Why you should have little pockets of savings

Does a broken mail box count as an emergency? I mean, not being able to get my mail seems like a pretty big deal to me.
This last week has been filled with little things, and the reason we have not just an emergency fund, but a small amount of savings set aside for the little things that come up.
First, the Xbox 360 broke. It is $20 less to repair than to buy a “new” one. Considering we have the oldest generation, we decided to upgrade for the slightly larger cost. So, a couple hundred dropped there.
Then, the hubby’s keyboard had a letter stop working. Replacing it costs only $10 and doesn’t really mess with the budget one way or the other, but there it is.
And, as I mentioned at the start, our mailbox broke. The piece of metal that allowed you to easily open it broke off, making it sharp, difficult, and slightly dangerous to open. I’ve been leaving the door slightly ajar after getting the mail to make it easier for our mail delivery person. That means that we also needed a new mailbox- and given the amount of mail theft that’s been going on in our neighborhood lately, we got a more expensive locking mailbox for around $45.
I guess things really do come in threes.