Game Mechanics Revealed: Dual Cannons vs. Dual Heavy Cannons

Welcome to Game Mechanics Revealed.  Star Trek Online is filled with vagaries; the devs are not forthcoming with clarification; the forums are a source of confusing and contradictory knowledge; the chats are rife with conjecture and misinformation.  In this series, I will attempt to find the answers and dispel the myths that plague our game.

My partner in science is the ever patient and ever enthusiastic @JeanLPicard.

Game Mechanics Revealed: Dual Cannons vs. Dual Heavy Cannons (Updated with hitting power)

While dual heavy cannons are the standard armament of escorts everywhere, some players contend that the increased rate of fire of dual cannons leads to an increase in proc rate, and that therefore regular dual cannons are a more effective weapon despite dual heavy cannons’ 10% bonus to critical damage.  The dual cannons also have a smaller energy drain penalty, which some speculate might be more important than the critical hit bonus of dual heavy cannons.

Premise 1

According to the tooltip info, dual cannons have twice the rate of fire as dual heavy cannons, with the same dps.  Therefore the proc rate of the dual cannons should be twice that of dual heavy cannons.

Experiment 1

The aggressor is armed with 4 phaser dual cannons.  At a long range and low weapon power, the aggressor fires for 5 minutes at the target, and the number of times the target’s systems go offline is counted.  The test is repeated with 4 phaser dual heavy cannons.

Results 1

	Systems Offline
Test	Dual Cannons	Dual Heavy Cannons
1	12	5

Pretty clear cut, isn’t it?  But that’s why we test with large sample sizes.  Here’s the full table.

	Systems Offline
Test	Dual Cannons	Dual Heavy Cannons
1	12	5
2	8	7
3	6	10
4	13	12
5	10	13
Total	49	47

Analysis 1

It’s been 6 years since I’ve done any advanced statistics, so I’m only about 40% sure I’m using the right statistical analysis tool for this.

Null hypothesis, Ho, is that the two means of the number of procs are the same, or u1 – u2 = 0.  Therefore the alternate hypothesis, Ha, is that the two means are not the same, or u1 – u2 ≠ 0.  We wil compare the outcome with Student’s t distribution.  There are 5 data points per sample, implying 5 + 5 -2 =8 degrees of freedom and we are using a two-tailed test, Ta/2(8) = 2.306 at the 95% confidence interval.  Therefore we will reject the null hypothesis if t > 2.306.

n	5	5
average	9.8	9.4
sample standard deviation	2.863564	3.361547
sample variance	8.2	11.3
Pooled s^2	9.75
s	3.122499
t	0.202548

since 0.202548 is << than 2.306 the null hypothesis cannot be rejected.

Conclusion 1

49 is pretty darned close to 47.  In fact, I really did not need to do the statistical analysis; I just wanted to flex my intellectual muscles since it’s been too long since I used them.  The proc rates for the two types of weapon are the same.  We can calculate number of procs per weapon per minute.  There were a total of 95 procs for the total of 50 minutes of firing time, with 4 weapons firing at a time.  This works out to 0.475 procs per minute per cannon for this experiment.

In fact, the proc rate is based on the cycle.  The cycle for dual cannons and dual heavy cannons is 3 seconds long, during which time there are four hits counted for dual cannons, two hits for dual heavy cannons.  At the stated proc rate of 2.5%, this would work out to 0.5 procs per minute, very marginally higher than the proc rate as worked out in the experiment, and well within expected randomness of testing.

Premise 2

The energy drain of dual cannons is less than dual heavy cannons, and will result in a higher dps than the dhc’s bonus to critical hits.

Experiment 2

The aggressor is armed with 4 polaron dual cannons and 3 polaron turrets to simulate real battle weapons usage.  At 5km and 125 weapon power, the aggressor fires at a target until the target is destroyed.  The test is repeated with dual heavy cannons replacing the dual cannons.

Results 2

	Time to Kill Galor Cruiser, seconds
Test	DC	DHC
1	32	32
2	33	29
3	32.5	29
4	32.5	29
avg	32.5	29.75

Analysis 2

Null hypothesis, Ho, is that the two means of the time to kill are the same, or u1 – u2 = 0.  Therefore the alternate hypothesis, Ha, is that the two means are not the same, or u1 – u2 ≠ 0.  We will compare the outcome with Student’s t distribution.  There are 4 data points per sample, implying 4 + 4 -2 =6 degrees of freedom and we are using a one-tailed test, Ta(6) = 2.447 at the 95% confidence interval.  Therefore we will reject the null hypothesis if t > 2.447.

n	4	4
average	32.5	29.75
sample standard deviation	0.408248	1.5
sample variance	0.166667	2.25
Pooled s^2	1.208333
s	1.099242
t	3.537971

Since 3.537971 > 2.447 the null hypothesis is rejected at the 95% confidence interval.

Conclusion 2

The extra bonus to critical hits of the dual heavy cannon is more useful than the lesser energy drain of the dual cannons, to the tune of a nearly 10% increase in killing power under the conditions tested.

There you have it: Dual Heavy Cannons are better than Dual Cannons.

(*Jay. L. Devore, Probability and Statistics for Engineering and the Sciences, 5th Edition, 2000, Duxbury Thomson Learning)