Even if they understand little else, politicians at least should understand numbers. So should anyone making a living out of political commentary. Even so, the basic numerical logic of yesterday’s Liberal leadership ballot seems to have eluded many people.

Once the ballot became a three-way contest, its complexion changed fundamentally. Yet most of yesterday morning’s coverage seemed blissfully unaware of this, still treating Joe Hockey as the firm favorite. So he was, as long as there were only two candidates; not much doubt that he would have beaten either Malcolm Turnbull or Tony Abbott comfortably.

But in a three-way ballot, what matters most is who comes third; if you get eliminated, the fact that each of your rivals preferred you to the other is of no help. With Abbott and Turnbull in the race, representing opposed but coherent positions, it was always likely that Hockey, the compromise candidate, would be squeezed out.

Because Hockey was the candidate in the middle, tactical voting by his supporters made no sense. It would have been logical (although risky) for Abbott supporters to vote for Turnbull in the first ballot, in the hope of knocking out Hockey (as in fact happened). Ditto for Turnbull supporters switching to Abbott, if they thought (improbably) that there was a risk of him being eliminated.

But Hockey could only lose out from his supporters voting for one of the others. That’s why Tony Wright yesterday, in suggesting  that some of them did just that, “trying to give [Turnbull] a soft landing”, is accusing them of more than usual stupidity. (Unfortunately, it doesn’t follow that the accusation might not be true.)

In the ballot, Turnbull’s position was basically the mirror image of Abbott’s: each needed to keep the other in the race to make it a sharp contest, because either was likely to lose if matched against Hockey. But in the aftermath of the result, that symmetry breaks down.

That’s because Hockey, although the compromise candidate, is clearly on the left, and therefore closer to Turnbull than to Abbott. If Turnbull had won narrowly, the Hockey supporters whose preferences had elected him would have had an incentive to keep quiet: reopening the issue, while it might advantage Hockey, would also risk letting in Abbott, their least-preferred candidate.

So a Turnbull victory, had a vote or two gone the other way, would have a had a certain precarious stability.

But with the actual result, Hockey’s supporters have no such incentive. Their worst option has already happened, so they have nothing to lose by agitating in favor of Hockey, secure in the knowledge that he would have beaten Abbott in a head-to-head ballot.

That looks like making the next year or so a very interesting time in the Liberal Party. If more of them learn to count in the meantime, who knows what they might accomplish.