What you were expecting to happen, and what actually happened?
I expected that units had only a 10% chance of dying on the first turn after being inflicted by Death Mark. What actually happened was so unlikely that made me wonder if there’s something wrong with that number. All happened while fighting against Death.
Fighting Death, I lost 3 units to DM on the FIRST turn after the spell was cast. I probably can’t calculate that well enough, but it seems highly unlikely (1/1000?). Fought a few more Deaths that had a chance to cast, lost 2, 3 and 2 units (out of 4) in the FIRST turn after Death cast its spell. To sum it all up, my units had MORE chance of dying at the first turn than chance of not dying, when the chance of dying should be 10%.
So those were my results, 4 out of 4 attempts. It’s of course possible, but so, highly unlikely that I thought I should mention it. Maybe there’s a bug with the numbers? Also, I don’t remember DM having such a high kill rate as before.
A few months ago, they made a change to Death Mark so that it no longer had a 2-turn grace period before it could start triggering. It now gives the affected troop a 10% chance of death even from the very first turn, instead of the third turn.
I use the Creeping Death weapon pretty often, and I find that for every match where it instakills both death-marked enemies, there are plenty of other matches where the death marks cleanse off without doing anything at all. It’s just that the ones where it does happen are so much more memorable.
It’s just that, according to someone who explained the statistics needed, the chance of losing 3 troops on the first turn after Death has cast it spell is 0.36%. The chance of losing 2 troops on the first turn after Death has cast it spell is 4.86%. The chance of, on 4 consecutive spells by Death (even if different Deaths, on different matches), losing 2 troops twice and 3 troops twice on the first turn after the spell was cast is (gasp) 0.00001224440064%.
As long as no one else is experiencing this (I’m not), and you haven’t experienced a similar streak again, the most likely explanation is that you are THAT unlucky.
Feel glad that the bad RNG is only ruining a few matches and not affecting your chest drops instead? /shrug
Given as many players as GoW has, a 0.36% chance means that 36 of every 1000 players that get hit with Death only one time will see this. Last week, over ten thousand people were above 9000 rating. Assuming that each of those ten thousand playes faced Death at least once, 360 people experienced at least a triple kill first turn from Death casting. Knowing the meta as I do, I can say that Death was probably encountered more than once in the matches played by these ten thousand people. Each player above 9000 rating probably saw about three or four Death casts on their way to the rating that they got. Loose estimate. Based on these numbers, a triple kill with Death on the first turn after cast probably happened at LEAST 1500-2000 times last week.
Any less would be evidence towards a slightly LOWER proc rate.
This is not counting the large majority of players that I cannot quantify, having been in those top 10000 players myself and unable to see how many players only got one or two matches, and ALSO not counting anyone using Death in their invasion team.
Low odds? Yes. But it likely happened to thousands of people in the past week alone, statistically speaking. It just sucks that you happened to be one of them, and you have my sympathy.
I’d leave the statistical analysis to the ones with experience and/or education.
You’re entire methodology in arriving with your assumptions and numbers is flawed.
If the OP was the truth in what happened, that is an insanely rare set of occurrences that I can definitively say doesn’t happen 1500-2000 times a week
How can you say for sure that it doesn’t? Not every player posts on the forums. Not every player that posts on the forums posts about something that there is perfectly possible under the laws of RNG and in the game’s code.
Someone can get three or four legendaries in 50 gem/event keys, and nobody bats an eye. Don’t know drop rates, but that sounds like it might have roughly similar odds.
You can’t say that it doesn’t happen X times without having input from the millions of matches played every week.
Extending post because math.
10000 players above 9000 rating means that, if you round up the average PvP point per match average to a generous 50, and assume that everyone did all 3 trophy matches with no losses (which only lowers the pool size, mind you), each of those ten thousand players did 180 matches. 180*10,000 is very easily 1.8 million matches. This is a gross underestimate, and just the top >50% of players.
This assumes the minimum number of matches to get to the minimum of the top 10k player bracket. Far, far more than this is probably a number closer to what is indicative of the top 1000.
But then again, this also assumes that Death is in every single match and casts at least once. Which is not accurate either, but you could probably cut the number in half and it would be closer to an actual estimate of how many times this happens. Would help if I had the troop usage numbers in front of me.
I don’t know if that is possible, but if anyone has the usage rate for Death, it would be either Sirrian, who I don’t want to bother, because vacation, or @Lyya
The flaw in this concept is that it doesn’t take actual play into account. I face death many times a day. Yet, death rarely ever gets to cast against me. I can’t remember the last time I played PVP and let Death have a chance to cast. I’m sure I’m not the only player that neutralizes troops like Death quickly.
Ninja. And the few times CPU get Death ready to go, the enemy team is already very wounded, so it does not matter much if 1-2 troops dies. Sure it gives a little thrill the few times it happens, but thank god for the little thrill in a game there most has a win rate of 95%+
10% death mark chance is known.
Assuming it has one roll at that 10%, which is one turn, nothing changes.
Because statistics and math:[quote=“MakoSipper, post:3, topic:13324”]
the chance of losing 3 troops on the first turn after Death has cast it spell is 0.36%. The chance of losing 2 troops on the first turn after Death has cast it spell is 4.86%
[/quote]
0.36% is… 0.36 times in 100, 3.6 times in 1000, and 36 times in 10,000. Huh, I missed a digit. So I was off by a bit.
I got to 9000 PvP rating last week and there were somewhere around 11,000 people ahead of me on the PvP ladder. I rounded down to 10k people. All further math is done from there, with one exception.
I do not know how many people use Death and how often Death gets to cast in a match (maybe one in four matches it gets used?). That is the only number pulled from thin air, and that is something I can only roughly guess.
But it is an incredibly safe bet that Death did cast over 10,000 times in the last week, due to the sheer amount of games that get played, along with how popular Death is. Especially in the late game. Meaning that it happened to 36 people at the VERY least. Statistically speaking, anyway
I don’t have the usage rate for anything; my site doesn’t track actual usage, and that information could only be determined by having access to Infinite’s back end (which I definitely do not have).
That being said, your reasoning is valid, and what you’re describing is called the Law of Large Numbers. Yes, the chances of this event (exactly three troops dying on the first round of Death Mark) occurring are exactly 1 in 1000 (assuming Death Mark cannot wear off naturally in turn 1, and the more I play the more I am convinced that status effects cannot wear off on turn 1). Therefore, any given individual’s chance of encountering this is quite low, 0.1%. However, it doesn’t take too many instances to predict at least one occurance per week:
So with only 693 casts of Death in one week, there’s a 50% chance someone has seen him kill three troops. With 1,386 casts, the chance goes up to 75%, and with 2,302, the chance goes up to 90%. So it’s quite likely that, across the player base, some unlucky soul each week will get most of their troops killed by a Death cast. This sticks with you a lot longer than the average case (no deaths or only one death) because it’s so catastrophic, and cannot be countered.
Now, the odds described above by @MakoSipper (losing multiple units first turn across consecutive casts) are much lower. That’s some serious bad luck (one in ten million). My condolences. Maybe see if you can balance it out with a lottery ticket?
@Kurokazna: But that only account for ONE occurence. 0.36% is “real” enough for me as a single event. That was maddening at first, and I complained about it in guild chat, but I wouldn’t have come here just for that single occurence. But then I lost 2, and then 3 again, and then 2. Yeah, I had 4 in a row (ok, 2 of them wre slightly more likely than 0.36%, but still).
What other players get doesn’t really matter. The chances of one single player getting that streak with 4 Death casts in a row are abysmal. Maybe I did win the wrong lottery… Maybe the atmospheric noise suddenly became static due to the wrath of RNGesus? Sometimes I wish I recorded myself playing all the time, so I could show that happening.
But my calculations were simply this:
What are the odds of a single player letting Death cast its spell 4 times in a row and losing 2 troops twice and 3 troops twice in the FIRST turn after the spell was cast, in whatever order? The answer was: 0.00001224440064%. If the 10% chance of killing the troop is correct, that’s really low. Any data analyst would question that result, though, given it’s highly unlikeliness, and would try to come up with logical reasons for it.
I didn’t include more rare occurences, like losing 3 troops three times and 2 troops once, or 3 troops four times, or losing all 4 troops, but I doubt they’re significant.
P.S.: In the end, in order to prevent Death’s spell, I made some changes to my PvP attack team and I REALLY like the outcome a lot better than the team I had before. So maybe it all happened for a reason. (And Death was never able to cast again…)
My goal with things like this is to assist the best I can and either point in the direction of someone that can help more or until someone better than me at the thing arrives.
For things like this, you are magical, Lyya. Thank you.
I thought it would’ve been 1/1000, but I’m also fairly bad at this particular area of math, so I am far more likely to take someone else’s word for any given percentage.
And as for this: [quote=“Kurokazna, post:8, topic:13324”]
if anyone has the usage rate for Death, it would be either Sirrian, who I don’t want to bother, because vacation, or @Lyya
[/quote]
I don’t exactly know how much you know on any given topic, and you have given some information on troops and such before I had seen them anywhere else, so I have no idea what you do and don’t know. But, as said, if anyone but Sirrian or another dev had those numbers, it would probably be you, Though I’m not entirely unsurprised that you don’t have access to that information.
I misread that. I am sorry.
In addition[quote=“Lyya, post:14, topic:13324”]
the more I play the more I am convinced that status effects cannot wear off on turn 1
[/quote]
I am completely and utterly convinced, myself. I think I’ve read something somewhere about some official explanation of status effects. I don’t think they can wear off turn one. I have never seen it. Nobody I knows has ever seen it. I have never seen it in a video or on stream. I think it’s a safe assumption.
I don’t use Death Mark anymore, but I remember a game where it killed 3 troops at once. Since that is the only game I remember, the chance of a 3 troop kill is obviously 100%.
Mako’s odds are right, assuming that his four troops are alive when Death casts, because the chance of 3 dying on the first turn is the chance of three dying (0.1%) times the chance of one living (90%) times the number of combinations (4 because each troop could be the one alive), which is 0.36%.
Similarly, his odds of 2 dying at 4.86% are correct.
So the chances of this happening in 4 games in a row is 0.36% x 0.36% x 4.86% x 4.86% x 6 = 0.0000184% or a bit over 1 in 5 million.
However, if Mako plays 20 games against Death where Death gets to cast at least once and this streak happens at least once in those 20 games, the odds are trickier to calculate but they increase a lot to around 1 in 350,000 or so, which while very unlucky is not outside the realms of possibility.
Just feeding you, although I shouldn’t.[quote=“actreal, post:18, topic:13324”]
So the chances of this happening in 4 games in a row is 0.36% x 0.36% x 4.86% x 4.86% x 6 = 0.0000184% or a bit over 1 in 5 million.
[/quote]
I think I multiplied that by 6, since the order of these 4 event doesn’t matter, but yeah, that’s about it.
Probability is somewhat magical to me sometimes. Depending on what you focus, you get different results. But 4 in a row is still 4 in a row.
Actually, I made a miscalculation, and @MakoSipper is right about the per-cast chance. I said that the odds of losing three of four troops was 1 in 1000, but it’s actually higher than that. It would be 1 in 1000 if you had exactly three troops, but because you have four, one must apply a binomial distribution instead:
f(k, n, p) = n!/(k!(n-k)!) * p^k * (1-p)^(n-k)
k = 3 (troops that die)
n = 4 (troops in total)
p = 0.1 (probability of any one troop dying)
f(3, 4, 0.1) = 4!/(3! * 1!) * 0.1^3 * 0.9^1 = 4 * 0.001 * 0.9 = 0.0036
The chance of two dying immediately is
f(2, 4, 0.1) = 4!/(2! * 2!) * 0.1^2 * 0.9^2 = 6 * 0.01 * 0.81 = 0.0486
So with a 0.36% chance of losing three troops, a 50% chance of this happening once a week is (log 0.5 / log 0.9964) = 192 casts. It’s 384 casts for a 75% chance and 638 casts for a 90% chance.
