Sunday 19 August 2012

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)

7 comments:

  1. I am sorry but premise n°2 is completly wrong, DHC are more energy efficient than DC, this has been known for a while now, this is because of the difference in their firing cycle, namely 1 sec of shoting (and power draining) followed by 2 sec of rest for DHC versus 2 sec of shoting and 1 sec of rest for DC.

    For short the DHC drain -12 weapon power 1/3 of the time while the DC drain -10 weapon power for 2/3 of the time resulting in a higher average power level with DHC versus DC. A forum user named Nagorak made EXTENSIVE testing about this a couple years ago and found the same (10%) difference in killing speed betwen DHC and DC so your empiral test are valid at least. Sadly that was done on the old STO forum, not the new PWE forum.

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  2. I'm different from the Anonymous on 12 Jan. I believe what he/she said is incorrect. The -12 or -10 weapon power is not per shot fired, it is per weapon cycle. Regular dual cannons are more energy efficient than dual heavy cannons. Yes, they fire twice per weapon cycle, but that does not mean that the -10 is applied twice.

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  3. Apparently Anonymous from january 28 didn't understand at all january 12. Nobody said the energy drain is applied multiple times, the question was never magnitude it's about duration.

    Anyway thanks a ton for these test, now I can finally shut up all the people claiming that the proc is per shot fired even though it's doesnt match at all what my Polaron weapons are doing.

    Now that I think about it there is now an imunity period to the phaser proc after you've been hit by it, was this test made before that was patched in?Because that would screw up the result.

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  4. DEM and Tet Glider are per shot. Weapon flavor is per cycle. Bort said it but it was before the forum changeover. Omega Weapon Amplifier, IDK.

    @RedRicky

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  5. Best reason to use dual cannons is if you use ONLY cannons. Rapid Fire results in more shots being fired with dual cannons than with dual heavies. This is simple logic.

    If rapid fire increases shots fired by 50%, and over a 3 second cycle time dual cannons fire twice while dual heavies fire once, than in a 6 second block the dual heavies will have fired 3 times and the dual cannons 6 times. Now, I know this is a great exaggeration, but it shows my point.

    For critical damage, dual heavies are better because each shot hits. But in situations where you can not guarentee 100% hit, dual cannons are better.
    DHC [acc]x3 are amazing weapons, but if you can not get them than you should go with DC [acc]/[acc]*2. More shots fired means that less chances all your damage misses.

    if you fire a dual heavy, and it misses, that is damage gone. But for the same damage done, it takes more shots with dual cannons. This means more chances for the shots to actually hit.

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  6. I made similar tests and also tested acc/crtD/crtH although I forgot all the statistical maths since it's been so many years since I did it and not needed it since. I used plasma cannons because that's what I had to hand. Not sure about using phaser since I've not used them in a very, very long time but players could have an immunity to future procs (obviously for a small time but enough to affect the results).

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  7. I believe this test was done before the immunity to the phaser proc happened. If certain things are indeed applied per shot then a case might be made for DCs. It would be interesting to;
    1. Find out what does proc or get applied per shot
    2. See how much of a difference it really makes to uptime of proc or effectiveness of applied buff/debuff.

    ReplyDelete