# Math May Tell Which Marriages Last

Calculus, More Than Chemistry, Predicts Future Divorce Rates

From the WebMD Archives

Feb. 13, 2004 -- "Chemistry" may get the credit as the foundation for a good relationship, but new research suggests that calculus may better predict whether it stays intact. Researchers say that a mathematical formula they devised can predict with at least 94% accuracy which couples will eventually divorce.

"We actually were at 100% accuracy for most of our study, but a few couples we didn't think would get a divorce based on our formula did, which lowered our accuracy," says mathematician James D. Murray, PhD, DSc, FRS, of the University of Washington and Oxford University. "Still, after testing it on 700 couples, it's incredibly accurate."

The formula, which will be officially presented Saturday at the annual of meeting of the American Association for the Advancement of Science, predicts future divorce rates based on positive or negative numerical scores given for specific expressions or comments made as couples discussed a point of contention while being interviewed by a marriage counselor.

"It could be about money, sex, in-laws, housing -- whatever," Murray tells WebMD. "We videotaped couples during a 15-minute conversation and then tracked scores based on their actions and reactions onto a graph, so it wound up looking like a jagged-lined, cumulative Dow Jones average stock report."

For instance, a roll of the eyes by one mate scored a negative 4 score; a nod indicting interest or well-placed use of humor when discussions got heated warranted a positive 4.

Add the scores and it comes to this bottom line: It's not whether a couple frequently argues that predicts their success. It's how they argue.

## Masters and Disasters of Marriage

"When couples whose marriages are stable over time talk about an area of contention or disagreement, their discussions have five times as many positive comments or expressions as negative. In couples who eventually headed to divorce, ratio of positive-to-negative was 0.8 to 1," says psychologist John Gottman, PhD, a noted marriage expert who conceived the mathematical formula and enlisted Murray's mathematical skills to help develop it some 13 years ago.

The scores for these ratios are based on two coding systems that Gottman developed -- a checklist of 13 behaviors scored for the speaker, and nine behaviors that are scored for the listener on each turn at speech, in both contentious discussions as well as any type of conversation.

"When the masters of marriage are talking about something important, they may be arguing, but they are also laughing and teasing and there are signs of affection because they have made emotional connections," Gottman says. "But a lot of people don't know how to connect or how to build a sense of humor, and this means a lot of fighting that couples engage in is a failure to make emotional connections. We wouldn't have known this without the mathematical model."

## Make or Break Factors

Some of the most significant factors were the nonverbal cues. "For example, there's a facial expression of contempt in which the left lip corner moves to the side and creates a dimple. We see it all the time in couples who are going to break up - and it's huge in our mathematical formula," Gottman tells WebMD. "Eye rolling and sighing in response to a partner's comment are also very big negative behaviors."

Scoring high on the positive end: Words or actions that show empathy, support, or just interest in what the mate expresses about contentious topics -- for instance, supporting words or gestures such as an "I-hear-you-sweetie" nod.

"On the positive side, humor and affection are probably the two most important," says Gottman, who directs the Relationship Research Institute in Seattle and is professor emeritus of psychology at UW. "But you even get some, but not many, positive points for just bringing up a problem in neutral terms, without emotion."

In addition to predicting divorce with the 5-to-1 ratio of positive-to-negative interactions, Murray says the model can actually predict when it's likely to occur: Couples with a steep drop from a neutral point on their "stock chart" typically divorced within five years; a more gentle downward spiral suggested a breakup after 16 years of marriage.

The 700 couples were drawn from six separate studies conducted by Gottman over the past 32 years. "They include the entire spectrum of married people -- young newlyweds, couples with small children, those with teenaged kids, seniors, even same-sex relationships." The actual mathematical formula has been tested on them for 13 years, and many couples are still being tracked.

So how do you stack the numbers in your favor?

"If I have to give one piece of advice based on this for heterosexual relationships, I'd say it's the importance of a man honoring his wife's life dreams, and showing his support," Gottman tells WebMD. "For women, it's having a gentle approach to raising issues. For instance, rather than saying, 'You don't pay enough attention to me', you say, 'Honey, I'm getting that lonely feeling because I really miss you and need more of you in my day.'

"Basically, in good relationships people pussy-foot around each other. They think about how their partner is going to react before they act or speak."

Susan Heitler, PhD, a marriage therapist in Denver and author of The Power of Two, a book on improving relationships, tells WebMD that the mathematical formula for predicting divorce indeed adds up.

"What this does is put into mathematical form what clinicians, relatives, and neighbors see for years before people they know get a divorce," she says. "The more negativity there is in a relationship, the less happiness. And at some point, the couple says, 'this isn't worth it.'"