Raven, one of DC Comics’ Teen Titans, the statuesque daughter of a demon, killed her father in order to purge herself of evil. My own 5-foot-8 teenager, Kate, showed me this vintage issue in mid-December. Raven’s dad was red-hued with horns and fangs, but he went down hard after she blasted him with white light.

Kate’s point was that as badly as she had hurt me the previous week, it could have been worse.

It happened when I was sitting down to watch TV. All 120 pounds of her leapt into my lap, causing me four days of back spasms. When I recovered, she slam-bumped me as we walked arm-in-arm to the school bus, again realigning my spine.

I admit, I started it. My father loved to wrestle with me and my brother as kids in Westchester in the 1960s. I didn’t mean to pass on the tradition. It evolved gradually from the days when I twirled Baby Kate through the air. As she aged, acrobatics advanced into hand-to-hand combat. Getting me in a headlock was her way of dragging me from my den and forcing me to notice her. To let off steam, we wrestled.

For my wife, who grew up with a younger sister and two immigrant Irish parents, there was no brawling among kids, no lamps crashing in her Bronx living room. This was the way I bonded with Kate. Yes, we talked. I manned the sideline flag for her soccer games, and packed her ravioli lunches. But our tussles cut through our age discrepancy and gender gap. And if we didn’t spar I feared that we wouldn’t be as close.

Recently I explained to her that clipping me in my soft belly by surprise was not O.K. Wrestling was one thing; a sudden jab at dinner was another. I knew that in order to develop a discrete identity, girls had to metaphorically kill off their dads. So, we boxed once in a while when she needed to cut loose. Since turning 13 last June, she sometimes flew at me with fists flailing. I didn’t know whether this was therapeutic or aberrant. Kate’s adolescence arrived with my 60th year, and the girl had a mean left jab.

“Kate,” I interrupted her one evening as she sat in the kitchen, texting rapidly with her thumbs. “What if we didn’t fight anymore? I keep getting injured.”

Her eyes glinted hurt. “No way!”

We were entering a phase of Kate’s development when dads and daughters often phased out horseplay. But a musician friend had confided to me that, 40 years back, when she got her period at 12, everything changed with her dad — no scraps, touchdown passes, chases or hugs — and she’d grieved it. Kate was sprouting curves but was still largely the same tomboy. As long as I avoided punching her in the chest, I didn’t see any reason to treat her differently. Other than quelling my back spasms.

I was never the parent who made Kate feel safe by handling every little detail. That was her mom, a psychotherapist. She researched summer camps and chauffeured visits to Lululemon. My parenting style mirrored what I do in my work as a kids’ musician: show up, burn brightly, then high-tail out. Yet hobbling through a Wednesday work day, my torso skewing to the right, I wondered if our roughhousing was my way of clinging to youth, a denial of aging. I hated meeting other parents who were young enough to be my offspring.

I told my wife that Kate seemed wounded when I suggested that we stop brawling.

“Kate finds it hard to get your attention,” she said sharply. “We both do.”

I looked at my shoes, chastened by her tone.

“Maybe,” she said, softening into a professional timbre, “you could find some middle ground.”

I didn’t know what that might look like. Graceful aging didn’t run in my family. The last year of my father’s life, when he was 62 and I was 27, we’d set out on bicycles from Rye, N.Y., to the ferry to Martha’s Vineyard, a trip of more than 200 miles. Dad bailed in New Haven. Three months later he died on his town’s indoor tennis courts. I needed to create my own legacy and take a new tack with Kate.

On a family vacation to Puerto Rico in December, I changed my approach. The first day I played a swimming-pool dunking game with my daughter and her cousin, Max, also 13. I negotiated a reprieve after each douse. When Kate cannonballed onto my shoulders from the side of the pool, I begged out. To the kids, I was being stubborn. I was proud of my happy compromise between belly whop and rocking chair.

The next day, Max tried to swipe the hat off my head as I accelerated up a sand bank. I collapsed in a heap with a pulled calf muscle. A barrel-chested tourist from Minnesota helped me to my chair, as I explained that my legs no longer react fluidly to stress.

By the time my muscle healed, it was mid-January. Kate reminded me of the annual foot race we’d run since she was 5. She wanted a rematch. At 10, she’d already been at my heels. Back then, I’d staked out a distance that was far enough for my 35-inch-inseam legs to overcome her quick start, and close enough that I wouldn’t get winded. Last year, at 12, Kate had tied me. I felt her coming, and maneuvered in front to avoid defeat. Now her legs were longer.

We walked to the park, reviewed the course and lined up even with an elm tree.

“On your mark, get set, go,” I cried. She shot ahead of me, and though I churned for all I was worth, I never got close.

“I hate losing!” I howled, staggering crookedly toward her, pain shooting from my side. Kate put her arm around my shoulder.

“Oh Dad,” she said, “you’re much more lovable when you’re pathetic.”

Just the same, I’m looking for noncompetitive activities we can share. I’m hoping we can see the new “Teen Titans” movie that came out this month and leave the fighting to Raven and her dad.