When my son told me that the adjusting band had broken off his beaten-up black Dave & Buster’s baseball hat, I have to admit I was secretly glad. To say the hat had seen better days was a severe understatement.

First, it had first lost the metal button on top. Then, over years of exposure to sun and rain, it faded, growing more and more distressed. Nine months out of the year, he wore the hat nearly every time we stepped outside, a habit encouraged by me in order to protect his fair skin. In winter, I managed to convince him to wear a winter hat, instead, one that covered his ears.

Because of his larger-than-average head, we’d bought him a one-size-fits-all hat, adjusting it for the smallest setting. As a result, its large brim cast a shadow over his face, ruining many outdoor photos.

While I didn’t mind its distressed appearance, lately the hat had begun to go downhill severely, first with a loose thread on the brim, which I clipped. Another thread followed, and soon the entire brim was frayed, with the black plastic of the brim protruding slightly through the cloth that covered it.

But still, the hat was my son’s favorite, and so I kept hand washing it in the sink, clipping off the fringe, and attempting to make it somewhat presentable. Of course, since it was one-size-fits all, little hope existed of him outgrowing it, and I was increasingly more embarrassed sending him out in it. Yet, he loved the hat so much that I had trouble hardening myself and making a huge decision, like refusing to let him wear it.

So when the little voice called from the back seat to say that “something important fell off my hat,” I had to stifle a little cheer. I took a look at it and proclaimed it unwearable but headed off tears by reminding him he had several other hats to choose from (hats I’d bought in the mistaken belief I could entice him into wearing them).

This morning, on his way to school, he consented to wear one: a bright orange and green cap featuring a surfer with the word “California” on the back. At first, he seemed OK with it. After all, the cap contained one of his favorite colors, green. But then, as I’d feared, he dissolved into tears.

I got down at his level and asked him what was wrong. He told me, “I don’t feel like myself without my hat.” I kissed his tears away and reminded him he wears different clothes every day, and he’s still the same person.

By the time we got to the bus stop, he was smiling again, receiving a compliment from his bus friend on the cap.

But between you and me, I’ve covered my bets. Just in case, I’ve ordered a black baseball cap from eBay.