Is there a right troop ratio?

Introduction

In my last post I wrote about the rally battle simulator I am building. This is the follow-up: a record of asking an AI about troop ratios (Infantry : Lancers : Marksmen).

For many battles, the simulator's win estimates and losses now roughly match what actually happened. Since chance is involved, it can also tell whether a result sat in the middle of the expected spread or out at the edge. Beyond results, it can now suggest how to improve, for example by adjusting the troop ratio.

This time I am sharing part of what I asked this battle consultant AI, mostly about troop ratios. Keep in mind that it is an AI: it can hallucinate, and the simulator itself may have errors that the answers inherit. The real game mechanics have not been published, so that cannot be helped. Please read this in a "believe it or not" spirit.

Rally ratios have standard setups. Attacks use 5:2:3, and recent defenses in my generation use 6:4:0. Few people can explain why. So I kept the troop count, stat bonuses and heroes of a real battle exactly as they were, changed only the ratio, and had the simulator fight it out hundreds of times.

Below, Q is me and A is the AI. The AI's answers have been lightly edited for readability.

The battle used for the tables

The tables in Q2 to Q8 all come from one real battle. Total troops, stat bonuses (the displayed buffs) and heroes were kept as they were in the real battle. Only the ratio was changed.

• All hero skills are at level 5.
• When a ratio adds a troop type the side did not have, it is calculated with the tier, Fire Crystal level and stats of that side's largest troop type.
• Each win rate is the share of wins over 40 to 60 simulated battles per pairing. Expect about ±8 points of noise.

Why this battle

• It was close enough for the ratio to matter: differences between ratios only show up in battles where either side could win. In a lopsided battle every ratio gives the same winner, so there is nothing to compare. In this one the simulator gave the defense about a 70% chance, and in reality the attacker won. It was razor-thin.
• It uses today's standard lineups: Hector, Norah and Lynn with Patrick and Gwen on defense; Jeronimo, Mia and Gwen with Jessie on attack. These are combinations you see all the time.
• The data is complete: troop counts, stats and losses for every player were copied from the report, so the simulation has no missing inputs.

It started when I asked the AI to review this battle, and the ratio question grew out of that. To check that the findings are not specific to this one battle, the same tables were built for the six other battles I have (see Q3 and Q4).

This is not an equal matchup in troops, stats or heroes. The defense has fewer troops but higher stats, and with the real ratios the defense is slightly favored (about a 70% chance to win). The win rates in the tables apply to this battle only, so look at how they rise and fall when the ratio changes rather than at the numbers themselves.

Q1Is there a "correct" troop ratio?

A.There was no single answer that works against every opponent.

For both sides of the seven battles I have, I kept troops, stats and heroes fixed and tried every ratio in 10% steps (66 in total). The best ratio was different in each battle, and what decided it was the opponent's composition. Roughly speaking, the best move is to add more of whatever beats the opponent's largest troop type, and cut what loses to them.

Q2But attack and defense seemed to want different ratios. Why?

A.It is not about attacking or defending. The opponents had different compositions. Damage is calculated with the same formula for both sides.

To check, I took the battle above, changed only the attacker's ratio, and searched again for the defense's best ratio.

Against an opponent with only infantry and lancers, even the defense does best with lots of marksmen. The third result, though, cannot be explained by the simple triangle of counters alone (marksmen beat infantry, lancers beat marksmen, infantry beat lancers). By that rule, the answer to a lancer-heavy opponent should be more infantry.

Besides the counter triangle, I think two more things are at work (this is a guess).

• Formation order: attacks hit the front-row infantry first and move to the next row only after the infantry is wiped out. How much of which type stands in front changes when the troops behind start taking hits.
• How firepower grows with troop count: a troop type's firepower does not grow in proportion to its count. Four times the troops gives twice the firepower. The more you pile into one type, the less each extra troop adds, so spreading troops out raises total firepower.

Q3When you meet an opponent for the first time and don't know their composition, is it just luck?

A.Not necessarily. Once you build a table of both sides' ratios, you can choose a ratio by asking how well it does in the worst case.

Here is the defense's chance to win for each pairing of ratios, using the battle above. Everything except the ratio is as in the real battle, so these are not general numbers. Rows are the defense's ratio and columns are the attacker's. The "Worst" column is the lowest value in each row: the win rate when the opponent picks the ratio that hurts you most.

Look at the "Worst" column. Lopsided ratios such as 6:4:0 or 4:0:6 are strong against certain opponents but collapse when countered. The balanced 5:2:3 and 4:2:4 never drop below 85%, whatever the opponent brings.

Between 5:2:3 and 4:2:4, which one is ahead changes from column to column. The gap is a few points, within the noise from the number of battles (about ±8 points). Neither is clearly better.

Because the defense has higher stats in this battle, its win rates are high across the board.

I built the same table for all seven battles. In four of the five battles where the ratio could change the winner, the defense's best worst case came from 5:2:3 or 4:2:4. The exception was a battle where the defense was badly outmatched to begin with.

Q4So the standard 6:4:0 defense is risky if it gets read?

A.In the simulation, yes. In all five battles where the ratio could change the winner, the attack ratio that hurt a 6:4:0 defense most was a marksman-heavy one (4:0:6 in four battles, 3:1:6 in one).

The standard 5:2:3 attack, on the other hand, turned out to be a sensible shape that holds up when you don't know what you'll face.

Q5Then is it worth guessing the defense will be 6:4:0 and opening with 4:0:6?

A.Yes, if you are fairly confident in the read. But a wrong guess costs a lot. Here is the battle above, seen from the attacker's side.

The attacker's chance to win, in the battle above with everything but the ratio unchanged. The attacker has lower stats here, so its win rates come out low.

By this table, 4:0:6 pays off if you think there is more than a 20% chance the defense is set up like 6:4:0. But after the first battle report, the defense knows your composition too. It is not a trick you can use repeatedly.

Q6If the defense gets hit by 4:0:6, how will it adjust?

A.In the simulation, keeping the infantry and adding 20 to 30% marksmen worked better than adding lancers.

Once the defense moves back to 5:2:3, the attacker's best answer is also back to 5:2:3. If both sides keep reading each other, they settle around 5:2:3. 4:0:6 is a surprise move that only works while the opponent sticks with 6:4:0.

Q7Why do all these ratios use relatively few lancers?

A.Lancers tend to end up in an awkward spot: too fragile to hold the front, and not hard-hitting enough to shoot from the back.

• In base stats, infantry has high Health and low Attack, marksmen have high Attack and low Health, and lancers sit in between. As damage dealers, lancers do not reach marksmen.
• While infantry holds the front row, the lancers in the middle take almost no hits, so their extra Health rarely matters.
• For most of a battle, both sides are shooting at the other's front-row infantry. When hitting infantry, only marksmen get the counter bonus (+10%). The lancers' favorite target, marksmen, stands in the back row and is hard to reach.

They still don't drop to zero, for these reasons.

• The lancers' Ambush can hit the back-row marksmen directly.
• Once the infantry falls, lancers become the next wall.
• Piling too much into one type slows the growth of firepower (each type's firepower grows with the square root of its troop count).

Q8In Generations 1 to 3, both attack and defense mostly used 5:2:3. In Generation 5, defense moved to 6:4:0. Is that because of the heroes?

A.Partly, I think. But what matters is not hero skills or Exclusive Gear. It is the generation gap in the heroes' base stats. Even that does not explain everything. It is a factor that nudges the standard toward 6:4:0, not the decisive one.

Here is what I checked, in order.

Hero skills: swapping the defense's rally heroes for Generation 2, 3 and 5 lineups barely moved the best ratio. Skill differences do not explain it.

Exclusive Gear: Exclusive Gear multiplies one displayed stat (Attack, Defense, Health or Lethality) by 1.15. It applies to all troop types, so it gives no reason to favor one type.

Hero base stats: this was the strong candidate. A hero's base expedition stats (Attack % and Defense %) apply only to that hero's own troop type, and they get higher with each generation.

Here are the usual Generation 5 rally heroes, by troop type.

Gwen, the Generation 5 marksman, is an attack-type hero. The marksman hero available for defense is Lynn from the previous generation. That leaves the defense's marksmen alone lagging behind, which pushes toward fewer marksmen. On attack it is the other way around: the newest marksman hero, Gwen, leads them.

In the battle above (with the attack fixed at 5:1:4), adding this gap (74) back to the defense's marksman stats step by step made 6:4:0 drop in the ranking.

The direction fits. But the shift is gradual, and the win rates differ by only a few points.

Some things remain unexplained. In Generation 4, the newest defense heroes were infantry (Ahmose) and marksmen (Lynn), so by this reasoning the push should go the opposite way from 6:4:0.

Q9So what should I actually do?

A.From the simulation, here are rules of thumb.

• When you can't read the opponent's composition, use a balanced ratio (around 5:2:3).
• Only lean toward a counter when you know their composition. Don't change much at once; move 10 to 20% at a time.
• On defense, keep 20 to 30% marksmen. It makes a marksman-heavy surprise attack much less effective.
• After a change, check the result in your battle reports.

Q10How far can these results be trusted?

A.Honestly, how ratios play out is a part of the simulator that has not yet been confirmed with real battles.

• The battles I have all use similar ratios, so there is no real data where only the ratio changed a lot.
• The more extreme the ratio, such as zero lancers, the less reliable the numbers.
• Different heroes, buffs and troop counts will give different numbers. The tables above are one example from one battle.

Please read this as "here is what you get when you solve the mind game in a simulation."

Closing

The standard ratios do seem to have reasons behind them. The 5:2:3 attack holds up well, and the 6:4:0 defense may have its roots in hero generations. At the same time, 6:4:0 is vulnerable once it gets read.

To confirm any of this, I need real battle reports from fights with different ratios. If you have tried something like that, please let me know.

More soon, with numbers.