These are always fun to read about, although hellish to live through.
You can’t really quantify insanity, but these were some loonies, to be sure. Were they crazier than Vlad Tepes, Olga of Kiev, The Zhengde Emperor, Qin Shi Huang, Erik the allegedly 14th, etc? I don’t know how to measure that.
As usual in lists like these, there are failures in fact-checking.
Here are two examples that I know off the top of my head (suggesting that there are many others that would be noticed by professional historians, or with some research):
Caligula’s famous horse was named Incitatus, not Invictus
“Little Boots” threatened to make the horse a senator or consul, but never followed through, perhaps because death intervened (per Cassius Dio), or perhaps because he was just taunting the senators and never intended to do it. Caligula did pamper the horse outrageously. Historian Aloys Winterling, author of “Caligula: A Biography,” argues that insanity isn’t the only logical explanation for such behavior. Winterling suggests that many of the emperor’s more outrageous shenanigans, including his treatment of Incitatus, may have been designed to humiliate the senators and other aristocrats. By threatening to bestow a high public office on his horse, Caligula aimed to show the elites that their work was so meaningless an animal could do it.

Waiting for Trump to appoint a horse as Fed Chair.
Does appointing a horse’s ass as FBI Director count?
He already appointed the jackass that’s there.
No love for Heliogabalus?
All those other Roman Emperor’s were posers.
Not one of them has an album by John Zorn dedicated to them.
We might know something about him, since Cassius Dio wrote his histories during the life of Heliogabalus.
In contrast, everything we think we know about Caligula was written at least two generations later, and it could be filled with exaggeration and embellishment. Tacitus and Suetonius were born after Caligula died. When they were writing, they could have encountered elderly people who remembered Caligula’s reign, but those memories have questionable value as historical evidence.
So maybe ol’ Helio was even nuttier than Caligula or Commodus.
But …
From what I’ve read, many modern scholars have grave doubts about Dio’s ability to view Heliogabalus objectively.
Ludwig II of Bavaria, The Fairy Tale King, though some now argue that diagnosis