The person who will have had the most influence on the fourth Wimbledon women's singles final between Venus and Serena Williams is also likely to be the person most glad not to be on the Centre Court to watch them compete.

Richard Williams, their father, who had visions of creating world-beating sisters even before he had any knowledge of tennis, who imaginatively coached them to within reach of the pinnacle, and who retains a powerful emotional influence, would rather stick his head in a cupboard than see his daughters purvey their special brand of violence in the direction of each other.

When Venus and Serena meet at this stage, before the final he sometimes prowls the site; occasionally he hides in his room; before last year's Wimbledon showdown he was halfway across the Atlantic. "He likes it like that, because it means his job has been done," Venus said. But he also hates it, because of the pain of imagining what they might inflict on each other – and after departing there are important anaesthetising details to consider.

Richard claims he tells the captain on the flight home not to tell him the outcome of the final and he gets another surge of disquiet if he hears someone discussing it as he goes through the terminal.

Some downplay his significance now. They remember how he used to hold up placards during his daughters' matches and was criticised by Martina Navratilova for distracting opponents. They remember when Venus won Wimbledon 2000 that he shouted "straight out of Compton" (the poor Los Angeles district where they once lived), jumped over the NBC broadcasting booth, and performed a triumphant dance. Chris Evert claimed that broadcasters "thought the roof was coming down".

And they remember his remarks a couple of years ago which encumbered his daughters with questioning. "I don't think Venus or Serena was ever accepted by tennis," he said. "They never will be."

His critics see him as an eccentric, no longer in touch with the strictures of an ever-evolving game, a professional anachronism. But in one important respect they miss the point. Richard Williams is a symbol of emotional continuity. Without that his two very unusual, slightly maverick daughters might never have survived the sceptical media, the hostility at the Indian Wells tournament which ensures they will never return, the murder of step-sister Yetunde and the break-up of their parents' marriage, which now causes them to watch Serena and Venus from different sides of the stadium.

Father taught them a hierarchy of values, which still influences them today: God first, family second, education third, business fourth, and then only tennis – some way back in fifth place. The perspective, even in modified form, may have served them well.

Besides which, the common heritage is an intense force. In February, while deploring the Israeli Shahar Peer's exclusion from the UAE, Venus recalled her father's early experiences of discrimination in America's deep south when one wrong word could cost him his life. How much she now valued her ability to speak freely, she said. It brought a hush to her audience.

In the circumscribed coaching world too he still appears to possess some relevant savvy. Serena still consults with him before some of her matches. He is reported to have walked out during her loss to Svetlana Kuznetsova in Paris, claiming she had strayed from the agreed match plan. So stressed was he on Thursday that he left for a few games during Serena's marvellous semi-final with Elena Dementieva.

The sisters could not have had more different routes to the final, which might influence the outcome. Serena finished drained, Venus was still fresh after dismissing the world No1 Dinara Safina for the loss of just one game.

They are tied 10–10 in head-to-head results, and two-two in grass court matches. Serena has won two of their three Wimbledon finals, but Venus has won three of the last four Wimbledon titles, and five of the last nine.

The elder sister is possibly the greatest grass-court player of her era, with her steep serve, great reach and amazing long legs which get to most things in two bounding strides. But she carries a knee injury, while Serena has been serving extremely well, her 60 aces being far and away the most by any woman this Wimbledon. But, of course, it is a toss-up who will win. The only obvious possibility is that it should be a better match than some of their earlier ones, which had an exhibition flavour: with time they seem to have become able to compete more intensely and – perhaps – to endure the emotional consequences.

And, if they haven't persuaded him to stay, they will leave Richard Williams to go away and do familiar things – riding his motor cycle, working around the house, or cutting the grass. Cutting the grass, he says, is what he really likes best.