Gordon Strachan, the fourth member of the endangered quartet, theoretically has the option of crossing that white line and doing something to alter his destiny, but injury may confine him too to the role of onlooker.
So, one down - Nottingham Forest - and two out of four to go, from Souness's Southampton, Reid's Sunderland, Robson's Middlesbrough and Strachan's Coventry. That, in descending order, is how the clubs stand and how the bookmakers rate their chances of staying up.
Only a week ago, Coventry were the favourites - in betting terms, rather than popular support - to make it. A home game with Derby offered promise of a win that would leave them placed to pull off the latest outrageous piece of brinkmanship they have patented over 30 years.
But Strachan himself demonstrated the mixed blessing of being able to strip for action when his frustration with a poor refereeing decision led to a free-kick from which Derby scored their first goal. Their second, combined with wins for so many of Coventry's rivals in the past week, has left the Sky Blues in as dire a plight as Highfield Road has known since first reaching the top level in 1967.
Like the other three stragglers, they must play away this afternoon which, given their poor home form, is no great hardship. Nor is the opposition, Tottenham having been doing little more than going through the motions all season.
No team has greater experience of cheating the hangman, and no player is quite as familiar with the emotions involved as Coventry's goalkeeper Steve Ogrizovic, whose 555th League game today will conclude a seventh fight against falling through the trap-door. In his first season at the club, 1984-85, they had to win their last three games to stay up - and did it. The following year, victory in the final match meant a reprieve by two points.
A blissful period of security (including that famous FA Cup final victory over Tottenham) followed, but five times in the past six years, the amiable 6ft 5in Oggy has been at the sharp end again. At White Hart Lane he will inevitably learn from either friend or foe behind his goal how Coventry's rivals are faring. "You do hear things," he says, "but you never quite know what to believe. All we can do is go there and win the game and then if we do, just wait and pray."
Southampton and Sunderland are in the happier position of being able to dispense with prayer if they draw and win respectively at Aston Villa and Wimbledon. While Southampton have the hardest game of the four, even a narrow defeat would suffice, as long as Middlesbrough do not win by three goals against George Graham's misers at Leeds. Boro's more realistic hope is to win by any margin and bank on Wimbledon's famous commitment - which did for Liverpool in midweek - preventing a Sunderland victory for 15,000 visiting supporters to celebrate at Selhurst Park.
What Southampton have already demonstrated is the importance of winning football's equivalent of marginal seats. Despite three long runs without a victory, for instance, they achieved 1-0 successes at first Middlesbrough, then Sunderland, and remained unbeaten in six games that really mattered against that pair and Coventry. Souness has bought as well as anyone; and there is an argument too that the 50 goals his team and Middlesbrough have scored - more than Uefa Cup contenders such as Villa and Sheffield Wednesday - are better credentials than Sunderland's 35 or Coventry's 36.
Reid took a dangerously long time to replace Niall Quinn, injured last autumn, yet may have found a saviour at last in Chris Waddle, the flying doctor who will have a notable double to his name if Sunderland join Bradford City in staying up.
Souness, Reid, Robson, Strachan; each appointed because of their passionate approach to the game. It will be a long and grinding road home for two of them tonight. And the cat may be kicked at the end of it.
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