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Megarom
Illustrious Continuum
12
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Posted - 2014.10.02 22:27:00 -
[1] - Quote
TDLR; I think there is a better model for that mathemathics involved.
Because the mathemathics is the only part I have any competence to comment on I'd like to propose an alternate model that has it's own pros and conns, but I'll get to those after I've introduced it.
As I understand the goal of the mathemathics at play here are as follows.
Enforce a cap for sustained travel speed.
Allow bursts of couple of jumps to break that cap.
Be simple.
In the system proposed the highest possible sustained travel speed is archived by waiting the fatigue to decay under 1 which takes LY traveled times 10 minutes unless you are about to reach destination or log off anyway. This leads to top sustained speed being roughly equal to the fatigue decay rate.
If you jump before fatigue has decayed you get the burst of speed but you pay a huge price in the loss of sustained speed.
My proposal is this:
1. On jump the lightyears travelled are added to the fatique value which decays at the famaliar rate.
2. Jump cooldown is 6^(fatigue/5) minutes
(Yes there is an exponential function there don't be scared, the numbers are selected to provide roughly similar results on the first 2 jumps)
Let's look at some examples. Each jump is 5 LY. The time it takes to jump is assumed to be zero.
Both my model and what I call Grayscale model work the same way when you wait for the fatigue to decay meanng you can jump 5 lightyears every 50 minutes.
If we instead jump whenever the cooldown has passed we get very different results.
Grayscale model
After first jump you wait 6 minutes.
after second about 32 minutes
after third about 3 hours 10 minutes
after fourth about 19 hours.
Total: alot
If you are smart you would in destination in 2 hours 18 minutes. Which accounts for 2 50 minute waits and one 6, and one 32 minute wait because if you are reaching your target you can take the fatigue hit. Or if you need to keep jumping after that at full speed 3 hours 20 minutes.
Megarom model
after first 6 minutes
after second 29 minutes
after third about 62
after forth 40
Total: 2 hour 17 minutes, which is about the same as by waiting the decay 2 times and then making last 2 jumps as fast as possible. If you want to leave the burst speed open when you arrive it will take the 3 hours 20 minutes mentioned earlier
With more jumps the difference between the strategies oscillates between +-10 minutes converging on about -5 while the cooldown converges on 50 minutes, which means that sustained travel speed is limited to the same value in both travel strategies. IE. you can't break the travel speed set by the decay rate. On the other hand fatigue never gets out of hand, because it will decay enough while the cooldown is running.
Let's concider 2 different jump plans with 3 jumps 5 LY each.
1. jump 2. wait 6 minutes 3. jump 4. wait 50 minutes 5. jump
vs
1. jump 2. wait 50 minutes 3. jump 4. wait 6 minutes 5. jump
Both are possible in both models and take equal amount of time.
In the Grayscale model the first leaves you with a cooldown of 137 minutes and the second with 32 minutes. In Megarom model your total travel distance is 15 LY in both cases which causes 15 fatigue and you have waited in total 56 minutes so fatigue after 3 jumps is 9.4 and cooldown 29 minutes.
Let's concider 2 different jump plans with more variation
1. jump 4 LY 2. wait 20 minutes 3. jump 5 LY
vs
1. jump 2 LY 2. wait 3 minutes 3. jump 2 LY 4. wait 17 minutes 5. jump 5 LY
Both are again possible and take equal amount of time.
In Grayscale model the first leaves you with 7 minute cooldown and fatigue and the second with 38 minute cooldown.
In Megarom model in both cases your total travel distance is 9 LY which causes 9 fatigue and you have waited 20 minutes
which drops it to 7 giving you cooldown of 12 minutes.
Megarom model Pros
Enforces sustained travel speed, without punishing player with hours of cooldown
Allows burst of couple of jumps
Doesn't require arbitary fatigue limit, because fatigue is naturally capped.
The fatigue is a clear concept related to the distance the pilot has jumped.
Planning the jump schedules is way easier, just don't try to go faster than the decay rate and the schedule is doable.
It doesn't care about number of jumps or pacing only distance traveled in total and the decay time.
Cons
The math for the cooldown is trickier
Doesn't allow shooting yourself in the foot with crazy fatigue amounts
All in all I think the way Grayscale model allows shooting yourself in the foot in such a severe way that it's not too far fetched to call it user unfriendly. On the other hand many people like the game when it punishes hard for your mistakes.
Math being technically trickier is balanced system being easier to understand in practice.
PS. I just paid you 15Gé¼ to post this. Seriously  me. |
Megarom
Illustrious Continuum
12
|
Posted - 2014.10.03 08:24:00 -
[2] - Quote
I think it was a bad idea to have the extreme example in the dev blog. Many people seem to think that if you travel by jump drive you will always hit hours of cooldows. Those hours of cooldown only come into play if you are stupid or are going to log of anyway and can sleep on the longer cooldown. If a cap is trying to travel as fast as possible it can reach the speed of 0.1 LY / minute or 5 LY jump every 50 minutes. Making total travel time in the example 10 hours which is still pretty extreme, but not the wall you hit if you jump the moment the cooldown is over.
I'll add my voice to the crowd that says the sustained travel speed is too low. Grayscale mentioned that the benchmark speed from gate travel was 3M/ 1LY which equals 1/3 light years / minute making jump travel speed 0.1 less than one third of the benchmark 0.333...
I'm heading into notes to self territory now, but I noticed that there were at least couple of people interested in the maths so I'l post anyway.
After posting my earlier post I tried to go to sleep and started wondering why is it that the sustained travel speed matches the decay rate regardless of coeficients in the cooldown function. It dawned to me that the cooldown function has nothing to do with the travel speed cap only how fast it is reached so effecting the burst travel speed. Only requirement for the function is that it grows faster than linear growth though for practical reasons you want it to reach 5/(decay rate) (50 in our case) in 2 to 3 jumps.
Simple polynomial function like
cooldown = (fatigue +1)^2
will also reach the cap and be limited by and by tweaking the numbers you can similar cooldowns on the first 2 jumps as in Grayscale model.
I would describe the jump speed limit system as an inverse resource system. This means that when you do something you generate negative resource that you have to let decay before doing the action again. Similar results could be reached with a more traditional resource system where you would generate 0.1 LY of jumpability / minute and you consume jumpability acording to the lightyears traveled. The distance of burst travel would be limited by the maximum storage capacity of jumpability for example 10.
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Megarom
Illustrious Continuum
12
|
Posted - 2014.10.03 10:47:00 -
[3] - Quote
I've though about this a little more and come to the conclusion that there is no need for any fancy math.
Here's my simplified model.
Distance traveled in LY is added to fatigue that decays at 0.1 / minute.
If fatigue is over certain limit, for example 10 you can't jump.
Simple and elegant.
Enforces sustained travel speed.
Allows burst travel of up to 15 LY from rest and 10-fatigue LY in general
Only part of the Grayscale model this doesn't have is the punishing player with with long cooldown if he is stupid enough to jump with partially decayed fatigue.
As a sidenote I'd like to add my voice to crowd that is saying 0.1 LY /minute is just too slow. The benchmark of 3m/LY ie. 0.3333... LY /minute so there is some room there anyway before gate travel obsoleted again. |
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