When Kathryn Kerns asked 30 teens and preteens to come to her laboratory and talk about their parents, many of their dads scored low on a standard yardstick her research team was using to evaluate the parent-child bond.

The children described rich, warm relationships with their fathers, however, says Dr. Kerns, a professor of psychological sciences at Kent State University in Ohio. They said things like, “My dad gives me encouragement to do things,” or, “My dad tells me he thinks I can do well.”

To get an accurate assessment of fathers’ contribution, Dr. Kerns revised two assessments in her recently published study, adding questions about whether parents provided encouragement and instilled confidence, and the dads started drawing higher scores.

Illustration: Linzie Hunter for The Wall Street Journal

Dr. Kerns is one of a growing number of researchers creating new tests and techniques to document the father factor. More than a dozen studies in the past two years are yielding new insights into the nuances, and the value, of the seemingly random, sometimes silly play many dads engage in with their children.

The research could offer dads more leeway in their play with children, suggesting there’s no need for moms or others to worry when fathers stir up or challenge their children—as long as the kids are happy and having fun. Also, dads sometimes can stop a child’s fussing or crying through joking or physical play.

The ability to form close, trusting bonds with parents early in life predicts the quality of a child’s future friendships, social skills and romantic relationships. Parents serve as a secure base for exploration and risk-taking and provide a safe haven for a child in times of distress. Yet many of the standard assessments scientists have used to analyze the parent-child bond underemphasize the importance of exploration and risk-taking and fail to capture dads’ role in encouraging it.

Illustration: Linzie Hunter for The Wall Street Journal

The new research is sparking some freewheeling antics. In one study, when a preschooler grew tired and started crying, his father flipped the child upside-down into a midair headstand. Another dad sparked his toddler’s interest in playing by yelling in mock distress, “Ow, that smarts!” when the child used a toy doctor’s kit to give him an imaginary shot in the arm.

Both men and women have a hormonal response to becoming parents, marked partly by increases in oxytocin, a neuropeptide that fosters bonding and trust. Oxytocin is linked with different responses in new fathers’ brains than in mothers’, research shows. In women, it is associated with activation of brain regions based in the amygdala and expressing emotions. In men, it is linked with increased activity in regions of the cortex associated with planning and mentalizing, or understanding others’ viewpoints.

New parents also exhibit differences in bonding behavior. In a study of 100 mothers and fathers interacting individually with their five-month-old infants, mothers tended to gaze into their babies’ eyes, mimic their babbling and touch them affectionately, according to a 2013 study in Attachment & Human Development. Fathers were more likely to arouse the babies, using quick motions to get them to laugh or encourage them to explore.

Illustration: Linzie Hunter for The Wall Street Journal

Of course, both genders can engage in both types of interaction. The brains of homosexual fathers who are their babies’ primary caregivers show as much activation of the amygdala-based parenting network as the brains of mothers, according to a 2014 study led by Ruth Feldman, a neuroscientist and psychologist at Bar-Ilan University in Israel. This suggests the brain’s parenting network can be developed by anyone who takes the lead on infant care.

Parents using either kind of behavior can form close attachments with children. Beyond parents’ behavior, this process depends on synchrony—the degree to which interactions are well-timed, reciprocal and pleasant for both parent and child.

The yardsticks researchers typically use to assess parent-child bonding have been tested mostly with mothers, and work best in capturing the soothing, comforting behaviors more common to moms. That is partly because it is difficult to get fathers to take part in lab studies, says Natasha Cabrera, a professor of human development at the University of Maryland in College Park and a leading researcher in the field. Fathers tend to work long hours, to be less likely to live with their children, and to be more private about their parenting. Dr. Cabrera once spent three years finding 50 fathers willing to take part in a study.

Illustration: Linzie Hunter for The Wall Street Journal

Criteria for good parenting aren’t always the same for moms and dads. For example, many yardsticks code “intrusiveness” or pushiness—such as interrupting a child’s play or choosing a game instead of letting the child decide—as a bad thing. It is true that children tend to react badly when mothers are intrusive, but “when fathers are intrusive, children aren’t that unhappy,” Dr. Cabrera says. Researchers are taking note of such nuances, she says: “If the father is happy and the child is happy, it’s not intrusive.”

One new father-friendly assessment being tested by researchers is called “The Laughing Task.” In this procedure, researchers leave parent and child alone in a lab without toys for two or more minutes and ask the parent to make the child laugh.

One dad snatched a rug off the floor and wore it on his head, says Jean-François Bureau, an associate professor of psychology at the University of Ottawa in Canada and lead author of a 2014 study of 107 parents using the Laughing Task. Others chased their children around the room or made funny faces.

Children got more hyped up and showed a wider range of emotions when playing with their fathers than with their mothers. “This is the zone where they learn” to control themselves if they get excited or upset, Dr. Bureau says. “A landmark of optimal fatherhood” may be the ability to maintain sensitivity and emotional rapport during rambunctious play, he says.

Other fathers scared or unnerved their children by using monster voices. Fathers who aren’t sensitive during play can disrupt a child’s ability to form attachments, fostering insecurity and fear.

Mothers in the study tended to feel more stressed than dads by the lack of toys, but they were just as able as fathers to get their children moving and having fun, and more likely than dads to achieve synchrony in the process, the study shows.

“Dramatic play antics” are among the hallmarks of paternal bonding researchers at Utah State University tried to capture in a 2013 study testing a parenting scale for fathers, says lead author Sheila Anderson, who is now an assistant professor of child and family studies at Weber State University in Ogden, Utah. Researchers coded 428 videotapes of fathers using a choice of toys to play with their 1- to 3-year-old children on a blanket.

Dads in the study often used novel means of encouraging their children. One father was holding his 1-year-old son in his lap when the child became frustrated trying to fit plastic shapes through matching holes in a hollow plastic ball. The father leaned down and nuzzled the baby’s neck with his chin. The baby laughed, calmed down, returned to the puzzle and solved it, Dr. Anderson says.

Researchers used the findings to add new criteria to a checklist used to evaluate parenting, including engaging in playful “pretend” behavior, making sound effects or behaving in surprising ways to encourage children to try new toys.

Write to Sue Shellenbarger at sue.shellenbarger@wsj.com