Ignoring any time dependence, solar+lunar and solar+earth are the most successfuly combinations; they would have succeeded on 246 and 235 respectively of the existing 374 datapoints.
Note, in my remarks on individual mana types I may include information on other mana types.
Solar:
Solar seems to have a 27 day cycle with 3 peaks within it (so 9 day cycle?) but which peaks are stronger has been changing over time. The current cycle, cycle 14, has been weird with days 15-20 of the cycle (days 366-371) being higher than expected. The last 3 days (372-374) are low, but not far from expected. Other slightly weird cycles include cycle 8 (slightly higher than expected values from days 12-14 of the cycle, i.e. days 201-203) and cycle 10 (slightly higher than expected values from days 20 to 25 of the cycle, i.e. days 263-267). I’m counting “day 1” of a cycle to be the one that’s a multiple of 27 from the day 1 of the overall data.
If solar is back to its normal pattern, on day 384 it should be on the way down from a high peak and approaching a high trough, so still doing pretty well (>40 expected), making solar a good candidate for one of the mana choices.
Lunar:
Lunar, like solar, shows a 27 day cycle (shouldn’t it be 28 days?) with 3 peaks changing which is stronger over time; outliers include days 26 of cycle 8 to day 1 of cycle 9 (days 215-217) which are unexpectedly weak. Like solar, lunar should be declining to a high trough on day 384, I expect >35. Assuming solar is back to normal, solar + lunar should succeed.
Ocean:
Ocean varies greatly from single digits to over 60. While some possible patterns appear (e.g. some short range autocorrelation, and a degree of autocorrelation at a 4-day displacement almost as high as at 1-day displacement) it does not seem to have a fixed period of variation. The possible high values make this a potentially interesting choice if it can be predicted, but more analysis needed to determine what ocean will be at at day 384.
Breeze:
Breeeze looks fairly random, distribution peaks at 13 and varies from 6 to 20.
Flame:
Like Ocean, has short-range autocorrelation but no single period. Varies from 11 to 41.
Ash:
Like Ocean and Flame, has short range autocorrelation but does not seem to have a single period. Varies from 2 to 10, so of scientific interest only.
Earth:
Looks random except for some possible 1-displacement autocorrelation. Varies from 9 to 74, so definitely of interest if a pattern can be found.
Void:
Looks fairly random, varies between 17 and 31. This is the same size of range as for Breeze, but has a fatter and asymmetrical distribution.
Doom:
8 days sawtooth pattern with some possible random variation (peak on day 2, bottom on day 3, then steady rise). Notable outliers from expected pattern: Day 9 of cycle 1 (i.e., day 9), day 5 of cycle 22 (i.e. day 181), day 3 of cycle 11 (i.e. day 91), and day 1 of cycle 31 (i.e. day 249).
On day 384, it will be day 8 of the cycle, and something in the range of 27-33 is likely. Not as good as solar and lunar, even discounting the risk of a miscalculation with one of the dangerous mana types.
Spite:
28-day periodicity with lots of peaks and troughs within the period; the troughs are often (but not always) 0. A reliable spike on day 5 gives the period away. Seems to also prefer specific values instead of a smooth distribution. Day 384 will be day 20 of the period, and a low value can be expected (7 or 0).
Preliminary answer:
So far Solar+Lunar seems the best choice.
This is also the choice that looked best before getting time dependence information for Solar, Lunar, Doom and Spite, so further research on the time dependence of other mana types (especially Ocean or Earth which can have high values) might find an alternative, better answer.
Edit after reading aphyer’s solution:
Aphyr found that Earth and Ocean are anticorrelated and their sum has a smooth 22-day pattern. As Aphyr reports, day 384 should be close to the peak. Expected value 75-80 or so. This looks like a good, safe solution.
I actually expect Solar+Lunar to be slightly higher, since the peaks and troughs have been shifting in height/depth over time, and while they will be near a trough at day 384, the trough is one that has been shifting upward. I expect ~43- 45 from Solar and ~36-40 from Lunar on day 384. However, this is less certain than the Earth+Ocean expectation and as Aphyr notes Solar has been weird lately. Solar+Lunar is definitely the riskier pick and probably is objectively not what one should pick based on the available info, so I’d switch to Aphyr’s solution in real life but I’ll stick with Solar+Lunar as what I want to get credit for (for now) since I have an excuse that it might be better and it’s what my analysis was on.
Not had time for this recently (fortunately extra weekend though) but after checking gjm, Jemist’s and GuySrinivasan’s comments:
Whoops so much for Lunar.
Only a little further remarks as time running out:
The following predicts solar with +-1 accuracy:
28 day cycle: 32,32,32,27,27,27,27,27,27,32,32,32,34,34,35,36,37,40,41,42,42,41,40,37,36,35,34,34
9 day cycle: 9,10,10,10,9,3,0,0,3
anomalies: +8 days 61 and 62, +12 dats 201-204, +9 days 263-268, +24 days 366-371
predicted result for day 384 is 45+-1, unless there’s an anomaly.
Doom’s 8 day cycle is 30,32,18,20,22,24,26,28 plus 0-5 with anomalies on days 34, 91, 181, 249. Unlike solar there are both positive and negative anomalies. Expected result (no anomaly) is 28-33 on day 384.
Solar+doom should give (with no anomaly) 72-81, does not look as good as Earth+Ocean’s 74-80 (from GuySrinivasan) though obviously Doom is better than Lunar’s known value of 16 at day 384.
With respect to Earth and Ocean, both include many values larger than the minimum of the sum of the two, and Ocean has a sharp minimum value at 4, while Earth’s minimum value is not so sharp with 9 being the smallest but more of the bottom edge of the Earth-Ocean x-y plot being at 11 or so. This probably says something about how they are made but I have not thought of it. So far, nothing better than Earth+Ocean found.
also (whoops, this postdated the eval, and was apparently spurious to boot):
Obviously, the best candidates for beating earth+ocean are solar+ocean or solar+earth (whichever we can find out will be bigger).
Spite correlates a bit with Ocean and anticorrelates a bit with Earth. Not a super large effect but relating ocean/earth (which we need to predict) to Spite (which we know deterministically) is very interesting)
What will element A do, what will element B do, and
What will they do together? (That said, I haven’t done a lot of poking around for correlations and just found S+L like you. I’m mostly waiting for -
This next part is a double spoiler, so don’t open it if you haven’t gone through the prior D&D Sci stuff.
- a ‘surprise! one of the ones that was low had a specific pattern which allows for a super combination!’, though that’s mostly because of how some of the stuff in the submarine one turned out.
Observations and results so far:
Ignoring any time dependence, solar+lunar and solar+earth are the most successfuly combinations; they would have succeeded on 246 and 235 respectively of the existing 374 datapoints.
Note, in my remarks on individual mana types I may include information on other mana types.
Solar:
Solar seems to have a 27 day cycle with 3 peaks within it (so 9 day cycle?) but which peaks are stronger has been changing over time. The current cycle, cycle 14, has been weird with days 15-20 of the cycle (days 366-371) being higher than expected. The last 3 days (372-374) are low, but not far from expected. Other slightly weird cycles include cycle 8 (slightly higher than expected values from days 12-14 of the cycle, i.e. days 201-203) and cycle 10 (slightly higher than expected values from days 20 to 25 of the cycle, i.e. days 263-267). I’m counting “day 1” of a cycle to be the one that’s a multiple of 27 from the day 1 of the overall data.
If solar is back to its normal pattern, on day 384 it should be on the way down from a high peak and approaching a high trough, so still doing pretty well (>40 expected), making solar a good candidate for one of the mana choices.
Lunar:
Lunar, like solar, shows a 27 day cycle (shouldn’t it be 28 days?) with 3 peaks changing which is stronger over time; outliers include days 26 of cycle 8 to day 1 of cycle 9 (days 215-217) which are unexpectedly weak. Like solar, lunar should be declining to a high trough on day 384, I expect >35. Assuming solar is back to normal, solar + lunar should succeed.
Ocean:
Ocean varies greatly from single digits to over 60. While some possible patterns appear (e.g. some short range autocorrelation, and a degree of autocorrelation at a 4-day displacement almost as high as at 1-day displacement) it does not seem to have a fixed period of variation. The possible high values make this a potentially interesting choice if it can be predicted, but more analysis needed to determine what ocean will be at at day 384.
Breeze:
Breeeze looks fairly random, distribution peaks at 13 and varies from 6 to 20.
Flame:
Like Ocean, has short-range autocorrelation but no single period. Varies from 11 to 41.
Ash:
Like Ocean and Flame, has short range autocorrelation but does not seem to have a single period. Varies from 2 to 10, so of scientific interest only.
Earth:
Looks random except for some possible 1-displacement autocorrelation. Varies from 9 to 74, so definitely of interest if a pattern can be found.
Void:
Looks fairly random, varies between 17 and 31. This is the same size of range as for Breeze, but has a fatter and asymmetrical distribution.
Doom:
8 days sawtooth pattern with some possible random variation (peak on day 2, bottom on day 3, then steady rise). Notable outliers from expected pattern: Day 9 of cycle 1 (i.e., day 9), day 5 of cycle 22 (i.e. day 181), day 3 of cycle 11 (i.e. day 91), and day 1 of cycle 31 (i.e. day 249).
On day 384, it will be day 8 of the cycle, and something in the range of 27-33 is likely. Not as good as solar and lunar, even discounting the risk of a miscalculation with one of the dangerous mana types.
Spite:
28-day periodicity with lots of peaks and troughs within the period; the troughs are often (but not always) 0. A reliable spike on day 5 gives the period away. Seems to also prefer specific values instead of a smooth distribution. Day 384 will be day 20 of the period, and a low value can be expected (7 or 0).
Preliminary answer:
So far Solar+Lunar seems the best choice.
This is also the choice that looked best before getting time dependence information for Solar, Lunar, Doom and Spite, so further research on the time dependence of other mana types (especially Ocean or Earth which can have high values) might find an alternative, better answer.
Edit after reading aphyer’s solution:
Aphyr found that Earth and Ocean are anticorrelated and their sum has a smooth 22-day pattern. As Aphyr reports, day 384 should be close to the peak. Expected value 75-80 or so. This looks like a good, safe solution.
I actually expect Solar+Lunar to be slightly higher, since the peaks and troughs have been shifting in height/depth over time, and while they will be near a trough at day 384, the trough is one that has been shifting upward. I expect ~43- 45 from Solar and ~36-40 from Lunar on day 384. However, this is less certain than the Earth+Ocean expectation and as Aphyr notes Solar has been weird lately. Solar+Lunar is definitely the riskier pick and probably is objectively not what one should pick based on the available info, so I’d switch to Aphyr’s solution in real life but I’ll stick with Solar+Lunar as what I want to get credit for (for now) since I have an excuse that it might be better and it’s what my analysis was on.
Not had time for this recently (fortunately extra weekend though) but after checking gjm, Jemist’s and GuySrinivasan’s comments:
Whoops so much for Lunar.
Only a little further remarks as time running out:
The following predicts solar with +-1 accuracy:
28 day cycle: 32,32,32,27,27,27,27,27,27,32,32,32,34,34,35,36,37,40,41,42,42,41,40,37,36,35,34,34
9 day cycle: 9,10,10,10,9,3,0,0,3
anomalies: +8 days 61 and 62, +12 dats 201-204, +9 days 263-268, +24 days 366-371
predicted result for day 384 is 45+-1, unless there’s an anomaly.
Doom’s 8 day cycle is 30,32,18,20,22,24,26,28 plus 0-5 with anomalies on days 34, 91, 181, 249. Unlike solar there are both positive and negative anomalies. Expected result (no anomaly) is 28-33 on day 384.
Solar+doom should give (with no anomaly) 72-81, does not look as good as Earth+Ocean’s 74-80 (from GuySrinivasan) though obviously Doom is better than Lunar’s known value of 16 at day 384.
With respect to Earth and Ocean, both include many values larger than the minimum of the sum of the two, and Ocean has a sharp minimum value at 4, while Earth’s minimum value is not so sharp with 9 being the smallest but more of the bottom edge of the Earth-Ocean x-y plot being at 11 or so. This probably says something about how they are made but I have not thought of it. So far, nothing better than Earth+Ocean found.
also (whoops, this postdated the eval, and was apparently spurious to boot):
Obviously, the best candidates for beating earth+ocean are solar+ocean or solar+earth (whichever we can find out will be bigger).
Spite correlates a bit with Ocean and anticorrelates a bit with Earth. Not a super large effect but relating ocean/earth (which we need to predict) to Spite (which we know deterministically) is very interesting)
What I’d get from Aphyr is that
What’s important for every pair is:
What will element A do, what will element B do, and
What will they do together? (That said, I haven’t done a lot of poking around for correlations and just found S+L like you. I’m mostly waiting for -
This next part is a double spoiler, so don’t open it if you haven’t gone through the prior D&D Sci stuff.
- a ‘surprise! one of the ones that was low had a specific pattern which allows for a super combination!’, though that’s mostly because of how some of the stuff in the submarine one turned out.