Raid revenge- Against a lower rated opponent (Make the System of Revenging Feel Fairer) – Get as many trophies back for revenge as you lost

You’re essentially trying to imagine a system where it’s easier to win trophies on an initial attack than on a revenge, it seems.

It’s a good question for someone like @Gryphonknight or @Garanwyn whether that would even work within an Elo system. My gut sense is that trophy counts would be fairly stagnant if people were constantly just winning back all the same trophies they just lost.

But I guess my bigger question is this — why do you feel differently about the net loss of trophies when losing a defense and winning a revenge vs. those you lose when raided to begin with? That same system is how you got your own trophies to begin with.

(And I do mean this as a sincere question, I’m trying to understand what about the current system makes it feel unfair on one side and not the other.)

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It would be a broken system for sure. Current system works just fine and has for 2 years…

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I think it would break the system too, but to be fair, there are shortcomings in the current system in the sense that any momentary snapshot of trophy count and ranking bears little relationship to skill or team strength. But people do seem to end up hovering into a stable range for a given defense team.

This helped to demonstrate that, I think:

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Revenging a lower rated opponent

You answered your own question the trophies were +18 / -48 for you and +48 / -18 for your opponent.

If you want more than +18 trophies, pick an enemy with a higher rating.

Unless you have a PhD in statistical analysis, I am not being sarcastic, you are unlikely to improve Elo’s math.

Raid rewards are a whole different discussion and the balance between fun, grinding, F2P, P2P, etc. is an interesting one.

Trophy distribution at each tier of team power

What was interesting about the data collection was not Defense power to trophy ratio - that is flawed from the beginning because this is an MMO - but the statistical distribution of trophies for each tier of team power. An interesting analysis of opponent pool, tanking, raid rewards and Wanted mission hero chest reset timer.

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There’s actually a very easy modification that would correct for the “home-court advantage” that attackers have.

This gets a little technical

ELO assumes that the probability of win for people with equal trophies is 50%. But the devs have said the true number is more like 70%. This means we need a home-court advantage factor to adjust the equation.

The core ELO equation says that:

P(attacker beats defender) = 1/(1 + 10^(Trophies(Def) - Trophies(Att) )/400)

But we’re going to need to add a “home-court advantage” adjustment factor, F, to account for the fact that equal cups gives the attacker a 70% chance of win, instead of a 50% chance of win.

P(attacker beats defender) = 1/(1 + 10^(Trophies(Def) - Trophies(Att) + F)/400)

When the players are at equal cups in E&P:

Trophies(Def) - Trophies(Att) = 0
P(attacker beats defender) = 0.7

So, making these substitutions into the equation:

0.7 = 1/(1+10^(F/400))
1/0.7 - 1 = 10^(F/400)

We can simplify, because:

1/0.7 - 1 = 1/.7 - 1 = 0.429

So:
0.429 = 10^(F/400)

We take the logarithm of both sides:

Log10(0.429) = (1/400)*F

F = 400 * Log10(0.429)

F = -147.2

This means we should treat the defender as though they had 147.2 fewer cups than they really do when deciding how significant a win actually is. Here’s an example of how this adjusts things:

Attacker Trophies Defender Trophies Assumed P(win) current Assumed P(win) Corrected Current Trophy Gain For Win Corrected Trophy Gain For Win
2000 1500 94.68% 97.65% 3.25 1.44
2000 1600 90.91% 95.89% 5.55 2.51
2000 1700 84.90% 92.92% 9.21 4.32
2000 1800 75.97% 88.06% 14.66 7.28
2000 1900 64.01% 80.58% 21.96 11.85
2000 2000 50.00% 70.00% 30.50 18.30
2000 2100 35.99% 56.75% 39.04 26.38
2000 2200 24.03% 42.46% 46.34 35.10
2000 2300 15.10% 29.33% 51.79 43.11
2000 2400 9.09% 18.92% 55.45 49.46
2000 2500 5.32% 11.60% 57.75 53.92

The bottom line is that the defender is effectively 147.2 trophies weaker than their trophy score would suggest, due to attacker advantage.

So SG should use an “effective trophies” for the defender of (Current_Trophies - 147.2) in the calculation for figuring trophy gain/loss in a raid.

We’d see a lot less motion in trophies overnight if SG made this change. Indeed, they’d tend to be fairly stable until people actually improved their game or improved their team.

The SG speed-of-change factor of 61 in the calculation is probably also too high, but that’s a discussion for another time.

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You are correct, that is in fact a simplification of Elo’s Bell curve assumptions on win/ loss/ tie that is close enough for this discussion.

But.

Game developers want that error, intentionally. The attacker must always have an unreasonable advantage. The trick is finding the percentage that makes the most players happy without sacrificing income.

This is not professional sports this is a game.

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This actually doesn’t change the built-in overwhelming advantage at equal cups at all; it enshrines it.

In essence, your cups will settle out at a point where you are winning 70% of your matches under this modification, instead of the algorithm trying to drive you up the rankings to the (unreachable) 50% win point that the current algorithm does.

This change would makes things even “better” from the getting-easy-matches perspective, because you rise in cups more slowly when you win, and drop in cups much faster when you lose, moving you down to where you legitimately can win 70% of the time.

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Even when I win, although, I may not win back all my cups I still win more hams and steel than you took. So as far as I see it I’m glad ya raided me because overall…I’ve won and I can color stack the next guy and win more cups

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Win record

What?!

That is not what the Devs or Elo said.

The Devs said matching ratings the attacker wins 70% of the time, not the attacker wins 70% of the time.

Elo’s math does not drive you to 50% win, Elo’s math tries to PREDICT 50% of your wins and 50% of your loses ( hence the Bell curve of the win/ loss/ tie assumption). If Elo’s math drove you to 50% wins it would have much higher variance. Instead of +30/ -30 rating per match it would be +750/ -750 rating per match.

Using an Elo based rating the only way you can win more than 50% of the time is if you are 2400+ rating OR you can choose you opponent.

In Empires we can choose our opponents.

Example
Deliberately lose to an opponent that costs you 48 trophies
Beat three opponents that gain you 16 trophies.
You now have a 75% win record and the same rating when you started.

Nightly loses

Your complaint seems to be people are losing too many trophies over night.

So your solution is to adjust the defender so it has less trophies for matching. Effectively making the defender stronger. So the player wins less trophies than they should and loses more trophies than they should. Or to put it another way, matching based Elo rating deflation.

Devs could easily do this by doubling the defenders HP or doubling time for 1 raid energy recharge or changing the hard limit for matching to plus or minus 10 rating.

Self Correctly Algorithm

But regardless, it is only temporary.

Similar to 3000+ scores after Barracks was introduced, your new normal would self correct to the 0- 3000 range. The underlying principle of a self adjusting rating forces this result. You are just suggesting tinkering with the per match variance.

This is very similar to the fallacy that Field Aid (WR) favors the other side, in fact it favors both sides equally but make war less stabby ( a technical term).

In my opinion your change would be similar to Field Aid (WR).

More choices

The Devs could adjust the ratings so 0- 1000 rating was the target for the algorithm, and the hard cap for matching was plus or minus 500 rating, this would flatten the curve and allow more opponent choices. With more opponent choices you could easily increase your win rate higher than 75%.

Devs are satisfied

The Devs have chosen the current raid matching algorithm because it produces a satisfactory daily ratings movements. If it did not, after 2 years of use, they would have tinkered with the algorithm.

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It’s simple. It seems lately that lower level teams are defeating higher level teams. I do alot of raiding. And yes I work on lower trophies and higher raiding, vice hier level higher trophy gains. So if I am revenged on by the players that I defete and they defete me then sure they should get the higher reward. That is not the issue I have. It is when a lower level hits a higher level it seems lately that they always win. I have lost more in the past two months to teams that I normally defete then before. I am not the only one to notice this. Maybe it’s just me.

I wouldn’t even qualify that with “lately.” I know I’ve been routinely blowing away teams 200-1000 tp stronger than my attack teams for months.

Raiding hugely favors the attacker. At least if you know what you’re doing.

Probably not always, but if their raid records are like mine, I’d bet it’s around 70% of the time, or even a tad higher. I definitely beat stronger teams far more often than not.

Have your defense team and your attack teams been constant along the way?

I’m just wondering if part of that might be that you’re in a little bit different trophy range than you were more than a couple months ago, which might affect the sorts of heroes the revengers have to work with against you.

You might also be seeing more cup dropping/raid bait defense teams, perhaps, where people are intending to be beaten so they can revenge easily.

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I have done nothing but improve my defense. It is the same team and I am usaly between 2200 and 2400 cups. I am not talking about when I raid. Yes I know about Tha baiting. Fully accept that. I am talking about when I get attacked. Teams that two months ago could not touch my then weaker team are now blowing me out of the water. Then when I go raid them in a revenge I get less Than half the trophies back. Like I said before it is the revenging not the raiding. When I pick a fight and I lose or am beaten in the second round oh well. I take the loss. That’s part of raiding. I expect that. But I have a hard time with this low-level team first beating me when this seems unlikely not impossible just not as often as it seems to be now, and then not being able to win back what I lost. Sorry if I’m not clear in what I am trying to say. With the Raiding the system is great. You select what you want to risk and you roll the dice. Then if you picked a lower level opponent and they revenge you sure they should get a good reward. But when a low level hits you and wins then you revenge you should get the trophies back. No more than what you lost just that amount. That’s all I am saying.

Ok, got it. I thought you were also talking about you getting revenged too.

Sorry for creating more confusion, that was my bad.

 

Of course we don’t really know what team attacked, since we can only see the defense. And obviously hardly anyone uses their defense team for attacking in the 2200-2400 cup range.

But I get what you mean, I think, which is basically a player whose roster overall is probably weaker than yours.

 

This make sense to me. I’m in the same 2200-2400 trophy range roughly, and I typically get matched with a lot of 3700-4050 tp defense teams that I’m beating regularly with 3300-3450 tp attack teams.

And just for context, my Defense Team is 3500 tp.

 

I get this philosophically, it feels more fair.

I’m just not sure how it would work in practice, since weaker attack teams can readily beat stronger defense teams.

 

Using myself as an example, a few minutes ago I won 3 raids in a row against defense teams 500-600 tp stronger than my attack teams. I won +48, +50, and +46 trophies for those raids.

Given the trophy amounts, I guess Elo thought my odds weren’t so great. :man_shrugging:

 

Now, my Defense Team is clearly way weaker than their Attack Teams are likely to be. And we already know a weaker team can beat a stronger one anyway.

So in all likelihood, if each of those players revenged me and I lost all of the trophies, I’d always just end up right back where I started.

Plus I’d lose plenty on defense too. After all, we already know a weaker team can beat a stronger one.

And my Defense Team is handing out :cookie: to pretty much every passerby.

 

So What’s It All Mean?

My feeling is that while this feels unfair when you’re revenging, it’s also what makes the whole system work when you’re the one on the attack side of the equation.

Not being able to reclaim all of your lost trophies from a revenge — and having to get more back by attacking a new opponent — is what makes the system work, I think.

 

Does that make sense?

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Yes you have made it clear. I not a fan of the system but I now have a better understanding. Between you and Gryphonknight things are clearer. I still think there is room for improvement but I’ll leave that to the Devs. I see what you are saying how people would not progress with what I had suggested. Thank you for taking the time and your patience.

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You’re welcome, and glad it’s helped a bit!

I think you’ve identified the core “request” for the devs, too — make the system of revenging feel fairer.

How exactly that could work while still allowing players to progress, I’m not sure. But I think that’s what you’re ultimately after.

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Yes. That is it precisely.

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Where do you want your happy?

If anyone wants, I will happily chat about Elo’s break through system for hours.

But it is not his system it is the MMOs implimentation.

The question is were do you want your happy?

Must fight opponents selected by the algorithm? Rewards are based largely on raid energy spent.

A.I. defense always has the advantage? Rewards are based on building up a good defense team like classic tower defense games, but run by the A.I.

Player attack always has the advantage? This is the system the Devs have currently gone with. Reroll for easier/ harder opponent. Reroll for better food, iron or recruit rewards. Reroll for more trophies gained or less trophies lost.

My personal opinion

I think Revenge does not fit with the core concept of raids in Empires.

However, Revenge is now solidly intertwined with Empires. When Book of Heroes tried to fix the Haste stat, the players revolted and the stat was reverted. Revenge, and other parts of Empires, may be unbalanced or out right broken, but better to change the game balance going forward than to nerf parts of the game players have heavily invested time.

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You’re misreading what I’m saying, I think. Under the modification I’m proposing, the equal-trophies match will yield a 70% win rate for the attacker.

The difference between what I’m proposing and the current system is, under my proposal, your trophies will vary around their current level if you’re winning 70% of your equal-trophies attacking raids. Under the current system, you’ll shoot up if you win 70% of equal-trophies attacking raids. The current system only arrests your trophy rise when you fall to an equivalent 50% win rate in equal-trophies attacks.

You’re matched based on ELO rating, with the target matchup being equal-trophies on average. If it was just a predictor rather than the agent of deciding who to match, you’d be correct. As long as your matches are uniformly drawn around your current rating, and as long as you aren’t getting better or worse than your competition, your win rate will be 50%

The other point is, the whole probability structure moves together. There isn’t one predictor for weak matches and a different one for equal-trophies matches. Winning 90% of attacking raids when you’re 381 trophies higher produces the same result as winning 50% of of attacking raids at equal trophies.

So if you win more than the predicted percentage, you move up the ranks and match with stronger opponents. Your rise only stops when your equivalent equal-trophies win rate falls to 50%. And vice versa if you win less than 50% of equal-trophies attacks.

What you’re calling variance comes from the K factor (gain term) that SG has chosen to use. It controls the magnitude of shift in predicted win probability based on the outcome of a match.

They have chosen a K of 61, which is pretty noisy.

This is inaccurate on two fronts for E&P. First, the attack/defense asymmetry means that if you start out at your “logged out for a while” trophies level, you will be dramatically stronger on attack than your trophy level suggests. You’ll rise quite quickly, because you’re winning way more than 50% of your equal-trophies matches.

Even in a normal ELO environment like chess, what you’re saying is only true for people whose ability has plateaued. The main way you win more than 50% of the time on equal-trophies matches is by improving over your equal rating cohorts. If you get better, you win more than the predicted rate and rise in rating.

This is the way ELO is supposed to work. Significant shifts in rating are supposed to indicate actual ability change, rather than just a change between attacking/defending.

My main complaint is that the attack/defense asymmetry in this game means ELO doesn’t work as designed in E&P. The see-saw pattern we observe of rising very high in rating when on attack, then falling in rating on defense, is a symptom of this problem, not the problem itself.

What I’m proposing to do is to correct the math so that the equal-trophies expected win rate for attackers matches the de facto measured equal-trophies win rate. This is a very normal thing to do. If you look at ELO ratings systems that cope with “home court advantage”, this is exactly how they do it. Our attackers in this game always have a “home court advantage.” Why not adjust the math to account correctly for this?

This is wrong. I’m not changing the K factor at at all. If you look at the math in my previous post, you’ll see I’m actually adjusting the expected win rate for attackers at equal trophies. And this will produce a durable shift in where people settle out.

There are lots of things the devs haven’t tinkered with that could be improved. I’d say, rather, that they consider it to be working well enough not to prioritize changing it. That’s not necessarily the same thing as “satisfied.” Of course, suggesting an easy change like this might make it palatable to actually prioritize making a change.

Then again, it might not. I suspect sales of raid energy to people trying to ride attacker’s advantage to #1 probably accounts for a tidy profit every month. Never kill the goose that lays the golden eggs :slight_smile:

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Reading a defense team

In my opinion, you are forgetting that any user can view a match and reject it.

By making the defense team lower in trophies, effectively stronger, more players will reject the match and simply re roll the match.

Especially with the heavy incidence of tanking in Empires, players quickly learn to decipher enemy teams based on power, stars and special skills, regardless of their supposed trophies.

In my personal opinion, in the end, your proposed modification would cost more food, cause more re rolls and not have the effect you intended.

Re rolling an obvious loss

In my opinion, you are confusing a Elo rating system based on set matching with an Elo rating system based on optional re rolls.

Your rise stops when the number of re rolls becomes more odious than the trophies, and other rewards, gained by continuing to raid.

You are suggesting devaluing the trophies of the defense team so it matches with weaker attackers. This will lead to more attackers viewing the team going “Gorram that Guinevere, I am out of here” and rerolling.

Asymmetry and noise

In Book of Heroes, a live PvP ( shudder ) with set Elo matching ( no re rolls allowed ), there is an interesting asymmetry in several of the the six class match ups.

Example
War Mages destroy 95% of Shadow Walkers but Justicars destroy 95% of War Mages. Since it is live PvP ( shudder ) you must pick one of your heroes ( think teams in Empires ) BEFORE you are matched and you cannot change your hero ( team ) after you are matched. Though you can forfeit the bout. However forfeit come with several penalties like losing a substantial amount of raid energy and all rewards ( both winners and losers get the same rewards but rewards are based on arena ).

While I deliberately re roll raid matches to consume excess food in Empires. Not only is the penalty for rejecting a ratings match inconsequential, it is often desirable to the user. Which does violate one of Elo’s base assumptions.

But that Book of Heroes extreme asymmetry between classes just contributes to rating noise. While a 3000 trophy War Mage will have a higher win record against Shadow Walkers and a lower win rate against Justicars, the War Mage will still destroy most 500 trophy opponents - if they are not new or tanking - regardless of class.

The asymmetry between attack/ defense in Empires just contributes to rating noise.

Example:

What the devs said “equal match up results in a 70% win”, players look for easy matches. So many players who would have lost in a set match up, re roll.

But the A.I. is not allowed a re roll if the attacker is too strong. Even though the attacker is allowed to change all five attacking heroes AFTER the match is made.

Really your Empire rating is a combination of five heroes on your defense team and the 200+ heroes on some people’s hero roster.

What is the REROLL percentage on equal rating match ups? I would love to see a distribution of re rolls based on standard deviations from an equal rating.

Not sure which one is the K factor. Is it the sub equation that decreases as a player progresses in matches and a season progresses?

Because the one that decreases as a player progresses in matches produces a durable shift in where people settle out.

In my opinion, you are duplicating that sub equation.

I will agree with two out of your three statements.

Guess. Which. One. I. disagree. with.

Dead horse

This has been lots of fun ( not being sarcastic ).

But I think we just killed the horse, chopped it up in to sub atomic components and transported it to a parallel dimension.

I will call this a “We definitely agree to definitely disagree”.

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Sold.

Thanks for the thoughtful discussion and analysis! Your example, and your concern about the rerolls, definitely give me some food for thought. I really appreciate it when someone is willing to take an idea, shake it, and kick the tires. I can’t tell you how much I appreciate having you on the forum. IMO you’re an incredible asset to the community.

Just in the interest of clarification:

What I’m calling the K factor is the 61 they multiply the win/loss probability by to produce an update to trophies.

…number 3? What do I win? :smile:

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