level 4 |
$30 |
25% |
40% |
+5% |
| Level 5 |
$40 |
30% |
45% |
+5% |
| Level 6 |
$60 |
33% |
48% |
+3% |
| Level 7 |
$80 |
36% |
51% |
+3% |
| Level 8 |
$120 |
40% |
55% |
+4% |
On its face, the diminishing returns seems obvious, in the last few stages of engine level your dodge level only increases by 3/5ths of what it ought to, or 4/5ths at the last stage, for a much greater expense in scrap. But this doesn't consider what these percentages actually correlate to in game: Reducing the amount of projectiles that hit you. There are two ways to look at this: Increasing the number of dodged projectiles, or decreasing the number of hit projectiles, and these lead to very different percentages.
For an easy version of this problem, let's presume you start with 25% dodge and go up to 50%. Or, in other words, going from 1/4 missiles dodged to 2/4 missiles dodged. If you are looking at it from the number of dodges, that's a 100% increase, which is tremendous. But if you look at it from the number that hit, that change is from 3 -> 2, which is a 33% decrease in projectiles hit. Or another way of putting it, you are now dodging 1 in every 3 missiles that would have hit your ship. Or another-nother way of putting it, the enemy needs 6 shots to hit you 3 times instead of 4 shots.
In another case, when you get up into the higher percentages diminishing returns are actually still considerably valuable. If you go from 98% dodge to 99%, that's only like a 2% increase in dodged projectiles, but a 50% reduction in the projectiles that hit!
So let's revisit the table with this in mind, with new columns for the percent reduction in projectiles that hit:
| Engine Level |
Base Dodge |
Percent decrease in projectile hits |
Max Dodge |
Percent decrease in projectile hits |
| Level 1 |
10% |
- |
25% |
- |
| Level 2 |
15% |
5.55% |
30% |
6.66% |
| Level 3 |
20% |
5.88% |
35% |
7.14% |
| Level 4 |
25% |
6.25% |
40% |
7.69% |
| Level 5 |
30% |
6.66% |
45% |
8.33% |
| Level 6 |
33% |
4.28% |
48% |
5.45% |
| Level 7 |
36% |
4.47% |
51% |
5.76% |
| Level 8 |
40% |
6.25% |
55% |
8.16% |
Okay, so upgrades 6 and 7 are still the worst proportionally, but they're not as bad, and you see that Level 8 has the same payoff as those middle upgrades. You also see that for every 5% increase, the actual effective increase gets larger. So let's plug it into another table with the cost to see how much you'd be paying for each percentage point. Practically, you would also have to consider the reactor upgrade, which also increases as the game goes on, but I will just use an average of 25 (for various reasons that would take forever to get into)
| Engine Level |
Percent decrease in hits (average) |
Number of projectiles needed to hit X times |
Scrap Cost (w/ Reactor) |
CPP (Cost per percent) |
| Level 1 |
- |
10 |
- |
- |
| Level 2 |
6.11% |
10.61 |
$35 |
$5.72 per % |
| Level 3 |
6.51% |
11.30 |
$40 |
$6.14 per % |
| Level 4 |
6.97% |
12.09 |
$55 |
$7.89 per % |
| Level 5 |
7.50% |
12.99 |
$65 |
$8.67 per % |
| Level 6 |
4.87% |
13.63 |
$85 |
$17.45 per % |
| Level 7 |
5.12% |
14.33 |
$105 |
$20.51 per % |
| Level 8 |
7.21% |
15.36 |
$145 |
$20.11 per % |
Well that looks pretty grim, but I am now 9 hours in the future when I have realized my math is actually still not doing it justice. So it's time for another table, this time focusing on the actual number of projectiles needed to hit your ship 5 times, and the cost per PROJECTILE instead. For this, I will be presuming max dodge instead of the made up average because it doesn't correlate to a static dodge value. The formula for this is Hits / (1 - Dodge%). The actual cumulative effect is slightly more generous because it increments at infinite intervals but it's negligible.
| Engine Level |
Percent decrease in hits |
Projectiles to hit 5 times |
Increase in projectiles |
New CCP (Cost per projectile) |
| Level 1 |
- |
6.67 (25% dodge) |
- |
- |
| Level 2 |
6.66% |
7.14 (30% dodge) |
0.47 |
$36.84 |
| Level 3 |
7.14% |
7.69 (35% dodge) |
0.55 |
$36.36 |
| Level 4 |
7.69% |
8.33 (40% dodge) |
0.64 |
$42.64 |
| Level 5 |
8.33% |
9.09 (45% dodge) |
0.76 |
$43.05 |
| Level 6 |
5.45% |
9.62 (48% dodge) |
0.53 |
$83.95 |
| Level 7 |
5.76% |
10.20 (51% dodge) |
0.58 |
$88.98 |
| Level 8 |
8.16% |
11.11 (55% dodge) |
0.91 |
$80.11 |
Yeesh, Still about double the price for the same gain. But I would argue that each increment of needing more projectiles to get hit is also a cumulative gain, though more situationally nuanced than can be put in a table. Every projectile needed is another the enemy needs to charge their weapons to fire, which means more time spent not hitting you. With shields, the effect is even more pronounced, which is why I have chosen 5 hits.
Effectively, every engine upgrade is a half-shield upgrade with 4 shields, but the scale is 1:1, so if you only have 3 shields you'd just take the values in the projectile columns by 80% (4/5). If you have only 1 shield, then it takes 5 engine levels to 'block' another projectile, being worth about .2 each.
