Nick Clegg has offered to be the Conservatives’ heart or Labour’s head in any future coalition, but in what circumstances could this happen?

Nick Clegg said on Wednesday that the Lib Dems’ politics of conscience and stability were the only alternative to “a coalition of grievance”. But will his party – on about 9% in the polls, down 14 points from 2010 – have any say in who forms the next government?

Could the Lib Dems be in government again – and how?

The answer is quite possibly yes, with either the Conservatives or Labour. However, the potential scenarios after 7 May look far trickier than the formal two-party coalition arrangement of five years ago.

Clegg has offered to be the Conservatives’ heart or Labour’s head in any future coalition. During the leaders’ debate two weeks ago, Nicola Sturgeon said the SNP would be the backbone and guts of a Labour government. Stitching a government together may end up being the easy bit: getting it to walk could prove far more difficult.

What do the polls tell us?

Based on current projections, the most important numbers to follow are on the one hand the combined Labour-SNP bloc, and on the other the Tory-Lib Dem bloc. These calculations matter as they will most probably determine which of David Cameron or Ed Miliband forms the next government.

Labour is currently projected to win 271 seats and the SNP 54. This adds up to 325, enough to win a confidence vote in the Commons, and there could be an “anti-Tory” outright majority once the votes of Plaid Cymru (three), the SDLP (three) and the Greens (one) are also included.

The Conservatives are projected to win 270 seats and the Lib Dems 29. Even once possible support from Ukip (four seats) and the DUP (nine) is co-opted into the mix, the current government coalition would fall well short of a majority.

Could there be a repeat of the Cameron/Clegg double act?

A key test is the Tory v Labour seat count. The Lib Dems’ role in this contest will be more about who their supporters may vote for tactically between the two main parties. First, if we look at the 28 seats the Lib Dems are projected to lose, eight are to Labour:

To make a difference to the overall arithmetic, the Lib Dems would need to retain most of these seats as well as those it is projected to lose to the SNP in Scotland. Although support for Clegg’s party has been edging up in recent weeks, this would need a comeback of historic proportions in both England and Scotland.

Second, if we consider the 29 seats the party is projected to retain, 21 have the Tories in second place. And any of these that go to the Conservatives would make no net difference in the bloc’s total count.

Cameron’s chances of extending his stay in Downing Street depend on the Tories not only beating Labour to be the largest party, but doing so by some margin. But if the Tories do emerge with the most seats, Clegg would probably talk to Cameron first, as he did in 2010.

So yes, Clegg could be Cameron’s deputy prime minister again. But he would need the Conservatives’ and Lib Dems’ tally of seats to add up to at least 326, because without the numbers in parliament a government wouldn’t see the light of day.

What about Labour?

In a Miliband-led government, the Lib Dems’ role and influence would be defined by numbers, necessity and politics.

As things stand, the SNP are the most likely kingmakers – no feasible option of government can discount the 50 MPs that Sturgeon’s party is expected to have in the next parliament. Even if the SNP wins fewer seats, the ones it doesn’t gain would stay with Labour. As with the Tory-Lib Dem contests, this would make no difference to the overall count, it simply rearranges the deckchairs.

In order for a straight Labour-Lib Dem deal to become a possibility, one of two things would need to happen: a significant swing back to Labour in Scotland (with the SNP winning only 20-25 seats), or Labour gaining roughly double the number of seats it is currently projected to take from the Conservatives.

Neither scenario is very likely. From a probabilistic point of view, a Conservative majority (8%) is more likely than a Labour-Lib Dem coalition (7%).

Based on current evidence, for Miliband to enter Downing Street he would need to begin with a conversation with the SNP. However, a Labour-led government sustained by a parliamentary majority of a handful of seats is unlikely to be stable. It would require the support of other parties beyond the limited firepower that could be provided by Plaid Cymru and the Greens.

Enter the Liberal Democrats

The combined Labour-SNP-Lib Dem tally would take a Miliband government above 350 seats. The balance of power between the three parties would depend on the number of seats each wins, and the difference between an SNP on 35-40 seats or 50+ seats, and the Lib Dems on 25 or 30 seats, will matter in terms of the two parties’ bargaining chips.

Then there is the politics

A first factor would be the form of government. While both the SNP and Labour have ruled out a formal coalition, a minority Labour government sustained by the Lib Dems and Sturgeon’s party is a rather different proposition to a Labour-Lib Dem coalition externally supported by the SNP.

A second factor likely to emerge in any dealing between Labour and the Lib Dems could be whether Clegg remains leader of the party, even if he holds on to his Sheffield Hallam seat. In 2010 Clegg was adamant in saying he could work with Labour but not with Gordon Brown. Five years later his departure could be the price the Lib Dems have to pay for a deal with Miliband.

And all this before we even begin to consider the parties’ policies and pledges.