As Ed Miliband and David Cameron hobble towards next year's general election, one is helped and the other held back. I owe this image to an internal briefing document for the BBC written by David Cowling, the corporation's polling expert, which is called "The Crutch and the Wound".
The crutch, in Cowling's analysis, is what Miliband is leaning on. It consists of those Liberal Democrat voters who defected to Labour when Nick Clegg went into coalition with the Tories. Miliband's hope of becoming PM depends on these new recruits staying loyal.
The wound, which is holding Cameron back, is another group of voters who have changed loyalty since the last election: those Tories who defected to Ukip. Cameron's hope of staying on as prime minister depends on the wound healing, or at least getting no worse.
Both leaders have struggled to deal with their disability. It was, possibly, a misunderstanding of the importance of his "crutch" that persuaded Miliband that last week's Labour election broadcast, attacking Clegg as the Un-credible Shrinking Man, was a good idea. Even if it had not been one of the worst political broadcasts I have seen, being rude to Clegg was never likely to be effective with Lib Dem defectors. As Cowling comments, their attitudes are "generally less harsh towards the Lib Dems" than those of other Labour voters. Why any responsible adult thought it was a sensible use of Labour's resources to aim fire at a party already ruined is beyond me.
Cameron, meanwhile, has tried different approaches towards Ukip. He has insulted it. He has tried appeasing its supporters with Eurosceptic poses. He has tried ignoring it. Now that Ukip seems poised to win the most votes in the European Parliament elections, he is trying to engage with it.
None of which has made much difference, and Cowling's analysis explains why. It looks at polling carried out in January by Michael Ashcroft, the Tory peer and truth-seeker. This tested the line that the Tories hoped would work for them, asking people if they agreed with the statement: "A vote for Ukip at the next general election makes the prospect of Ed Miliband becoming prime minister more likely."
This is a tactical consideration that Miliband understands. As we report on page 8, Labour is putting up a token effort in the Newark by-election hoping to help Ukip at the Tories' expense.
But half of Ukip voters disagreed with the statement in Ashcroft's poll. It is not a good start if half your target audience will not accept the premise of your questions. Even among the minority of Ukip supporters who agreed that a vote for Ukip would help Miliband, most said it wouldn't change how they would vote in the general election. As Cowling comments, "How on earth does Lynton Crosby put the fear of God into atheists?"
New research published last week by the British Election Study confirms this analysis. It casts doubt on the assumption, which I admit I shared, that a huge Ukip protest vote in the European election this month will fall to single figures (mostly in the Tories' favour) in next year's general election. People who intend to vote Ukip on 22 May are more likely to say they will vote the same way in the general election than Ukip voters were before the 2009 European election. Ukip won just 3 per cent of the vote in 2010, but, if the same relationship holds, Nigel Farage's party could win 14 per cent next year.
Ukip voters are like punks. They don't care. They don't care if their votes help Miliband because Cameron is just as bad. And they don't care if their votes fail to elect a single Ukip MP because they are simply voting against "the establishment". We know that Ukip is the anti-politics protest party, yet there is something strange about it, because the party depends to a remarkable extent on the personality of Farage.
Cameron must wonder sometimes about his would-be nemesis. Farage became Ukip leader the year after Cameron became Tory leader. The Ukip leader is the anti-Cameron, personifying the reaction to Tory modernisation. When Godfrey Bloom, the rogue ex-Ukip MEP, accused Farage last year of doing a secret deal with the Tories, I bet the Prime Minister half-wished he had. Imagine if he could have bought him off with a peerage a few years ago: suppose Ukip had been led by Tim Congdon, the economist Farage beat to return to the leadership after a one-year gap in 2010, or by Paul Nuttall, currently Farage's deputy.
However, I come back to a point I have made before. Despite his crutch, Miliband is only three points ahead in the opinion polls and, despite his wound, Cameron is only three points behind. And Ukip is on about 14 per cent, so if that is its share of the vote next May, it wouldn't make Cameron's position worse.
A three-point lead with a year to go is not enough for Labour: despite his open wound, Cameron can overtake.