Gathering more data now, I’m getting reports of data sets that have fewer plays than the minimum you’d get from 30% (confirmed perfect runs, no ravens lost) but still higher than 25%.
So, indications are that the the +/- 1 rule is either able to go above +1, (which is not how it was explained to work, and also not what I’m observing all based on tests) or the +/- 1 rule is applied based on your expectation of ravens encountered rounded (so it’d be more like +/- 1.5, and since you can’t encounter half a raven, that functionally means +/-2, and because each raven is 2 sigils and they can compound, that can be a difference of up to 12 sigils - not really something I’m observing either, because similar purchases seem to beget very similar or exactly the same outcomes on perfect runs) or the estimated appearance rate isn’t correct, or the +/- 1 rule works completely differently, or some combination thereof.
By the way, before someone brings this up, I don’t believe valravens are clamped to “exactly 1 guaranteed every set of x battles”, like Luck scrolls work (exactly 1 in every set of 4 tower floors starting at floor 5) and as common knowledge frequently asserts. I just did a short run on my last account, and I got my first five ravens on battles 2, 4, 7, 9, 14. Any set of “exactly 1 guaranteed every x battles” that could explain the first four ravens alone would be give us far, far beyond the amount of total plays we get now, and none can explain all 5 (eg., 1 raven every 3 battles would be possible for 2, 4, and 7 but would put 2 in the same set for 7-9 and 0 in the set for 10-12). I believe it is much more likely ravens are allowed or disallowed based on whether or not you within range of total projected plays (including sigils played to this point, missed ravens and the raven you are getting now), allowing a raven if you are less than 2 plays ahead, disallowing it if you are over 2 ahead, and forcing it if you are more than 2 behind. Obviously, this is contingent on the fact that you can’t get half a raven or half a sigil, so some rounding has to take place somewhere. Its still kind of murky how exactly this calculation is done, since it is unlikely a calculation as complex as one I’m going to be doing here is being done to determine if a raven can appear or not when a much simpler one could be used, but again, we need a model where “perfect runs” produce very similar results that is not just “guaranteed raven every set of x battles”.
Anyways, if we go with 30% appearance rate for ravens, @awryan’s Saturday set shows he got his 15th valraven at or before the average expectation was exactly 14 ravens. If we took a different hypothetical lower rate, say, 27.5%, the average expectation for number of ravens encountered at 50 battles would be 13.75 ravens. To get 52 battles with T4 on Saturday Bounty (8 + 2 + 3 + 4 + 5 = 22 initial sigils), you need at least 15 ravens at or before your 50th battle (obviously if you got one on your 51s or 52nd battle, you’d have more ravens and more battles). Any assumed rate of Raven appearance below 30% would have your expectation of ravens at the 50th battle be <14, and getting a 15th raven at that explanation is more than “plus one”… without rounding. If we calc how many ravens over the total amount of battles played for this set, we get 15 ravens in 52 battles, a 28.8% overall appearance rate. But the last raven appeared at 50 battles or before, which would have been a 30% appearance rate, and we don’t know if another raven was possible by battle 52 or not.
Before reset today, I just finished two alts all the way out of sigils with a t3 purchase on invasions and got 212 towers. The first stage has no towers, then its 5, 5, 10, 10, 15 and 15 for a total of 60 towers in the first 35 plays, and then 4 towers per play afterward for 38 more plays to reach 212, meaning I got a total of 73 plays from my initial 33 sigils on both those accounts in different guilds. I double checked this with the last tower level - 118 - citadel starts at 80 and advances 1 per win, so I spent 38 battles in the citadel, which again equates to 73 battles. Its possible raven rate is different from invasions to bounty, but 73 plays from 33 initial sigils is 20 ravens, which is much both too high for an assumed raven rate of 25% and any variant of rounding with the +1/-1 rule (65-67 plays avg, and 73 plays means we got our 20th raven when on the 71st battle or before our average expected ravens was <18) and too low for 30% (avg would have been 81-83 battles played, average expectation at 73 plays would have been 21.9 ravens and we would have only gotten 20). If I look at the amount of ravens I got so far, for total plays, its 20 in 73, which is about 27.4%, 20 in 71 or 28.2% when the last raven appeared.
So, lets pick another number based on calculated appearance rates, make an educated guess that the people that created the numbers did so with certain projections in mind, and do some tests. Interestingly, if we assume a 27.7777_% raven rate, our expectation of plays converges at around 2.25x starting sigils, and a 27.5% makes our expectation of plays around 2.2222_x starting sigils.
Checking these with what we have so far… Awryan’s sample yesterday has us at 50 plays with 14 sigils and needing a 15th. The average expected number of raven at this point would have been 13.75 - 13.88. We’d have to assume “expected number” can round for this model to (still not enough information to tell which rounding method is used). With our average expected plays from 22 starting sigils at 48.8 - 49.5 plays, 52 plays is still only within range with some kind of rounding, and seems more likely with the 27.78% estimate.
Checking with my 2 alts, at 71 plays, they had 19 ravens with an expectation of 19.52 - 19.72, so well within range (one of them got the raven on the last battle, one of them earlier). My total expectation of plays is in the 73.33 - 74.25 range based on that model, so spot on here as well.
More data might help narrow this down, but heres the tables for these on bounty (based on average expected plays):
27.5% raven rate
27.7777_% raven rate
So, is t3 possible with either of these? Obviously never recommended regardless, but with 21 starting sigils, your average expectation of plays would have you fall pretty far short based on either of these. A “perfect” bounty run needs 52 victories at 30x modifier (with 5k point leeway, but that isn’t much overall and does not meet the break point for a single battle, which is 6k points). Your average expectation of battles under either model would be ~47, so already not looking good. But lets stretch the limits of the +/-1 rule and assume you can keep getting lucky like before. At your 51st battle with a t3 purchase, you’d have already earned 15 ravens, and your average expectation would have been 14.166, which should shut the door then and there on being able to get your 16th. Remember, Awryan needed every battle to finish this with T4 on Saturday with one additional sigil, which what all indications point to as “good luck”.
(Note these also line up better with @Neritar’s statement above, needing a near perfect run and raven luck for t4 without ascenscion orbs at 26x modifier to clear reward 20 - 57 total plays required, 26 initial sigils at 27.7% or 27.5% raven rate is around 58 expected plays, plus or minus a couple)
Double checking with my invasion results today. First account got a raven on the 74th battle, which had 20 ravens with an average expectation of >20 <21, well within range for the 21st raven, and at 76 (22 expecting ~21, well within range), ending at 81 plays (from 37 start, 81-83 expected, spot on). Other alt got ravens at 75 (21 expecting and >20 <21, well within range), and 79 (22 expecting very slightly <22, right on the mark again). All these fit all estimates for 27.5% or 27.78% appearance rates.
Assuming 25% rate, 79th battle would already have 21 ravens expecting <20, and so would previous battles, so this doesn’t fit (and we are far far off “average expectation”) Assuming 30% rate, 24.3 ravens would be expected by the 81st battle, and we’d have only earned 22, which is also outside the model, and our expected plays would be ~93, far outside the model again.
Confirming with todays results from Awryan… a total of 58 plays, expectation of ~58… spot on. At 56 plays, average expected valravens would have been either just above or just below 15.5, depending on which number used, but a 16th sigil from that is well within range regardless. Both of these calculations come out to “too many sigils” for any 25% raven rate model, far above total plays expectation, far above average expected raven appearance rate. For a 30% raven appearance rate model, the 58th play would carry an expectation of 16.8 ravens with 16 earned so far… so it technically still fits the lax interpretation of the +/-1 rule, but our average expected plays would be 70, and we observed 58, so it wouldn’t fit there.
Well, thats it for now. I’ll have to come up with a new model if t3 bounty completion is possible, because that means there is another variable or discrepancy somewhere. I’m probably still missing something with respect to the +/- 1 rule.
tl;dr:
- +/- 1 rule could be tied to projected total plays rather than current number of ravens vs expected (or we’d see much more variance).
- Assumed raven appearance rate of 25% and 30% both failed tests versus hard data sets from invasion with any possible interpretation of +/- 1 rule, 30% might still be possible for bounty assuming they have different rates
- Rate of raven appearance for invasion/bounty(+raid/tower) is likely roughly 27.5% - 27.77777_% (2.22 to 2.25x expected plays per starting sigil, contingent on the fact that “half a sigil” and “half a raven” are not actual things) - though it is possible different modes have different rates
- Raven appearance rate in Faction Assault =
- Given a 27.5 - 27.778% raven appearance rate, T3 bounty should still be impossible even after Sunday. (note that awryan’s run had one more starting sigil by T4 Saturday, which is a difference of 2.25 projected plays, needed every battle to get reward 20 on Saturday, and was likely “ahead” on luck at that point)