I think you overestimate the importance of ninjas to the people who command navies.

The warlord Oda Nobunaga's notorious reputation led to several attempts on his life. In 1571, a Kōga ninja and sharpshooter by the name of Sugitani Zenjubō was hired to assassinate Nobunaga. Using two arquebuses, he fired two consecutive shots at Nobunaga, but was unable to inflict mortal injury through Nobunaga's armor.[51] Sugitani managed to escape, but was caught four years later and put to death by torture.[51] In 1573, Manabe Rokurō, a vassal of daimyo Hatano Hideharu, attempted to infiltrate Azuchi Castle and assassinate a sleeping Nobunaga. However, this also ended in failure, and Manabe was forced to commit suicide, after which his body was openly displayed in public.[51] According to a document, the Iranki, when Nobunaga was inspecting Iga province — which his army had devastated — a group of three ninja shot at him with large-caliber firearms. The shots flew wide of Nobunaga, however, and instead killed seven of his surrounding companions.[52]

The reference class of "most people" is a better starting point than maximum entropy. Particularly in light of the fact that significant visible differences of behavior would work against the whole secrecy thing.