That's the analysis of broadcaster RTS, which has waded through the data on federal councillors going back to 1848 – when the current Swiss system of government was founded – to determine who has the best chance of replacing outgoing foreign minister Didier Burkhalter when he steps down in October.
Burkhalter's surprise resignation means the Federal Council – Switzerland's seven-person government executive – will need to elect a new member midway through its current four-year term.
Under Swiss rules federal councillors are elected by the two houses of parliament – the Council of States and National Council. A candidate need not be a member of parliament, nor indeed, have much political experience at all – the only criteria are that he or she is Swiss and has the right to vote.
But the stats tell their own story. According to the analysis, the new federal councillor is likely to be:
Currently just two of the Federal Council's seven members are women, including president Doris Leuthard, though that figure has been higher – in 2010 there were more women than men in the government for the first time.
However, Switzerland's remarkably late granting of women's suffrage means, statistically, only six percent of all federal councillors have been women.
After women finally gained the vote in 1971 it took another 13 years before Elisabeth Kopp became the first female member of the Federal Council. She was ousted four years later after a scandal but is now, at age 80, being touted by Swiss media for a potential return to politics.
2. Aged around 50
According to RTS, the average age of a federal councillor at the time of their election has fluctuated over the past 170 years, with the youngest cabinet (average age 39) in the 1850s and the oldest (average age 58) in 1900. However since 2010 the average has been 50 years and 10 months.
The youngest ever federal councillor, Numa Droz, was aged 31 and the oldest was 71-year-old Gustave Ador who only served for 2.5 years.
The current Federal Council with the federal chancellor. Photo: Philipp Zinniker/Pool/AFP
3. From a German-speaking area
According to RTS' analysis, out of the total 116 members of the Federal Council since 1848, 73 (or 62 percent) have been from the Swiss German region, compared with 35 (30 percent) from French-speaking Switzerland, seven (six percent) from the Italian region and only one (0.8 percent) Romansh native.
That's roughly in line with the language split in Switzerland. Though that has fluctuated over the years, official figures for 2015 show that 63 percent of the country's permanent population speak German or Swiss German as their first language, compared with 22.7 percent French, 8.1 percent Italian and 0.5 percent Romansh.
According to Swiss media many feel Burkhalter's replacement should be from the Italian-speaking region, since it's been 18 years since the last one. Given they have been slightly underepresented so far, perhaps they are right.
Under the rules for electing a new federal councillor, parliament must seek to establish a linguistic and regional balance.
Source: Swiss Statistics
4. Already a senator
If you've never been a senator – a member of the Swiss upper house of parliament, the Council of States – then you're less likely to get the gig of federal councillor, according to RTS.
Despite the fact the upper house is far smaller than the lower house – the National Council – a senator is twice as likely to become a federal councillor than a lower house MP.
But there is still hope for others. Out of the 116 federal councillors since 1848, 13 had not already served in the federal parliament, though most were members of their cantonal governments. Only two had not held any political office at all.
Every single Swiss federal councillor since 1848 has been white, according to the government's list.
Confounding the stats
Despite all this, none of those currently touted to replace Burkhalter fully reflect the statistical portrait. Pierre Maudet is a Geneva government minister who has never served in the federal parliament. Laura Sadis is both female and from Italian-speaking Ticino. Vaud MP Isabelle Moret has never served in the Council of States.
So whatever the statistics say, Switzerland could be in for a refreshing change come October...