How the Arena works Part One: What is a deathmatch, anyway?
DNA3000
Member, Guardian Guardian › Posts: 19,693 Guardian
This is the first part in a multipart series that will go through some of the things I've learned about the arena after doing a deep dive on its behavior and mechanics. Technically, I'm still in the middle of that deep dive, so I have no idea how many parts this series will end up having. I do know it is going to be more than one, because I already have more stuff than can reasonably fit in a single post.
Also, while I will (out of necessity) try to summarize as much as possible, this post will cover some of the details and the methodology of my testing along with its conclusions, so anyone bored by that kind of stuff should probably skip this one. However, if you're interested in how the arena actually works in terms of the details, strap yourself in: this will get a little deep into the weeds.
Probably the most common question people ask about the arena is "how do I avoid death matches" or alternatively "what's your infinite streak strategy?" That is what this article will delve into. So what is a death match and what is an infinite streak? Colloquially, most arena grinders understand that at higher streak counts, there's a certain "minimum team" you have to use. If you use a weaker team, you'll draw a super hard match up. Why does this happen?
Here's the mind blowing thing most players don't know: death matches are not the arena breaking, they are the arena working. It is the easy matches before that which are broken.
I’ll start with a technical description of what the arena is trying to do first, and then explain how I determined this.
I hope that’s not too technical.
The arena wants to give you progressively harder matches as your streak counter rises. In theory, the higher your round counter gets, the harder the matches should be, at least up to a point. Two factors alter this behavior, one in a small way and one in a very large way. The first one is that there is a random factor to the match ups. While the arena might attempt to find a match of strength X, it picks from a range plus or minus some factor (more on that later). As a result the difficulty of the matches doesn't increase in a nice straight line. The other thing that creates the "Infinite Streak/Death Match" behavior is that the arena has a maximum strength match up contained within it. The Trials arena, for example, only contains 4* and lower champs. There is a highest 4* PI team that exists (and the arena is aware of). So what happens if the game tries to find a team with a PI that is so high no such team exists? The arena match algorithm "breaks" and starts sending relatively weak teams at the player.
What are we looking at here? The blue curves are the three different match ups faced by 5/50s, the orange are the 4/40 match ups, and the green are the 3/30 match ups, shown relative to the PI of the player team. In all three situations there's a run up of increasing difficulty, and then a sudden drop in the difficulty of the arena matches. This happens sooner with 5/50s and later with 3/30s. During the flat part of the curves you're seeing Kang/Thanos teams. They tend to be very similar and very consistent in relative difficulty. Kang/Thanos teams consistently end in round 16, where the match ups start to become more varied, but of similar average difficulty. This is what people describe as being in "infinite Streak." You'll see that behavior indefinitely, so long as you don't use too low a team.
Although the three curves drop in difficulty at different times (in different rounds), in a sense they are doing so at the same time. Here's the exact same data, but plotted by opponent PI instead of opponent relative PI:
Notice every set of curves rises until a certain point, and then drops to a lower level. The maximum PI that is reached before the sudden drop is relatively consistent. It corresponds to about 22500 PI (total team rating). What's special about 22500? Well, so far in my testing the highest PI 4* team that has shown up in the Trials arena has been 22518. That's probably the highest, or close to the highest team that's actually in there.
So what appears to be happening is, the game wants to keep delivering higher PI matches, but at some point if the player uses a strong enough team and the multiplier gets high enough, it can't. When it can't, the arena "breaks" and starts sending weaker Kang/Thanos teams, until round 15. Then from round 16+, it starts sending matches where the normal random variability rules are still present, but the teams are being pulled from the normal arena matches rather than the Kang/Thanos teams. But they are essentially base difficulty teams (between about 0.6x and 1.2x the player PI).
Is there a "lowest safe team?" Yes and no. In rounds 20 and higher, yes there is. But in rounds earlier than 20, the minimum safe team is not a constant value. Why? Because the strength of the team the game is looking for is rising. So what's safe for round 20 won't be safe for round 19. If this is difficult to understand, pretend the game wants to find a 10x team at round 20 and a 5x team at round 15. If the highest possible opponent team the arena can send against the player is 22500, then in round 20 any player team higher than 2250 will be impossible to find a match for. So anything higher than 2250 is "safe" - the arena won't be able to find a match, and you'll get "infinite streak" easy teams. But in round 15 the arena is only looking for teams 5x higher, so the minimum safe team is 4500. Anything lower than 4500 is a team the game can still find matches for, and you'll get a 5x opponent - a "Death Match."
So what's the actual strength multiplier the game is looking for, round by round? I have to guestimate from the data I have, which is fuzzy. It is almost impossible to get good data for early rounds, because it is hard to "break" the ceiling in early rounds. I do have some multiplier estimates for many of the middle rounds and specifically round 20 because I tested breaking streak at round 20 several times. The closest match to the data I can find is one where the strength multiplier increases roughly linearly from round one to round ten, and then increases quadratically from round eleven to round 20, then stays constant from round 20 onward. Those numbers, rounded to the nearest tenth, look like this:
The curve actually doesn't fit the data for the first three rounds for reasons I haven't been able to figure out yet, but it then starts to fit fairly close.
Let's play a game. Let's play "guess when Kang shows up, and when Mr. Death Match shows up." Here's a graph of what the minimum predicted "safe team" would be, if the highest possible team was 22518, and what would happen if I used my 4* roster (actually from a second account) in descending order starting at round 1 (minimum safe team in blue, my own 4* roster in orange).
So where does Kang show up, and where does the first Death Match show up?
Kang shows up very close to when my roster climbs higher than the "minimum safe" curve (round 9 on the chart), which remember if I'm higher than that curve the game can't find a proper match for me - it is "broken." And the first death match happens almost exactly where I cross back below the blue curve (hopefully obvious), which remember is when the game *can* find matches for me, and the game does. And it is a match approximately 4x higher than I am (I am showing the strongest match of the three options for clarity purposes).
To return to the graph at the beginning of the article, this is what the arena is attempting to do:
The arena wants to throw progressively harder matches against the player, rising all the way up to almost 4x the player PI. The problem is if the player uses a high enough team, the arena can't find any such match, so it is forced to throw an easy set of matches at the player. In early rounds it throws Kang teams at the player, but eventually it just decides to throw easy "regular" teams at the player, hoping the problem will fix itself.
If the player brings a team that is too low, the problem "fixes itself" and the game happily does what it has been trying to do all along: throw a ~ 4x team at the player.
The only way to know what's safe in early rounds is to do the calculations, but past round 20 the answer to the question of what's safe seems to be:
Also, if the arena is trying to send some multiple of the player's PI against them, what's "player PI?" Is it the intrinsic PI of the champs, the visual PI shown on screen (which includes things like masteries, synergies, and boosts) or something else? I *think* it is the PI of the champs including masteries but *not* including either boosts or team synergy effects. That too is currently a question I'm working on resolving.
Still, I should answer the question I started with. What's a Death Match anyway? A Death Match is what happens when the game has been trying but failing to find a very hard match to send against you, until you bring a team that is low enough that the game suddenly finds such a match, whereupon you suddenly get a much stronger match up than previously. Infinite Streak is what happens when the game tries to send a very hard fight against the player, but can't because the strength of the team it wants to send against you doesn't exist (in the arena in question). To stay within this broken infinite streak range, you must bring a team of a certain PI or higher, not counting boosts or synergies. If you bring a team lower than this, you get a Death Match (at high enough streak). How strong is strong enough? For the 4* arena, it is approximately this:
For the 6* arenas, it is this:
If your team PI is higher than approximately this number, you’ll get Kang/Thanos teams before round 15, and opponents about 0.8-1.0x your team above round 15. If your team is lower than this number, your opponents will be about the estimated multiplier times higher than your team.
These numbers are not precise: they are predictions based on the math, but they have a margin for error due to the limited data I have collected and some random effects in the system itself. There are also some additional technical details, such as how the three different matches work and what the variability is in them that isn’t important for now, but I might cover in a future article. Down the road I hope to improve the precision of these numbers, but my next arena article will probably delve into arena scoring: How does the arena calculate your arena score, what impacts scoring, and how to optimize your scoring in the arena.
Also, while I will (out of necessity) try to summarize as much as possible, this post will cover some of the details and the methodology of my testing along with its conclusions, so anyone bored by that kind of stuff should probably skip this one. However, if you're interested in how the arena actually works in terms of the details, strap yourself in: this will get a little deep into the weeds.
Probably the most common question people ask about the arena is "how do I avoid death matches" or alternatively "what's your infinite streak strategy?" That is what this article will delve into. So what is a death match and what is an infinite streak? Colloquially, most arena grinders understand that at higher streak counts, there's a certain "minimum team" you have to use. If you use a weaker team, you'll draw a super hard match up. Why does this happen?
Here's the mind blowing thing most players don't know: death matches are not the arena breaking, they are the arena working. It is the easy matches before that which are broken.
I’ll start with a technical description of what the arena is trying to do first, and then explain how I determined this.
I hope that’s not too technical.
The arena wants to give you progressively harder matches as your streak counter rises. In theory, the higher your round counter gets, the harder the matches should be, at least up to a point. Two factors alter this behavior, one in a small way and one in a very large way. The first one is that there is a random factor to the match ups. While the arena might attempt to find a match of strength X, it picks from a range plus or minus some factor (more on that later). As a result the difficulty of the matches doesn't increase in a nice straight line. The other thing that creates the "Infinite Streak/Death Match" behavior is that the arena has a maximum strength match up contained within it. The Trials arena, for example, only contains 4* and lower champs. There is a highest 4* PI team that exists (and the arena is aware of). So what happens if the game tries to find a team with a PI that is so high no such team exists? The arena match algorithm "breaks" and starts sending relatively weak teams at the player.
Infinite Streak is what happens when the player breaks the arena, and makes it impossible for the algorithm to find a match as difficult as it is programmed to send against the player.
For people who love to see this kind of stuff, this is an example of the kind of data I've been collecting. This is what the match ups look like when I run 4* 5/50s, 4/40s, and 3/30s through the Trials arena:What are we looking at here? The blue curves are the three different match ups faced by 5/50s, the orange are the 4/40 match ups, and the green are the 3/30 match ups, shown relative to the PI of the player team. In all three situations there's a run up of increasing difficulty, and then a sudden drop in the difficulty of the arena matches. This happens sooner with 5/50s and later with 3/30s. During the flat part of the curves you're seeing Kang/Thanos teams. They tend to be very similar and very consistent in relative difficulty. Kang/Thanos teams consistently end in round 16, where the match ups start to become more varied, but of similar average difficulty. This is what people describe as being in "infinite Streak." You'll see that behavior indefinitely, so long as you don't use too low a team.
Although the three curves drop in difficulty at different times (in different rounds), in a sense they are doing so at the same time. Here's the exact same data, but plotted by opponent PI instead of opponent relative PI:
Notice every set of curves rises until a certain point, and then drops to a lower level. The maximum PI that is reached before the sudden drop is relatively consistent. It corresponds to about 22500 PI (total team rating). What's special about 22500? Well, so far in my testing the highest PI 4* team that has shown up in the Trials arena has been 22518. That's probably the highest, or close to the highest team that's actually in there.
So what appears to be happening is, the game wants to keep delivering higher PI matches, but at some point if the player uses a strong enough team and the multiplier gets high enough, it can't. When it can't, the arena "breaks" and starts sending weaker Kang/Thanos teams, until round 15. Then from round 16+, it starts sending matches where the normal random variability rules are still present, but the teams are being pulled from the normal arena matches rather than the Kang/Thanos teams. But they are essentially base difficulty teams (between about 0.6x and 1.2x the player PI).
Is there a "lowest safe team?" Yes and no. In rounds 20 and higher, yes there is. But in rounds earlier than 20, the minimum safe team is not a constant value. Why? Because the strength of the team the game is looking for is rising. So what's safe for round 20 won't be safe for round 19. If this is difficult to understand, pretend the game wants to find a 10x team at round 20 and a 5x team at round 15. If the highest possible opponent team the arena can send against the player is 22500, then in round 20 any player team higher than 2250 will be impossible to find a match for. So anything higher than 2250 is "safe" - the arena won't be able to find a match, and you'll get "infinite streak" easy teams. But in round 15 the arena is only looking for teams 5x higher, so the minimum safe team is 4500. Anything lower than 4500 is a team the game can still find matches for, and you'll get a 5x opponent - a "Death Match."
So what's the actual strength multiplier the game is looking for, round by round? I have to guestimate from the data I have, which is fuzzy. It is almost impossible to get good data for early rounds, because it is hard to "break" the ceiling in early rounds. I do have some multiplier estimates for many of the middle rounds and specifically round 20 because I tested breaking streak at round 20 several times. The closest match to the data I can find is one where the strength multiplier increases roughly linearly from round one to round ten, and then increases quadratically from round eleven to round 20, then stays constant from round 20 onward. Those numbers, rounded to the nearest tenth, look like this:
The curve actually doesn't fit the data for the first three rounds for reasons I haven't been able to figure out yet, but it then starts to fit fairly close.
Let's play a game. Let's play "guess when Kang shows up, and when Mr. Death Match shows up." Here's a graph of what the minimum predicted "safe team" would be, if the highest possible team was 22518, and what would happen if I used my 4* roster (actually from a second account) in descending order starting at round 1 (minimum safe team in blue, my own 4* roster in orange).
So where does Kang show up, and where does the first Death Match show up?
Kang shows up very close to when my roster climbs higher than the "minimum safe" curve (round 9 on the chart), which remember if I'm higher than that curve the game can't find a proper match for me - it is "broken." And the first death match happens almost exactly where I cross back below the blue curve (hopefully obvious), which remember is when the game *can* find matches for me, and the game does. And it is a match approximately 4x higher than I am (I am showing the strongest match of the three options for clarity purposes).
To return to the graph at the beginning of the article, this is what the arena is attempting to do:
The arena wants to throw progressively harder matches against the player, rising all the way up to almost 4x the player PI. The problem is if the player uses a high enough team, the arena can't find any such match, so it is forced to throw an easy set of matches at the player. In early rounds it throws Kang teams at the player, but eventually it just decides to throw easy "regular" teams at the player, hoping the problem will fix itself.
If the player brings a team that is too low, the problem "fixes itself" and the game happily does what it has been trying to do all along: throw a ~ 4x team at the player.
The only way to know what's safe in early rounds is to do the calculations, but past round 20 the answer to the question of what's safe seems to be:
"Do not go lower than about the highest team that exists in that arena divided by 3.9."
For arenas with max 4* champs, that max team seems to be somewhere around 22518, which makes the minimum safe team post round 20 about 5774. For arenas with 6* champs, the max team currently seems to be somewhere around 56750, which means the minimum safe team is somewhere around 14550. These are ESTIMATES and I haven't collected enough data to do more than estimate, but I'm trying to make those calculations more precise. Right now they probably have about 1-5% margin for error right now.Also, if the arena is trying to send some multiple of the player's PI against them, what's "player PI?" Is it the intrinsic PI of the champs, the visual PI shown on screen (which includes things like masteries, synergies, and boosts) or something else? I *think* it is the PI of the champs including masteries but *not* including either boosts or team synergy effects. That too is currently a question I'm working on resolving.
Still, I should answer the question I started with. What's a Death Match anyway? A Death Match is what happens when the game has been trying but failing to find a very hard match to send against you, until you bring a team that is low enough that the game suddenly finds such a match, whereupon you suddenly get a much stronger match up than previously. Infinite Streak is what happens when the game tries to send a very hard fight against the player, but can't because the strength of the team it wants to send against you doesn't exist (in the arena in question). To stay within this broken infinite streak range, you must bring a team of a certain PI or higher, not counting boosts or synergies. If you bring a team lower than this, you get a Death Match (at high enough streak). How strong is strong enough? For the 4* arena, it is approximately this:
For the 6* arenas, it is this:
If your team PI is higher than approximately this number, you’ll get Kang/Thanos teams before round 15, and opponents about 0.8-1.0x your team above round 15. If your team is lower than this number, your opponents will be about the estimated multiplier times higher than your team.
These numbers are not precise: they are predictions based on the math, but they have a margin for error due to the limited data I have collected and some random effects in the system itself. There are also some additional technical details, such as how the three different matches work and what the variability is in them that isn’t important for now, but I might cover in a future article. Down the road I hope to improve the precision of these numbers, but my next arena article will probably delve into arena scoring: How does the arena calculate your arena score, what impacts scoring, and how to optimize your scoring in the arena.
46
Comments
oooOOoo0oo00OOh
Anyways, thanks for doing all that legwork.
Also, be wary if the devs ever release a champion that can break the top three in PI. That will cause the minimum safe time to become higher than now. The "safe team" is not dictated directly by the arena code. It is dictated by the strongest champions we players bring into the arena. Whenever someone brings something higher than has ever appeared before, the strongest team the arena can throw at you rises, and the higher the minimum safe team needs to be to prevent getting that new strongest team.
This is also why infinite streak guides always have to be updated when a new rarity or top tier rank becomes available. Someone gets it, uses it in the arena, and then the arena can use it against us. And then our minimum safe team rises.
As far as I can tell so far, rarity and rank seem to have no direct impact on how this works, just PI. Although sometimes it is intrinsic PI, sometimes it is mastery-boosted PI, and sometimes it is even more complicated. I haven't gone through all of that here, because that could fill an entire separate post.
Incidentally, if anyone was wondering why death matches in the 6* arena are often Doom, Doom, and more Doom, this is why. If you happen to use a team *just under* the minimum safe team, the only teams the arena can throw at you are the ones with the highest PI possible that have ever showed up in the arena. Which will almost always be teams with high rank high sig Doom.
Based on my previous tests the PI used for matching is the unawakened base hero rating (prestige) of a champion which is independent of any other pi modifiers including signature level.
I currently run through all my 5* r2’s in the higher arenas without ever seeing a death match. This is made possible by r3ing “legacy” Champions with low base prestige, juggernaut, black bolt etc. in the past I was able to run 1 r2 legacy champs with 2 r2 “newer” champions.
When I was working toward eliminating death matches from my grinds pairing 2 r2 legacy champions with any other r2 would trigger a death match. Pairing only one legacy would never return a death match.
If you use the auntm.AI prestige sorting system and filter by lowest prestige then draw a line down to something like the 25th and never pair two of those you shouldn’t see a death match.
Here is a video where I explain what I was doing back when I actually could see a death match. Due to selective ranking I haven’t seen a death match in months.
This is a comparison of mastery boosted PI and non-mastery boosted PI matching (using data collected by running the arena with literally no masteries) compared to the expected multiplier curve:
Best guess is that the first match is looking for an arena team that is about the intrinsic PI of the player team multiplied by the difficulty multiplier curve, plus or minus 10-20%, and the other two are progressively higher (but also plus or minus some random factor). However, based on my testing to date the point where the game decides to "give up" is about 3.9x player PI including masteries, not the intrinsic masteries.
It is possible something more complicated is going on that more data collection would illustrate, but so far the 3.9x breakage point was fairly consistent across different mastery set ups. However, it appears the behavior of the arena is composed of a number of overlapping behaviors that combine in sometimes difficult to predict ways. For example, Kang teams stop after round 15, but the difficulty curve keeps rising until round 21 (20 rounds completed). That suggests there's some patch work to the arena behaviors, that will take very specific testing to wedge into.
You may not have given this any thought, but if you happen to have given it some thought I'd be curious to know what you think the minimum teams might be in an R4 world, and how you came to that estimate, as this seems to be something you might have given some consideration.
To support my base pi assertion. I ask if you ever come across teams with HtD and Gambit as death matches since as 4* they both have higher base pi than doom. As 6* gambit is higher than doom and I want to say I have seen gambit in many of my maximum pi matches (death matches even when they are past streak 9 and before streak 20).
So the programmer implemented a "if search fails then" escape clause, which are the Kang matches. And someone, possibly someone completely different, added a separate escape clause which says "if Player x Multiplier fails, try Player x (Base) instead for just this one fight, and hopefully the problem will go away later."
Because the arena has a way to deal with exceeding the "multiplier ceiling" the arena never "broke" visibly. It just put people into failsafe modes which we called "infinite streak." And because no one complained about it, and the game didn't visibly break because of it, no one bothered to investigate and try to fix it, and it eventually became the norm. Good point. In every graph the X-Axis is the arena round counter. The Y-Axis is either team PI if the range is large, or the observed difficulty ratio of Opponent Team PI / Player PI if the axis range is small.
Thinking about it you can test Pi v naked Pi fairly easily with mystic desperation, suicides and legacy champs like scarlet witch, juggernaut and doctor strange.
📈📈📈📈📈📈📈📈
The distinguishing test between your theory and mine, I believe, would be to test my prediction of what the actual cutoff is for death matches, and who shows up in them. If I'm correct, then someone who triggers a death match very close to 14600 in the 4* arena or 56800 in the 6* arenas should see mostly teams with Doom in them, because factoring in masteries I believe Doom is the highest champ that can show up in either one of those. If you're correct, we should see more Gambit teams than Doom right near that point.
Below that point it would be more of a toss up, because significantly below the limit the game has a range of possible teams it can assemble and meet the criteria - whether that's your conjectured criteria or mine. But at the very top of the limit of what is possible, there are only a few teams possible, and if we could hit the exact bullseye there would really only be one possible match candidate - the highest possible team under the match criteria.
That's probably impossible to hit reliably, but we'd still expect the opponent match teams to be dominated by the top PI champ - as determined by what the game is counting as "PI" at the highest PI teams that can still trigger a death match at all. If I'm right, that most common champ at the very top will be Doom. If you're right, if I understand your theory correctly, it will be Gambit as he's the highest possible PI champ under the criteria that the game look at unawakened unboosted masteries.
(Incidentally, part of the reason I first suspected that masteries factored into matching is specifically because Doom seems to show up in my highest death matches, but Silver Surfer is extremely rare).
Second: I still haven't done what I would say is a complete analysis of how masteries affect every aspect of the arena system. They seem to affect different parts differently, and I do not know if masteries affect how the game determines if a match can be located. Part of the reason for releasing this article was my home that people willing to test the theory under a wide range of different roster and mastery conditions might offer some better insight into how those variables impact the system as a whole. It would take prohibitively long to test every possible combination of factors single handedly.