View source for Research:Jogloran's Portal of Cheaper Travel

==Casting Speed==
{| class="wikitable sortable" border="1"
! ma.sp.mi bonus !! Cast time (seconds)
|-
|26, 31, 37, 42, 47, 52, 58, 63, 68, 74, 79, 84, 89, 95, 100 || 80
|-
|102 || 78
|-
|105 || 76
|-
|107 || 74
|-
|110 - 112 || 72
|-
|113, 115 || 70
|-
|116 - 119 || 68
|-
|121, 123 || 66
|-
|124, 126 || 64
|-
|127, 129, 131 || 62
|-
|132, 134 || 60
|-
|136, 137, 139 || 58
|-
|141 - 145 || 56
|-
|146 - 150 || 54
|-
|151 - 156 || 52
|-
|157 - 163 || 50
|-
|164 - 170 || 48
|-
|171 - 177 || 46
|-
|178 - 186 || 44
|-
|187 - 195 || 42
|-
|196 - 201 || 40
|-
|202 - 204 || 38
|-
|205 - 207 || 36
|-
|208 - 210 || 34
|-
|211 - 214 || 32
|-
|215 - 218 || 30
|-
|219 - 224 || 28
|-
|225 - 230 || 26
|-
|231 - 236 || 24
|-
|237 - 246 || 22
|-
|247 - 255 || 20
|-
|256 - 267 || 18
|-
|268 - 284 || 16
|-
|285, 289, 292, 299, 303 || 14
|-
|308, 310, 312, 314, 318, 322, 324, 325, 326, 330, 331 || 12
|-
|332, 333, 351, 360, 363, 367, 370, 381, 387, 393, 399 || 10
|}

[[File:JPCT cast time.png|A scatterpoint chart showing the cast time of JPCT for bonuses from 26 to 299]]

If you'd like to contribute data points to this table, please use the following methodology:

Fill your command queue (e.g. with a few <code>score brief</code> commands) before casting so that the spell's timing begins on a server heartbeat. This will always be an even number.

Time the beginning of the cast on <code>You prepare to cast Jogloran's Portal of Cheaper Travel</code> and the end on <code>solidifies with a satisfying thump.</code> If you use Mushclient, you can see the timestamp for a line by hovering over it with your mouse.

JPCT's cast speed is affected by your [[ma.sp.mi]] bonus. You can modify it by changing your stats in various ways listed in [[Research]]. This will allow you to get multiple data points. [[User:Helia|Helia]] ([[User talk:Helia|talk]]) 00:36, 25 May 2021 (EDT)

----

Curious… can you elaborate on the methodology?  e.g. did you test every bonus level individually, did you perform multiple trials, did you consider the potential impact of methods skills as well, etc?

If it's correct, it suggests the equation is very close to (within expected nuances of rounding etc that are likely involved in the actual code):

[[File:Approximate JPCT cast time formula.png|250px]]

That predicts the next few steps in cast time reduction will be:

{| class="wikitable sortable" border="1"
! ma.sp.mi bonus !! Cast time (seconds)
|-
|300 || 12
|-
|318 || 10
|-
|340 || 8
|-
|370 || 6
|-
|412 || 4
|-
|480 || 2
|-
|624 || 0
|-
|}

It will of course be interesting to test this hypothesis with subsequent experiments.  The further that extrapolation the greater the error margin, and I'd also not be surprised if there's some kind of hard floor (practically speaking I can't see the casting happening in less than one heartbeat, for a start, but also I've never seen a casting faster than about six or eight seconds, even from some of the highest-level wizzards currently playing).

Anecdotally, my experience has been that JPCT cast time is an exact power of two - when I was first casting it, it was 64 seconds (exactly 32 heartbeats).  Then I advanced ma.sp.mi by a number of levels at once, and it fell to 32 seconds (16 heartbeats).  Another batch advancement and it dropped to exactly 16 seconds (8 heartbeats).  It's possible I just coincidentally happened to advanced in steps which hit power of two casting times, but that would be a bit of a coincidence.

Furthermore, when I've payed attention - on just a handful of occasions - to other players castings, they also have always been a power of 2 in seconds / heartbeats.  I'll keep more of an eye open now, to try to find a counter-example to this power of two rule.

--[[User:Pteri|Pteri]] ([[User talk:Pteri|talk]]) 16:30, 25 May 2021 (EDT)

:I tested each and every bonus level on the chart above so far and did multiple trials. I didn't investigate how methods could alter casting speed. Your extrapolated chart says that a bonus of 318-339 would have a casting speed of 10, but I just had a witch mock me to test a bonus of 324, and the speed was 12. I think we'll need more data points. [[User:Helia|Helia]] ([[User talk:Helia|talk]]) 17:32, 25 May 2021 (EDT)

:I made a newbie wizard alt and tested bonuses at low levels. I only raised [[ma.sp.mi]] and didn't raise any methods, and the cast speed increased. We can be quite sure that methods have no effect on cast speed. [[User:Helia|Helia]] ([[User talk:Helia|talk]]) 09:52, 26 May 2021 (EDT)

:What do you make of the strange change in trajectory at 201 bonus? Is that something you can write in a formula? [[User:Helia|Helia]] ([[User talk:Helia|talk]]) 09:57, 26 May 2021 (EDT)

:Hmm, I'm not sure about that assertion re. methods.  If raising [[ma.sp.mi]] changed the casting speed, that only proves that [[ma.sp.mi]] affects casting speed - it doesn't rule out anything else ''also'' being a factor.  In fact now I'm even more suspicious that there's more than just [[ma.sp.mi]] involved given this latest set of data, with a distinct 'kink' in the curve that seems suspiciously close to where your new & old datasets joined - datasets gathered from two different characters, I believe?  While it's certainly technically possible to have a complex curve like that, it runs counter to the intuition that the relationship should be pretty simple - just basic combinations of log, exponential, power, or at most polynomial functions.  I'm not aware of any such basic functions that would yield such a shape - it'd most likely be implemented (if real) as ''two'' equations, for two different ranges of skill bonuses.  And - call me cynical :D - I just can't think of any reason for the Creator(s) to do that extra work.  --[[User:Pteri|Pteri]] ([[User talk:Pteri|talk]]) 17:52, 26 May 2021 (EDT)

::I timed bonuses 208 - 299 on my main wizard and 26 - 230 on my newbie wizard. The cast times for the [[ma.sp.mi]] bonuses that both wizards timed, 208 - 230, were exactly the same despite their method skills being drastically different. That is why I'm so certain that methods have no effect on cast speed. The kink in the graph begins at bonus 201, a point earlier than where the two datasets joined.[[User:Helia|Helia]] ([[User talk:Helia|talk]]) 21:36, 26 May 2021 (EDT)

::Ah, perfect!  Thanks for doing that extra work to explore the overlap, that is indeed conclusive.  So a weird but real bifurcated curve.  Of course now the next question is, is it actually trifurcated, once one walks further up? :D  --[[User:Pteri|Pteri]] ([[User talk:Pteri|talk]]) 01:17, 27 May 2021 (EDT)

----

Okay, with a multi-segment curve model the equations look very clean and fit very accurately, giving me high confidence that they're correct.

* Up to bonus 100:   80.
* Between 100 and 200:  8000x^-1
* Between 200 and 300:  2000 • (x - 150)^-1

It appears there's a fourth segment in play, presumably for 300+…  the above curve (from 200 onward) fits somewhat but is clearly inaccurate for the 381+ data points.  I suspect there is in fact a third curve, for 300+, but it's a bit hard to derive it with the small sample set currently available.  It would help to pin down the transition points - where precisely does it go from 14 to 12, and from 12 to 10, and from 10 to 8.

--[[User:Pteri|Pteri]] ([[User talk:Pteri|talk]]) 12:38, 27 May 2021 (EDT)

:Thanks for doing the math. Quow told me that the fastest cast time possible is 10 seconds, and I assume he has a ludicrously high bonus, so I believe him. Once we find the breakpoints for 12 and 10 seconds, the research will be complete![[User:Helia|Helia]] ([[User talk:Helia|talk]]) 22:52, 27 May 2021 (EDT)