D04S02B04, on 21 October 2013 - 09:40 PM, said:
I done up the Math as well and I see where I gone wrong with my assumption in doing up the probability table. I can't see ur post in the forum btw.
What was the base that you used as a function of Total Shots / Total Time? I used 19.5 seconds as it was a common multiple of 1.5sec and 6.5 sec.
6.5? What 6.5? When it jams, it just sits jammed for 5.0 seconds and then it's ready to fire again. That was my impression with the weapon...
And, well, if you can't see my post through the link... Well... I guess i'll drop the thing here. It's a little bit big, though. /gulps
Anyways. %)
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AC/5 or UAC/5: the answer
...
Details and math.
1. Stats.
Most stats are the same:
- damage per shot (5),
- heat (1),
- projectile speed (1300),
- impulse (0.030),
- range (almost: AC/5 has range = 600, max range = 1700; UAC/5 has range = 620, max range = 1800),
- amount of ammo per ton (30) ( - since last patch).
Other stats are a bit different:
- weight (AC/5 = 8 tons, UAC/5 = 9 tons),
- slots (AC/5 = 4 slots, UAC/5 = 5 slots).
And of course, the main difference:
- AC/5 has plain 1.5s cooldown, while UAC/5 also has 1.5s cooldown, but: "can be shoot during cooldown but has 20% chance to jam. If jamed it needs 5.0s to unjam". That's what Smurfy's data says. Testing reveals it's not entirely correct (to say the least). See "Tests done" section at the end of this post.
2. DPS over (nearly) infinite time (1000 shots).
AC/5 = 3.33
UAC/5 = 4.0
- The latter is calculated by me using facts i found during in-game testing of the weapon, and assuming "non-jam cooldown" per shot being 0.75s (for simplicity; shouldn't affect the outcome even while in reality it's "pairs" of shots, because ~half of shots on which jam happens will be 1st shot of the pair, and the other half - 2nd shot of the pair). Math is: 5000 (damage, total) / ( 11.65% * 1000(shots fired) * 5s + 88.35% * 1000(short fired) * 0.75s ) = 4.016.
3. DPS over 2.25 seconds time frame
AC/5 = 4.44
UAC/5 = 6.8 average (actually 2.2 ... 8.9 - varies; the former is for when it jams after 1st shot, the latter is for when it doesn't jam for 3 shots in a row (1st ... 3rd shots).
- this kind of DPS is important for punching any standing mech, assuming it will go into very nearby cover once under heavy fire, and/or we need to. 2.25 seconds is close to average time one can keep firing at a target in such situations, and is "fair" average considering AC/5 fixed cooldown.
Note. It is useful to figure out chances here. Based on my tests and with a bit of probabilities' theory,
- chance UAC/5 will do exactly 2.2 DPS ( = single shot which jams the weapon) over 2.25 seconds: ~11.65%;
- chance UAC/5 will do exactly 4.4 DPS ( = 2 shots) over 2.25 seconds: ~10.29%;
- chance UAC/5 will do exactly 6.7 DPS ( = 3 shots) over 2.25 seconds: ~9.09%
- chance UAS/5 will do exactly 8.9 DPS ( = 4 shots, maximum possible during this time frame) = 68.97% (this is total for when 4th shot jams, and when it doesn't)
This (roughly) approximates to average DPS of 6.8, as shown above.
4. DPS over 8 seconds time frame
AC/5 = 3.75
UAC/5 = average 4.6 (actually 1.25 ... 7.5 - varies; the former is double jams on 1st shots, probability of which is ~1%; the latter is no jams whatsoever for 11 shots in a row, probability of which is 25.6%) - this kind of DPS is improtant for an average-length brawl. Longer than 8 seconds encounters will have DPS figures of both weapons being increasingly similar, as it becomes increasingly unlikely for UAC/5 to either jam all the time, or not to jam all the time.
- it is challenging to calculate average UAC/5 DPS here, considering all possible jam cases. Single jam early may end before 8 seconds are over, and more shots then may be fired. Single jam being "late" during 8s does not lower DPS over 8s as much as a jam "in the middle" of it. So, as my limited math knowledge allows, the best guess i can do is this: average must be not too far from to 4.6 DPS (which i put above). If i am mistaken with it, then hopefully not more than by 0.2DPS.
5. Supressing fire reliability (percentage of time a weapon is mauling the target, 1000 shots fired)
AC/5 = 100%
UAC/5 = 72.2%
- the latter is calculated by me using following assumtion: the target is considered "supressed" whenever it is hit by the weapon, and whenever it was hit by the weapon less than 1.5 seconds ago. Math is: (total time supressed) / (total time needed to fire 1000 rounds, see p.2) = ( 88.35% * 1000 * 0.75s + 11.65% * 1000 * 1.5s ) / 1160s = (662.6s + 174.75s) / 1160s = 72.2%.
That's pretty much it. Numbers here define conclusions both above and below.
AC/5 is clearly a winner in supressing fire ability (especially when paired with a 2nd AC/5 and fired one after each other), hammening the enemy often enough to shake him often enough and strong enough to make proper aiming nearly impossible - i heard that the shake is proportional to impulse * damage, and AC/5 has nearly same impulse as AC/2, but 2.5 times higher damage, so it kicks rather well. Also, 72.2% supression ability of UAC/5 is calculated for a 1000 shots; no enemy can stand for that long, of course. Important thing to realize here is that UAC/5 spends almost half of the total time being jammed (roughly (1160 - 663) / 1160 = 42.8% of the time), and during this time, enemy won't be dropped (if the only weapons used are UAC/5s), thus prolonging the firefight; and then if there is a lucky long sequence of no-jamming, - good chances are not all of it will be needed to drop the enemy down. Thus i'd say that real supressing ability of UAC/5 is lower than 72.2% - possibly something close to 60%.
In terms of DPS, UAC/5 is a winner in all sorts of DPS-needed situations on average, by some 20%...50%. However, due to random nature of jamming and long un-jamming time (5.0s), and due to its limited to double-that-of-AC/5 firepower, in case of real bad luck (jams on 1st shot) UAC/5 can do as little as ~40% of AC/5 DPS. Together, these facts define when UAC/5 is useful, and when it is not. Some certain colncusions which can be done out of this - are in the beginning of this post, in "short version" section, and basically are answers to when one clearly needs to use AC/5, and when UAC/5.
end of details and math
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Tests done.
Did some UAC/5 testing today (06 october 2013). The testing clearly establishes the following:
- its jam probability is present always - i.e. even on shots made more than 1,5 seconds after a previous shot;
- its jam chance per shot is significantly lower than Smurfy says it is;
- it can't fire more than twice during any given 1.5s period of time, apparently, limiting maximum possible DPS to double of AC/5's DPS.
// This completely invalidates initial conclusions and demands complete rework of this post, which i did. Old version is not saved, because it was utter {Scrap}.
1. clicking like mad, trying to make UAC/5 to fire any faster than when one simply holds its trigger down.
- Result: failure. It can't be fired more often than 2 shots per 1.5s. Period. ><
2. 500 rounds of UAC/5 fired with the fire trigger held down.
- Result: total jams - 58, of which a couple happened on very 1st shot after previous jam. This translates into 58 / 500 = 11.6%. From probabilities' theory, we know that series as large as 500 tries allow to find out the probability of an event quite precisely - plus-minus 1% or less. During this test, i had 2 UAC/5 cannons equipped, and was firing both (to speed up the procss - jams are easy to count).
3. 300 rounds of UAC/5 fired with the fire trigger held down.
- Result: total jams - 35, of which 7 happened on very 1st short after previous jam (which is ~3 more than expected, but this can be "bad luck", since during this sequence, there were 35 "first shots" obviously, and that's statistically low sample to make any conclusion). This test was done having only 1 UAC/5 equipped and firing, to find out whether jam chance depends on number of UAC/5s equipped/firing, or not. Well, it does not: 35 / 300 = ~11.7%. Very good confirmation of jamming chance, too.
Rounding that to ingeger (as well as previous test's result), UAC/5 has 12% jam chance - not 20%. Why then Smurfy is saying 20%, one might wonder. And i have a guess. Perhaps, Smurfy's 20% - is a chance that UAC/5 will jam on either 1st or 2nd shot of its 1.5s cycle. I.e., 20% chance to jam per PAIR of shots (or in other words, chance to jam during its 1.5s "normal" cooldown period) - and the jam can happen on either 1st or 2nd shot, with that. The latter would explain why jam chance is slightly higher than (otherwise expected) 10% per shot. I don't know if this guess is correct or not, but ~11.65% +-0.4% chance to jam per shot is the thing i am pretty sure about - 800 shots fired in total, counting jams, is statistically large enough sample to make such a conclusion. Also, during tests, i got a general "feeling" that the weapon is jamming on 1st shot of a pair nearly half the time, and on 2nd shot of the pair also nearly half the time - i.e. there is no difference on jam chance, apparently, between 1st and 2nd shots of a pair.
4. A long (40 UAC/5 shots) sequence without a single jam - amazingly, i happened in very 1st try, - alphaing UAC/5 paired with AC/5, alpha key held down for the whole duration.
- Result: for the whole duration, both weapons fired synchronously: for each AC/5 shot, there was a pair of UAC/5 shots. This allows to say that UAC/5 maximum DPS ("no jam mode") - is precisely double of AC/5's DPS, not more, not less.
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Fins