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Fire Emblem Heroes Wiki
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pages
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=== Color Distribution === Different colors of orb appear at different rates because there are unequal numbers of units in each color. Different [[Summoning Focus List|Summoning Focuses]] will also have different unit representation. For example, if a Summoning Focus has no colorless 5-Star Focus units, the chance of summoning a 5-Star colorless character will be reduced because the 3% Focus chance will not produce any colorless orbs. In the [[Brave Heroes (Focus)|Brave Heroes]] summoning focus, the 5-Star Focus rarity did not skew the orb distribution because there was one Focus unit of each color. The chance of an orb being a certain color under this focus was as follows: {| class="wikitable" |+Brave Heroes Color Distribution |'''Red''' |'''Green''' |'''Blue''' |'''Colorless''' |- |30.10% |18.99% |25.12% |25.78% |} Note that Green orbs appear less frequently because there are fewer Green heroes and Red orbs appear more frequently because there are more Red heroes as of August 31, 2017. A common misconception is that the chance of summoning a 5-Star Focus unit '''from a given color of orb''' is the same as the base Focus rate of 3%. The 3% is true when summoning randomly, disregarding orb colors. However, because the game gives the player extra information in the form of the orb's color, players summoning exclusively one color will find five stars at different rates. Using the above [[Brave Heroes (Focus)|Brave Heroes]] summoning focus as an example and given a 5-Star Focus rate of 3%, 5-Star rate of 3%, 4-Star rate of 58%, 3-Star rate of 36%, and no increased appearance rate, the chance of summoning a 5-Star Focus unit '''given that their orb color appeared''' is as follows: {| class="wikitable" |+Chance to Pull a Brave Hero from Each Hero's Respective Color |'''Roy''' |'''Ike''' |'''Lucina''' |'''Lyn''' |- |2.49% |3.95% |2.99% |2.91% |} A sample calculation detailing the 3.95% chance for a green orb to contain {{Ht|Ike: Brave Mercenary}} can be found below. As of the Brave Heroes focus on August 31, 2017, the unit distribution breaks down as such: {| class="wikitable default" style="text-align:right" !style="width:100px|Rarity !style="width:75px|Red !style="width:75px"|Blue !style="width:75px"|Green !style="width:75px"|Colorless !style="width:60px"|Sum |- |style="text-align:left"|{{Rarity|5}} Focus |1 unit||1 unit||1 unit||1 unit||'''4 units''' |- |style="text-align:left"|{{Rarity|5}} |28 units||20 units||14 units||18 units||'''80 units''' |- |style="text-align:left"|{{Rarity|4}} |28 units||24 units||18 units||24 units||'''94 units''' |- |style="text-align:left"|{{Rarity|3}} |15 units||12 units||9 units||13 units||'''49 units''' |- |} See [[Summonable Heroes]] for tables on which units are currently available in the pool (adjust for newly added heroes who do not appear on the chosen summoning focus, such as heroes not yet added to the {{Rarity|5}} pool). Using P(''event'') to mean the probability of that event happening, it follows that: *P(''5-Star Focus that is green'') = 3% * 1/4 = 0.75%<br> *P(''5-Star that is green'') = 3% * 14/80 = 0.525%<br> *P(''4-Star that is green'') = 58% * 18/94 ≈ 11.1%<br> *P(''3-Star that is green'') = 36% * 9/49 ≈ 6.6% Given that the orb is already green because the player is chasing Ike: Brave Mercenary, *{{Hover|P(''Specific Focus Unit'' {{!}} ''Orb is green'')|Chance of summoning a specific focus unit given that the orb being summoned from is green}} ≈ 0.75% / (0.75%+0.525%+11.1..%+6.6..%) ≈ 3.95% Similar calculations can be done for the other Focus units.
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