Even though Janelle probably always uses Beta and Maria probably always uses Delta, we can get an idea of the characteristics of each resonance type by comparing their hypothetical results against heteropneums weak enough for them to overwhelm.
From eyeballing graphs of strength v. heteropneum amplitude for each resonance type and both pilots:
The qualitative behaviour of each resonance looks similar between Janelle and Maria, but quantitatively different (likely a simple multiplicative factor, but I should check!). The multiplier per pilot is different for the different resonance types (so, e.g, Janelle is about as strong as Maria with Beta resonance, but weaker with other resonance types).
And for the different resonance types the graphs are as follows:
Alpha does not depend on enemy strength and maybe has two clumps.
Beta does not depend on enemy strength.
Gamma’s points seem to line up on straight, mostly slanted lines from a more-or-less common origin at zero enemy strength. Suggesting a strong dependence on enemy strength but one of the lines is flat and too low, so need to find a way to find out which line you’ll end up on.
Delta has a gentle upward trend for Maria (too noisy to detect for Janelle). This does not appear to be a selection effect as Maria is always handily beating the heteropneums.
Epsilon has a curve that looks like a parabola at first, but then slows down, so maybe a sine curve? It is very consistent looking (not noisy) so should be possible to have an accurate fit for it. The curve looks a bit distorted in places for Janelle but this is likely just rounding due to her very low values at this resonance.
Zeta and Eta have points lined up on flat lines. For Zeta one of those lines is at zero.
Based on this, some candidate responses:
If we can figure out which line we’ll end up on, possibly Gamma as used by Janelle. We need to be confident however that we’ll end up on a good line.
Ditto for Zeta as used by Corazon, but with the additional caveat that we need to know that her past hypothetical results of 1.98 were low tier results (and she’ll get high tier this time). If the 1.98′s were high tier, she’ll lose.
If we can’t figure out the information needed for either of the previous, the safe choice appears to be...Epsilon as used by Will. This may seem surprising at first glance since Will’s only hypothetical result with Epsilon resonance was a measly 0.21. However, this result was at Heteropneum amplitude 0.57, near the bottom of the Epsilon power curve as seen for Maria and Janelle. If Will has the same Epsilon power curve but with a multiplier, he is around twice as strong as Maria with Epsilon resonance (but check rounding error bars!), and should confidently beat Earwax as long as the Epsilon power curve doesn’t take a surprisingly sharp turn to decline between 3.12, where Maria last overwhelms heteropneums with Delta, and Earwax’s amplitude of 3.2. However, Will will not overwhelm Earwax, and either option 1 or 2 could do so if successful, so if we can figure out the necessary information for either of those options, they would be preferable.
Since time is pretty much up, summarizing where I’m at:
Afaict each resonance pilot strength result is a multiple of the result of a pilot-independent, resonance-specific rule times a pilot-specific power level with that resonance. (though, tbh, I haven’t checked this that closely).
With Maria out, the highest pilot power levels per resonance appear to be:
Alpha: Corazon. This resonance has apparently random variation about a constant value that jumped slightly somewhere around Floorday 500. It is too weak to save us.
Beta: Janelle. This resonance has apparently random variation about a constant value. It is too weak to be likely to save us.
Gamma: Janelle. Credit to GuySrinivasan for finding the specific formula of (1+k*amplitude) (times pilot gamma power level). The integer k is from 0 to 5 with 1 being slightly more common than 0 (could be random variation) but dropping off beyond that. Though that isn’t the most expected random distribution and may hint at something non-random, I haven’t found the pattern if there is one. Janelle needs k to be 1 or higher to save us or 2 or higher to overwhelm Earwax. Without knowing a pattern for the k value, this seems too risky.
Delta: Amir. This resonance has apparently random variation along with a moderate upward slope with heteropneum amplitude. It is too weak to save us.
Epsilon: Will. This resonance follows a cubic formula (credit to GuySrinivasan for reporting the cubic dependence first, though I hadn’t read his comment when I reported it). Though GuySrinivasan expresses low confidence in Epsilon, it seems to me that, assuming the assumptions of the cubic formula plus the multiplicative relationship between power values for different pilots is correct, there is no way the coefficients could possibly off by enough for Will not to beat Earwax. And these assumptions seem to me more solid than for Zeta below, so I see this as the safe choice (but not my current choice, because Epsilon will not overwhelm).
Eta: Will. This resonance has a non-random constant value with several jumps over time. One of the jumps appears to coincide with Alpha’s jump. Without any reason to expect a further jump since the last observed data, it is not strong enough to save us.
Zeta: Corazon. Zeta is either zero, or one of two non-zero values. Afaict whether it is zero is random, except that no zero values have been observed for heteropneum amplitudes above 2.27, so I weakly infer that there will not be a non-zero value against Earwax. It seems that which non-zero value occurs depends on which of two or more populations the heteropneum belongs to. The large majority of heteropneums belong to a population with amplitudes that are (before rounding) multiples of 0.142 or something very close to 0.142. These always get a low Zeta value if they get a non-zero result. The minority that are not in this population always get a high Zeta result if they get a non-zero result. Earwax’s rounded 3.2 value cannot be obtained by rounding a multiple of 0.142, so we can expect a high Zeta result and for Earwax to be overwhelmed. Thus, I pick this choice, despite my uncertainty as to whether I have enough evidence against a zero result.
A potential wild card is that we don’t know Flint’s power levels except for alpha, since he never overwhelmed any heteropneums. If there is a way to predict power levels without seeing a strength result with that resonance, this could reveal further opportunities with Flint.
It’s cubic not sine; I can fit Maria’s Epsilon data so that the curve rounds to the exactly correct value for every data point, and also for Janelle’s data (separately) to round to the exactly correct value; I still need to check if I can make a single curve and multiplier between Maria and Janelle to round exactly for both, but it does look like the curves are at least fairly close to exact multiples of each other.
Interestingly, no x-value rounding needs to be assumed, at least to get the correctly rounding values for Maria and Janelle separately. So, perhaps the x (heteropneum amplitude) values are exact?No, see below
The cubic curve does take a big dive at high heteropneum amplitudes, but fortunately not until after Earwax’s ~3.2 amplitude. Also, the fit for Maria’s 0.57 amplitude result of 0.1 is actually around 0.096. Will getting 0.21 suggests he is at least around 2.13 times stronger than Maria using Epsilon and is projected to get at least about 3.85 against a 3.2 amplitude heteropneum. So, Will using Epsilon still looks like a safe pick to survive if we can’t find guaranteed survival another way.
edited to add: note that the speculation that the x-axis values might be exact should only apply to the overwhelmed heteropneums—there are the these are the only ones we have epsilon data on and also the only ones we have data to 2 decimal places on. Irrelevant, see below
All overwhelmed heteropneums that are duplicates in power of another overwhelmed heteropneum is a multiple of an integer from 2 to 22 times 0.142 (the integers probably go higher than this, but Maria stops overwhelming them at that point). This value of 0.142 might not be the exact value, but it makes the numbers round correctly, whereas the rounded values are not exactly the right ratios, so presumably the amplitude values are rounded.
Eta is simply a multiplication of a character-dependent Eta power level and a date-dependent Eta strength. The date-dependent Eta strength is constant except occasionally it jumps. The lowest strength was from floordays 2-253, then second lowest from 280-297, then next level from 316-395495, then it jumped to the highest level from 516-746, and then dropped to the second highest level from 749-804. (no relevant data in the time gaps). It has never jumped back to a level after going to a different level.
Will’s sole eta value of 0.9 occurred on floorday 110 when Eta was at its lowest strength. This means Will is almost as strong as Maria at Eta (everyone else for whom we have Eta data is lower). Unfortunately, this is still not strong enough to beat Earwax if the Eta strength remains, now at floorday 814, at the same level it’s been from 749-804.
edited to add: Alpha also shows a jump between floorday 495 and floorday 516. (This is the reason for the bimodal appearance of its distribution). Since this jump occurred in both Alpha and Eta, but the others only occurred in Eta, this suggests that it might have a different cause than the other jumps.
Though duplicate amplitude values are common, all verifiably high-tier Zeta values so far have been against heteropneums with unique amplitudes. Admittedly, this is only 5 datapoints.
The good news: Corazon got her Zeta results against duplicate-valued heteropneums, so if the pattern holds true for her, her results have been low-tier so far and she is strong enough to overwhelm Earwax if she gets a high-tier result.
The bad news: Earwax has a duplicate amplitude value (as long as the formatting including rounding if applicable is consistent between Earwax and the other entries) so if the pattern holds true for Earwax, there will be no high-tier Zeta result against Earwax. Wrong, see below
Edited to add: Earwax and the “duplicate” (Divisor, floorday 389) have not been overwhelmed and are likely rounded to 1 decimal place, but all of our zeta data is from overwhelmed heteropneums, reducing the likely relevance of the “duplicate”. More detailed info below.
Further addition: I failed to mention earlier that all the non-duplicated entries have either high-tier or zero Zeta results (whereas all the duplicated entries have zero or low-tier Zeta). So, this is very likely significant.
On reviewing the relationships between the duplicated entries for which we have overwhelm results, all are equal to 0.142 multiplied by an integer from 2 to 22 (when that is rounded to 2 decimal places). The 0.142 might not be the exact value but it makes them round correctly. The 22 is probably not the highest but is simply where Maria last overwhelms heteropneums (3.12 amplitude).
Importantly, Earwax’s value of 3.2 cannot be rounded from a multiple of 0.142 (3.12 is too low, and the next value would be 3.266, which would round up to 3.3). If I try to lower the base value to 0.1419, this already prevents correct rounding of the known values (it would predict the 18x number would round to 2.55 but the 18x number needs to round to 2.56), and this too-low base value still predicts 3.2637 for the next multiple). Thus, Earwax is not from this population of heteropneums, which accounts for all the low tier Zeta results!
However, we still need to find a way to predict if we will get a zero result. Of the 9 non-duplicated overwhelmed heteropneums, there was a zero pilot strength Zeta result in 4 of these cases.
Still further addition: For amplitudes above 2.27, we have no cases of zero zeta. Among the overwhelmed heteropneums (which is all we have Zeta data for) we have 27 total cases of zero Zeta among 150 data points, and there are 41 cases with more than 2.27 amplitude. So, if all are statistically independent, then the probability of this happening by chance is (123/150)x(122/149)x...x(83/110)=0.00006457.
There are a variety of reasons not to be too impressed by this probability number.
We don’t have a very good reason to believe that the results are statistically independent. Duplicates in amplitude values do vary in whether they get zero Zeta (if amplitude less than or equal to 2.27), so they might be statistically independent, though.
I came up with the hypothesis (that Zeta is never zero above some amplitude) after seeing the data, not before, and need to adjust for the prior with possible hindsight bias.
Even if there is a non-random pattern causing the results, it doesn’t necessarily imply that it will hold for Earwax.
That being said, my expectation is that abstractapplic did leave us a way to overwhelm Earwax, so I’m confident enough (barely) to switch my proposed response to Corazon with Zeta. In real life, I’d stick with Will and Epsilon, which I am far more confident in.
Initial impressions:
Even though Janelle probably always uses Beta and Maria probably always uses Delta, we can get an idea of the characteristics of each resonance type by comparing their hypothetical results against heteropneums weak enough for them to overwhelm.
From eyeballing graphs of strength v. heteropneum amplitude for each resonance type and both pilots:
The qualitative behaviour of each resonance looks similar between Janelle and Maria, but quantitatively different (likely a simple multiplicative factor, but I should check!). The multiplier per pilot is different for the different resonance types (so, e.g, Janelle is about as strong as Maria with Beta resonance, but weaker with other resonance types).
And for the different resonance types the graphs are as follows:
Alpha does not depend on enemy strength and maybe has two clumps.
Beta does not depend on enemy strength.
Gamma’s points seem to line up on straight, mostly slanted lines from a more-or-less common origin at zero enemy strength. Suggesting a strong dependence on enemy strength but one of the lines is flat and too low, so need to find a way to find out which line you’ll end up on.
Delta has a gentle upward trend for Maria (too noisy to detect for Janelle). This does not appear to be a selection effect as Maria is always handily beating the heteropneums.
Epsilon has a curve that looks like a parabola at first, but then slows down, so maybe a sine curve? It is very consistent looking (not noisy) so should be possible to have an accurate fit for it. The curve looks a bit distorted in places for Janelle but this is likely just rounding due to her very low values at this resonance.
Zeta and Eta have points lined up on flat lines. For Zeta one of those lines is at zero.
Based on this, some candidate responses:
If we can figure out which line we’ll end up on, possibly Gamma as used by Janelle. We need to be confident however that we’ll end up on a good line.
Ditto for Zeta as used by Corazon, but with the additional caveat that we need to know that her past hypothetical results of 1.98 were low tier results (and she’ll get high tier this time). If the 1.98′s were high tier, she’ll lose.
If we can’t figure out the information needed for either of the previous, the safe choice appears to be...Epsilon as used by Will. This may seem surprising at first glance since Will’s only hypothetical result with Epsilon resonance was a measly 0.21. However, this result was at Heteropneum amplitude 0.57, near the bottom of the Epsilon power curve as seen for Maria and Janelle. If Will has the same Epsilon power curve but with a multiplier, he is around twice as strong as Maria with Epsilon resonance (but check rounding error bars!), and should confidently beat Earwax as long as the Epsilon power curve doesn’t take a surprisingly sharp turn to decline between 3.12, where Maria last overwhelms heteropneums with Delta, and Earwax’s amplitude of 3.2. However, Will will not overwhelm Earwax, and either option 1 or 2 could do so if successful, so if we can figure out the necessary information for either of those options, they would be preferable.
Since time is pretty much up, summarizing where I’m at:
Afaict each resonance pilot strength result is a multiple of the result of a pilot-independent, resonance-specific rule times a pilot-specific power level with that resonance. (though, tbh, I haven’t checked this that closely).
With Maria out, the highest pilot power levels per resonance appear to be:
Alpha: Corazon. This resonance has apparently random variation about a constant value that jumped slightly somewhere around Floorday 500. It is too weak to save us.
Beta: Janelle. This resonance has apparently random variation about a constant value. It is too weak to be likely to save us.
Gamma: Janelle. Credit to GuySrinivasan for finding the specific formula of (1+k*amplitude) (times pilot gamma power level). The integer k is from 0 to 5 with 1 being slightly more common than 0 (could be random variation) but dropping off beyond that. Though that isn’t the most expected random distribution and may hint at something non-random, I haven’t found the pattern if there is one. Janelle needs k to be 1 or higher to save us or 2 or higher to overwhelm Earwax. Without knowing a pattern for the k value, this seems too risky.
Delta: Amir. This resonance has apparently random variation along with a moderate upward slope with heteropneum amplitude. It is too weak to save us.
Epsilon: Will. This resonance follows a cubic formula (credit to GuySrinivasan for reporting the cubic dependence first, though I hadn’t read his comment when I reported it). Though GuySrinivasan expresses low confidence in Epsilon, it seems to me that, assuming the assumptions of the cubic formula plus the multiplicative relationship between power values for different pilots is correct, there is no way the coefficients could possibly off by enough for Will not to beat Earwax. And these assumptions seem to me more solid than for Zeta below, so I see this as the safe choice (but not my current choice, because Epsilon will not overwhelm).
Eta: Will. This resonance has a non-random constant value with several jumps over time. One of the jumps appears to coincide with Alpha’s jump. Without any reason to expect a further jump since the last observed data, it is not strong enough to save us.
Zeta: Corazon. Zeta is either zero, or one of two non-zero values. Afaict whether it is zero is random, except that no zero values have been observed for heteropneum amplitudes above 2.27, so I weakly infer that there will not be a non-zero value against Earwax. It seems that which non-zero value occurs depends on which of two or more populations the heteropneum belongs to. The large majority of heteropneums belong to a population with amplitudes that are (before rounding) multiples of 0.142 or something very close to 0.142. These always get a low Zeta value if they get a non-zero result. The minority that are not in this population always get a high Zeta result if they get a non-zero result. Earwax’s rounded 3.2 value cannot be obtained by rounding a multiple of 0.142, so we can expect a high Zeta result and for Earwax to be overwhelmed. Thus, I pick this choice, despite my uncertainty as to whether I have enough evidence against a zero result.
A potential wild card is that we don’t know Flint’s power levels except for alpha, since he never overwhelmed any heteropneums. If there is a way to predict power levels without seeing a strength result with that resonance, this could reveal further opportunities with Flint.
Update on Epsilon resonance:
It’s cubic not sine; I can fit Maria’s Epsilon data so that the curve rounds to the exactly correct value for every data point, and also for Janelle’s data (separately) to round to the exactly correct value; I still need to check if I can make a single curve and multiplier between Maria and Janelle to round exactly for both, but it does look like the curves are at least fairly close to exact multiples of each other.
Interestingly, no x-value rounding needs to be assumed, at least to get the correctly rounding values for Maria and Janelle separately.
So, perhaps the x (heteropneum amplitude) values are exact?No, see belowThe cubic curve does take a big dive at high heteropneum amplitudes, but fortunately not until after Earwax’s ~3.2 amplitude. Also, the fit for Maria’s 0.57 amplitude result of 0.1 is actually around 0.096. Will getting 0.21 suggests he is at least around 2.13 times stronger than Maria using Epsilon and is projected to get at least about 3.85 against a 3.2 amplitude heteropneum. So, Will using Epsilon still looks like a safe pick to survive if we can’t find guaranteed survival another way.
edited to add:
note that the speculation that the x-axis values might be exact should only apply to the overwhelmed heteropneums—there are the these are the only ones we have epsilon data on and also the only ones we have data to 2 decimal places on.Irrelevant, see belowAll overwhelmed heteropneums that are duplicates in power of another overwhelmed heteropneum is a multiple of an integer from 2 to 22 times 0.142 (the integers probably go higher than this, but Maria stops overwhelming them at that point). This value of 0.142 might not be the exact value, but it makes the numbers round correctly, whereas the rounded values are not exactly the right ratios, so presumably the amplitude values are rounded.
update on Eta resonance:
Eta is simply a multiplication of a character-dependent Eta power level and a date-dependent Eta strength. The date-dependent Eta strength is constant except occasionally it jumps. The lowest strength was from floordays 2-253, then second lowest from 280-297, then next level from 316-
395495, then it jumped to the highest level from 516-746, and then dropped to the second highest level from 749-804. (no relevant data in the time gaps). It has never jumped back to a level after going to a different level.Will’s sole eta value of 0.9 occurred on floorday 110 when Eta was at its lowest strength. This means Will is almost as strong as Maria at Eta (everyone else for whom we have Eta data is lower). Unfortunately, this is still not strong enough to beat Earwax if the Eta strength remains, now at floorday 814, at the same level it’s been from 749-804.
edited to add: Alpha also shows a jump between floorday 495 and floorday 516. (This is the reason for the bimodal appearance of its distribution). Since this jump occurred in both Alpha and Eta, but the others only occurred in Eta, this suggests that it might have a different cause than the other jumps.
update on Zeta resonance:
Though duplicate amplitude values are common, all verifiably high-tier Zeta values so far have been against heteropneums with unique amplitudes. Admittedly, this is only 5 datapoints.
The good news: Corazon got her Zeta results against duplicate-valued heteropneums, so if the pattern holds true for her, her results have been low-tier so far and she is strong enough to overwhelm Earwax if she gets a high-tier result.
The bad news: Earwax has a duplicate amplitude value (as long as the formatting including rounding if applicable is consistent between Earwax and the other entries) so if the pattern holds true for Earwax, there will be no high-tier Zeta result against Earwax.Wrong, see belowEdited to add:
Earwax and the “duplicate” (Divisor, floorday 389) have not been overwhelmed and are likely rounded to 1 decimal place, but all of our zeta data is from overwhelmed heteropneums, reducing the likely relevance of the “duplicate”.More detailed info below.Further addition: I failed to mention earlier that all the non-duplicated entries have either high-tier or zero Zeta results (whereas all the duplicated entries have zero or low-tier Zeta). So, this is very likely significant.
On reviewing the relationships between the duplicated entries for which we have overwhelm results, all are equal to 0.142 multiplied by an integer from 2 to 22 (when that is rounded to 2 decimal places). The 0.142 might not be the exact value but it makes them round correctly. The 22 is probably not the highest but is simply where Maria last overwhelms heteropneums (3.12 amplitude).
Importantly, Earwax’s value of 3.2 cannot be rounded from a multiple of 0.142 (3.12 is too low, and the next value would be 3.266, which would round up to 3.3). If I try to lower the base value to 0.1419, this already prevents correct rounding of the known values (it would predict the 18x number would round to 2.55 but the 18x number needs to round to 2.56), and this too-low base value still predicts 3.2637 for the next multiple). Thus, Earwax is not from this population of heteropneums, which accounts for all the low tier Zeta results!
However, we still need to find a way to predict if we will get a zero result. Of the 9 non-duplicated overwhelmed heteropneums, there was a zero pilot strength Zeta result in 4 of these cases.
Still further addition: For amplitudes above 2.27, we have no cases of zero zeta. Among the overwhelmed heteropneums (which is all we have Zeta data for) we have 27 total cases of zero Zeta among 150 data points, and there are 41 cases with more than 2.27 amplitude. So, if all are statistically independent, then the probability of this happening by chance is (123/150)x(122/149)x...x(83/110)=0.00006457.
There are a variety of reasons not to be too impressed by this probability number.
We don’t have a very good reason to believe that the results are statistically independent. Duplicates in amplitude values do vary in whether they get zero Zeta (if amplitude less than or equal to 2.27), so they might be statistically independent, though.
I came up with the hypothesis (that Zeta is never zero above some amplitude) after seeing the data, not before, and need to adjust for the prior with possible hindsight bias.
Even if there is a non-random pattern causing the results, it doesn’t necessarily imply that it will hold for Earwax.
That being said, my expectation is that abstractapplic did leave us a way to overwhelm Earwax, so I’m confident enough (barely) to switch my proposed response to Corazon with Zeta. In real life, I’d stick with Will and Epsilon, which I am far more confident in.