While World of Warcraft has since opened up the Mage class to several races, it's far more restricted in WoW Classic. Here's what the best race is for Mage for both Alliance and Horde.
Best Alliance Race for Mage in WoW Classic
In WoW Classic, the only Alliance races that can be a Mage are Humans and Gnomes. Of the two, Gnome is the better pick, considering the Escape Artist racial ability allows you to instantly get out of any sort of immobilization. That's a very strong ability in both PvE and PvP content.
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Humans are always a solid pick due to the Diplomacy racial ability that gives a bonus to reputation gains. However, that's not anything that's going to help in a fight, and that's what gives Gnome the edge here for me.
Best Horde Race for Mage in WoW Classic.
On the Horde side of things, you'll have your pick between Undead and Troll. This is a more difficult choice to make in my opinion, because both Horde races have interesting racial abilities. Troll has the Berserking racial that gives a big damage boost, and that makes it one of the best racials in all of Classic.
Undead have Will of the Forsaken, which gets you out of fears and sleeps, but it's more of a PvP ability than anything. For that reason, I'd pick Troll if I was sticking more with the PvE side of things, but Undead if I wanted to do PvP.
Best Mage Race in WoW Classic Season of Discovery
With Mages having the ability to heal in Season of Discovery, many people might be wondering if that changes anything in terms of best race. It doesn't look like that's the case, so your best race in regular Classic will be your best race in Season of Discovery.
Then again, Season of Discovery does encourage people to try out new things, so maybe you'll be rewarded for going with a weaker option. At the end of the day, your race doesn't matter a ton, and it's mostly personal preference when it comes to Mages.
For more WoW Classic news and guides, take a look at WoW Classic Leveling Guide: How to level up quickly on Pro Game Guides.