I've been playing a lot of Fire Emblem Heroes since its release. For a mobile game, it's quite fun. But the simplistic maps' designs are starting to become repetitive and unchallenging, so the bulk of the lasting entertainment the game provides is in the realm of character acquisition.
I've had some great summons, with favorites like Camilla, Setsuna, Arthur, Niles, and some other characters that didn't appear in Fates.
But I've made it clear to all my readers that Hector is my personal endgame for Heroes.
Even though I haven't spent any money on orbs, I've gotten almost all of the in-game orbs that have been made available thus far. I've been smart with them, summoning heroes in batches to maximize efficiency. But still no Hector.
Am I just unlucky?
Kotaku ran an interesting story where someone spent $1,000 on orbs and still didn't get Hector. What about this dude? Was he just unlucky? I figured I'd do some simple math to find out.
Hector is only available as a 5-star hero. This was done for obvious reasons. Hector is the best character in the franchise, so why would he possibly exist in a form where he could be objectively inferior to others? The problem is, there's only a 3% chance of summoning a non-focus 5-star hero (Hector hasn't been part of a focus yet). The problem is, there's 38 potential 5-star pulls.
So we divide 3% by 38. That's a whopping 0.079%. So what?
If we divide 100 by 0.079%, we can get the average number of summons needed to get Hector one time. Pull out your calculators, and let's see what we get.
1,265 and some change. Since summons are whole numbers, we'll round up to 1,266.
To take it one step further, let's assume that you're summoning in batches of 5, with an average cost per summon of 4 orbs. So multiply 1,266 by 4, and you realize it will take an average of 5,064 orbs to summon 1 Hector.
The best value for buying orbs is 140 orbs for $75. If you buy orbs in batches of 140, you'll need to buy 36 batches to get you up to 5,040 orbs, and then buy a set of 35 orbs for $20. That makes the total cost
Two thousand seven hundred and twenty dollars. ($2,720)
So that guy that spent $1,000? He barely spent a third of what the average player will "spend" to get Hector. So he's not particularly unlucky, either.
So a few disclaimers. First, the game does have a mechanic where your probability of summoning a 5-star increases for every session that you don't get a 5-star. This increase in probability resets after the session where a 5-star is summoned. Truthfully, this mechanic would only marginally increase the odds of pulling Hector through that stone, and would make for messy math, so I didn't figure that into my high-school level calculations.
Secondly, we are dealing with probability. Obviously, you don't have to summon 1,266 times to get Hector. This is the average number of summons it will take to get him. So, if a million different users summoned a million times each, the mean number of times it would take for a summoner to get their first Hector would almost certainly be 1,266. There would be a less likely chance of summoning him the further number of tries one gets on either side of 1,266, but one would expect these anomalies to still indeed occur. If this is confusing to you, go read up on normal curves.
As a shiny Pokemon hunter, I deal with these kinds of basic probabilities all of the time, and I like thinking in these terms. But at the same time, this has really taken the wind out of my sails when it comes to playing Heroes. There's a limited amount of orbs you can get in-game without spending money, and I'm not planning on spending any money on this game.
So what? The recent "Choose your Heroes" event showed us that Hector is the third most popular dude in Fire Emblem, and he's numero uno for characters that haven't appeared in at least two Smash Bros games. So I think it's a pretty safe bet that we'll see him as a Hero Focus at some point in the future. So I don't know about you, but I'm saving my orbs for that day.
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