Attack Miss Rate Experiment featuring Air Elemental and Time Mage
This week's Share Your Battle featured monster motivated me to write a different kind of battle post. Rather than using the card to win in Ranked matches, it will participate in an experiment to gather data.
Time Mage: Inspiring the Evasion Experiment
The lovely Time Mage is a new Life Splinter Chaos Legion card that sports an anime magical girl outfit and vibe. It has a decent magic attack that peaks at two in the Silver leagues and three at Diamonds and up. But it's her Slow ability that I find most attractive. It's the only Life monster with the skill in the Silver leagues. Divine Healer and Cave Slug have Slow too, but it's unlockable only beyond Silver.
So if you want Slow while playing a White team on Bronze or Silver, you only got Time Mage and Creeping Ooze as options. Swiftness is another ability that affects speed, but Life Splinter neither has that on Silvers. Neutral monsters Supply Runner and Speed Miner can be used instead. However, those haste-type neutrals won't be featured in this post to highlight speed debuffs brought about by Slow.
Read on to discover how significant the Speed stat's impact is on hit-and-miss probabilities. We know the calculation for hit chances, but let's dig deeper to see if the estimates hold true in actual battles.
What's the Miss Rate Calculation?
First, let's review the attack miss rate calculation. Or if you haven't known this before, then let it be an important introduction to dodge probabilities.
Miss Rate = Speed Stat Difference x 10%
If a Ranged monster with a 2-point speed stat is attacking a monster with a 5-point speed attack, then the miss rate is 30%. There will be a random roll to determine if the attack makes it to the hit threshold or not. Note that these only impact Ranged and Melee attacks; Magic never misses unless the defending card has Phase.
There are a few skills that supplement evasion rates. We currently have three:
|Dodge||Applies extra 25% miss chances|
|Flying||Applies extra 25% miss chances unless the attacker has Flying or Snare.|
|Blind||Applies extra 15% miss chances.|
If a monster has all three skills, either inherent or granted as an effect by a different card, that's a total 65% miss rate. It's said that it's possible to never get hit by physical attacks through perfect evasion. If there's a four-speed difference at the least with those skills active, then miss rate would go over 100% (65% + 40%). I've never seen 100% evasion ever, but that can be an exciting goal to target... hmmm...
Explaining the Miss Rate Experiment
The hypothesis: Calculated miss rates are close to rates in actual battles.
I would be doing several matches to measure the impact of the speed stat on evasion. For each battle, the attackers and defenders would remain consistent. Only the attacking team's speed would change.
I'll also be prolonging the match for as long as possible to gather a bigger sample size. Ideally, the opposing team would attack the same monster around 80 times in one battle. I would then count the misses and verify if it's close to the expected miss chance. I know it won't be totally accurate since battle probabilities in Splinterlands are True Random. But I'm expecting actual data won't be too far off.
The Experiment Subjects
The core participant in the experiment is the epic Life monster, Air Elemental. It has a high-speed stat at six points, even if only at level 1. But I'm using it at level 3 with its Dodge skill unlocked.
I chose Air Elemental as the primary defender since I needed a top-speed monster to dodge attacks. Monsters slower than the attacker don't evade. It's also much more relevant as a subject since it's the monster that I often use in actual battles to keep my backline safe from Sneak attacks. I know that it's nimble enough to dodge tons of times, but I just got to see the numbers.
These are the three Sneak monsters who would assault Air Elemental. I got them in different levels to have all their speed stats equivalent to four. We need the speed to be constant across all three, so we'll have an easier time calculating miss rates. It's nice that Silvershield Assassin attacks twice so we could have a larger sample.
I will be selectively introducing these cards to manipulate the opposing team's speed stat. There will be a battle where I'll have all three of them and another without any of the Slow cards present.
I want to extend the fight beyond Round 20. The more attack attempts we get, the more reliable our data would likely be. Thus, I prepared all these monsters to keep the battle at an impasse for a long while. There will be unavoidable damage, but there will be monsters who will restore health and armor. A Shield and Void card, Lord Arianthus, would be the enemy team's tank to keep them from sustaining fatal hits and ending the fight early.
The Simulated Battles
It took me over two hours to get the battles that I needed. Several rulesets were incompatible with the experiment, such as Aim True, which removes dodge chances; and Fog Of War, which disables my sneakers. Those and many other conflicting rulesets made my battle attempts go over 50, but only four were usable. 😣
Here are the four battles that I painstakingly waited for. Note that each match had a variable speed stat. I counted all the hits and misses to compare them later on with calculated evasion rates.
Battle #1: No Slow Skills
This is the base battle where I got no Slow skills on the field. All Sneakers are at four-point speed, attacking Air Elemental with six-speed and Dodge.
Notice that I had an armor Repairer and a tank Healer on both teams to force a deadlock. I would have placed Spirit Hoarder on Air Elemental's side for the Triage backline healing, but the ruleset doesn't allow legendaries.
However, since Equalizer raised everyone's health to 12. My Air Elemental evaded just enough to keep it alive until Round 24. The battle recorded 96 attacks attempted on our dodger, with 47 of them missed. The evasion rate is 48.96%. Almost one in two? Not bad.
Battle #2: One Slow Skill
I've included Creeping Ooze to debuff the enemy team's speed by a point. The attackers and defenders remain the same as in the previous battle. However, since the Healed Out ruleset negates heals, I would have to rely on armor repairs to keep the match running long enough.
It proved difficult to sustain the battle beyond the 20th round without healing. The defender lasted until Round 16. There were a total of 64 attacks rendered, and Air Elemental evaded it 29 times. The miss rate is at 45.31%. Oddly, it's a bit lower than the battle with no debuffs. That's random for you.
Battle #3: Two Slow Skills
We're now featuring speed debuffs twofold in this battle: one from Ooze and another from the summoner, Quix. The absence of armor due to the Unprotected ruleset was initially troubling. But Air Elemental had a higher dodge rate this time. With Spirit Hoarder's Triage, we reached the fatigue stages at Round 21.
The battle had 84 sneak strikes, but 56 of them were unsuccessful, bringing the evasion rate to 66.67%. That's two-thirds of the total attacks. Nice~
Battle #4: Three Slow Skills
This final battle had the full Slow arsenal with Quix, Ooze, and a level 4 Time Mage. The Sneakers' original four-point speed has been reduced to one. Isn't it cool that abilities like Slow stack?
The battle lasted beyond Round 21. Expectedly, Air Elemental had a higher evasion rate for this round. It dodged 60 times out of 84 attacks, causing an amazing 71.43% miss rate for the enemy team. 🙌
Expected Miss Rates Versus Actual
Let's see if the calculated miss rates match what we got in our battle simulations. As a reminder, we're not anticipating that it would be equal. Being somewhere close is more than sufficient. Perhaps, if we gathered data from multiple battles with a total of 100,000 attacks, the results would likely be more accurate.
Miss Rate = (Air Elemental's Speed - Sneakers' Speed) * 10% + Dodge Skil Evasion
Miss Rate = (6 - 4) * 10% + 25%
Miss Rate = 45%
|Battle Condition||Expected||In Actual|
The values are very close. Only the data from the second battle has a wide 10%+ gap. Splinterlands games are random, so that may happen if luck isn't on your side. Coincidentally, that's the match with the smallest sample size at 64. The rest had an attack total of 84 or above.
The evasion mechanic for non-magic attacks works as advertised.
So it would be valuable to know the miss rate calculation. Think that a four-point speed difference with an added Flying or Dodge abilities would result in a 75% evasion rate. That's pretty high at three misses out of four attacks.
Now, was the experiment to verify this really necessary? Not at all 😂 I realized I somehow wasted several hours for a theory that doesn't need proving. But at the time, I wanted to satisfy a curiosity, so there's that.
As a welcome benefit, I got to see a lot of action from one of my favorite cards, Air Elemental. I watched as it dodged attacks from a monster as intimidating as Silvershield Assassin. Air Elemental saved me from losses countless times. And it will continue to do so with the aid of a new important teammate in Time Mage.
Lmao, I ended up with a blog that was mostly about Air Elemental than Time Mage.
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