Crime statistics are never to be completely trusted, but it seems safe to say that about twice as many women get beaten up after a Rangers-Celtic game – the so-called "Old Firm" match – than would have been beaten up had the game not taken place. According to Strathclyde police, offences of domestic violence in the west of Scotland rise by 138.8% when the game is played on a Saturday, with smaller but still significant rises (96.6% and 56.8%) for games played on Sundays and weekday evenings. Women-beating is relatively private behaviour. Unlike violence on the field of play itself (13 yellow cards and three red at last week's Old Firm game, plus a managerial dust-up on the touchline), nobody has bought the television rights.

Nonetheless, when Scotland's first minister, Alex Salmond, convened his "summit" meeting in Edinburgh this week on how Rangers-Celtic clashes might be pacified, the phenomenon of men assaulting their female partners was acknowledged as one of the match's ugliest consequences. Celtic's chief executive, Peter Lawwell, said he understood and accepted that "around an Old Firm game violence and domestic abuse does take a hike, and we must address that".

This amounts to a small breakthrough in perception. Until now, Glasgow football has always been mourned and attacked for the way it inflames sectarianism, with civic good sense and tolerance as the victim. But societies can be divided by gender as well as by notions of creed and ethnicity. What about the woman who gets battered when her man's team loses? Is "Catholic" women-beating any different to the "Protestant" kind? Do men sing as they beat: "Hail, hail the Celts are here" or "Hail, hail the Pope's in jail", both to a tune stolen long ago from The Pirates of Penzance? Men may strike other men out of oppositional loyalties. But men seem to hit women for simpler reasons: because they are there to be hit.

Rangers came to play my local team in the east of Scotland on the day after Kennedy's assassination. The minute's silence was drowned in booing (Kennedy was a Catholic) and my only other memory of the day is a conversation with a pleasant-enough Rangers supporter who was standing among the local crowd on the terraces – this was before fans were strictly segregated. "If we get beat this afternoon," he said, "I'm going to go home and throw ma dinner at the kitchen wall." It was his own personal tradition, he said: every time Rangers lost, a dinner got chucked at the kitchen wall. We were amused. One of us said, "Well, if you supported Dunfermline [as we did], then you wouldn't see your wallpaper for chips and beans." Losing to Rangers and Celtic was what other teams tended to do, though their duopoly of success was less then than now, when the outcome of the Scottish championship has all the wide-ranging possibilities of the Boat Race.

We were teenage boys from orderly homes and I can't think that any of our mothers was beaten. We lacked imagination. Even if we'd taken time to construct the scene in our heads – waiting wife, supper in oven, supper on wall, orange beans dribbling towards the skirting board, angry wife, sobbing wife, black-and-blue wife – it would have been visualized as a Victorian slide-show for teetotalism, and therefore comical, in the year 1963. At that time not so much was heard about working-class women, or from them. Will Fyffe recorded I Belong to Glasgow, the song that became Glasgow's civic anthem in 1927, but only very recently was any attention paid to the lines: "There's no harm in taking a drappie/ It ends all your trouble and strife/ It gives you the feeling that when you land home/ Well, you don't care a hang for the wife." Few people 50 years ago would have seen those sentiments as a symptom of brutalism. It was accepted that men often came home drunk and sometimes assaulted their wives, and sometimes the wives deserved it. Outside the gossip of neighbours ("He gave her a good belting – I heard it through the wall") the crime had no public currency.

So much has changed since. Fifty years ago, a journey to Celtic's ground in eastern Glasgow took you past iron forges and engineering works and down tenemented streets packed with shops and pubs. Much the same held true for visits to Rangers and the city's other clubs: Patrick Thistle, Clyde, Queen's Park and Third Lanark. Football then was only a part of something much bigger, an industrial economy with a predominantly male workforce that counted religion and ethnicity, Scottish or Irish, among its divisions.

Today, in as much as eastern Glasgow has an economy, Celtic is most of it. A district that was once so dense and various – houses, factories, chimneys, spires – has been reduced to empty ground, with a football stadium as its biggest landmark. There it unmissably stands, no longer as a recreational adjunct to an identity, but the identity in itself. Across the city to the west, the same applies to Rangers. The churches and the chapels have emptied, the shipyards have closed, Ian Paisley talks to Gerry Adams, Ireland has beaten England at cricket, Scotland's prosperity has deserted the west for the east; but the two old brontosauri still have their claws at each other's throats because it's what they know how to do, having started in 1888.

The landscape around them is very bleak. A quarter of Glasgow men die before their 65th birthday; close to Celtic's ground, men live on average only to 55. On the indices of poverty and social turmoil – drugs and alcohol abuse, stabbings, obesity, teenage pregnancies, households where nobody works – the city is usually nearly the top of UK and sometimes EU figures. Other deindustrialised British cities have known the same kind of aftershock, but Glasgow's case is extreme; the city has "excess mortality" – death rates higher than warranted by the level of deprivation – which is inexplicable to demographers and known as "the Glasgow effect".

Carol Craig, in her disturbing book The Tears That Made the Clyde, published last year, speculates that it may be connected to personal happiness. In Glasgow, she writes, "relationships between men and women have traditionally been based on conflict and contempt, not love and affection". Wives ("the wife") were depersonalised to their household roles and went out to work more rarely than in other parts of Britain. The husband was king – he often denied his wife any sight of his wage packet and took his Saturday football and post-match drinking as a right. A lot of Craig's evidence is anecdotal or drawn from literary sources, but her argument is persuasive. If you ally a macho and heavy-drinking tradition – the old enemy of companionate marriages – to what Craig calls "a weakening male competence" brought about by new kinds of work or no work, then perhaps you have the perfect recipe for domestic battery.

"There is absolutely no place in football for those who let the passion become violence, and the pride become bigotry, and we commit to doing all in our power to maintain the good reputation of Scottish football," said a statement from the Old Firm summit this week. To which a man replies, crashing home long after the game has ended, "Where's ma tea, bitch."