If someone is 'off base', it means that person is wrong, or mistaken about something.
This phrase possibly originates with the sport of baseball, where a base runner may position 
himself a short distance away from a base plate, thus he is off base. This can be seen as 
potentially risky move to do, as the player whose foot is off the base plate could be picked off 
by the other team if he's not careful.

This saying goes back to at least the 19th century. For example, the Piqua Miami Helmet newspaper from the year 1880 uses this expression:

    "Yet today he is almost peniless. I saw him last night on his semi-weekly spree. As he said 'the old man 
     was off his base again.' I have seen him bet $50 on 'faro' when so drunk he could not see the cards."

* Tim thought that the milk he was buying had no sugar in it, but he was way off base, because when he checked the nutrition facts label, sugar was listed on there.
O-Letter Sayings  |  Know Your Phrase - Common Idioms and Phrases, Their Meanings and Origins

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Note: The origins for many common expressions are not clear. In cases like this, what may be provided on the page instead is a theory as to how a phrase may have originated. Or, if no theory is mentioned, then I'll at least try to include a quote on the expression's page to give you an idea for a old a phrase is, at minimum. These quotes are typically the oldest known citations of an expression being used in writing, and most of the time they come from newspapers, books, or poems. It's possible that older citations exist and I have overlooked them.
Phrases and Idioms Starting with the Letter - O.
Phrases and Idioms
A base plate from baseball.