There are multiple different break-even prices that people usually quote.
The fiscal break-even is the oil price at which the fiscal balance is zero.
The external break-even is the oil price at which the current account balance is zero.
Both prices can be very different from what it costs Saudi Arabia to pump oil from the ground. A good dicussion of the meaning of fiscal break-even price can be found here: https://www.cfr.org/content/newsletter/files/Breakeven_Oil_Summary.pdf .
A critique of fiscal break-even methodology by one of the authors of the CFR paper was published in the Financial Times in 2015 https://www.ft.com/content/1a106c00-9740-11e5-95c7-d47aa298f769 . I will quote some of it because you need a subscription to access their web site.
Last summer, when oil prices were still above $100 a barrel, people
had a theory for why they would never fall much below that number.
Many major oil-exporting countries had “fiscal break-even” oil prices
— prices required to balance their budgets — near that level. The
International Monetary Fund (IMF) put Saudi Arabia’s at $98.
Faced with oil supply that exceeded demand, these countries would cut
production to shore up oil prices and their finances, keeping crude
prices high. How wrong they were.
The folly of relying on fiscal break-even figures to forecast future
oil prices was driven home at the now infamous November 2014 Opec
meeting, when its members, led by Saudi Arabia, refused to cut at all.
But analysts still point to fiscal break-evens in everything from
geopolitical analysis to long-term price forecasts to advocacy efforts
aimed at persuading oil-exporting governments to pursue fiscal
reforms.
My colleague Blake Clayton and I recently studied the calculation and
use of fiscal break-even oil prices. We discovered that their
popularity exploded around 2008 as policymakers, particularly in
international organisations, grappled for a simple way to persuade
oil-exporting countries that they were running dangerous budgetary
risks. But they then took on a life of their own.
Market analysts pointed to them as oil price floors. Geopolitical
strategists warned of instability if they were breached. The most
facile uses of fiscal break-evens — particularly to predict short-term
oil price movements — are now discredited. And, while fiscal
break-evens do have valuable uses, people are still relying
excessively on them to anticipate political and economic developments
in oil exporting countries — and even to anticipate what will happen
to the oil price over the long run.
Perhaps most striking, then, is how shaky these numbers are. Most
organisations that publish estimates release little or no information
about their methodologies.
We chose to take a particularly careful look at the fiscal break-even
estimates produced by the International Monetary Fund (IMF), which are
widely used by firms, governments and international organisations, and
are more transparent and rigorous than most. Even these revealed
limits that should make users pause.
Estimates are just that. Despite the precision with which they are
typically presented — often down to the last dime — fiscal break-even
prices come from fallible calculations. Take the example of Saudi
Arabia in 2014. In May 2013, when the IMF staff first projected the
country’s 2014 fiscal break-even oil price, they pegged it at $88. It
was only in October 2014 that the IMF staff raised their estimate to
$98 — before increasing it further to $111 in May 2015.
These changes do not reflect big failures on the part of IMF analysts;
rather, they are an inevitable result of surprises in Saudi tax
collections, investment returns, government spending and other
essential ingredients that go into every estimate of a fiscal
break-even oil price. This case is typical of the fiscal break-even
enterprise more generally.
The case of Russia highlights another big problem. In 2014, most
analysts pinned Russia’s fiscal break-even somewhere around $100 a
barrel. Yet the oil price collapse swept the rouble down with it. As a
result, even when oil prices plunged in the wake of the Opec meeting
Russian rouble-denominated oil revenues were virtually unchanged,
leaving Moscow in a surprisingly strong fiscal position.
Failure to include exchange rate dynamics in break-even estimates
appears to be pervasive. Much of the burden for improving fiscal
break-even estimates lies with those who produce them. They should
publish bands of likely break-even prices rather than misleadingly
precise point estimates, describe their main sources of uncertainty
and explain revisions. They should also juxtapose fiscal break-evens
with other indicators, such as fiscal reserves, to provide more
accurate pictures.
But the ultimate responsibility lies with users. They should only use
fiscal break-even prices fully aware of the assumptions, forces and
uncertainties they reflect, and complement them with a much wider set
of indicators.
There is a broader lesson here. Before oil prices collapsed, otherwise
sophisticated market participants, aiming to factor geopolitics into
their oil price expectations, relied on simple assumptions about
fiscal break-even oil prices and their role in driving Saudi
decision-making. They were badly burnt.
This spreadsheet https://data.imf.org/regular.aspx?key=60214246 from the International Monetary Fund contains their estimates (for what they're worth, but I believe IMF to be pretty credible) for both breakevens for a number of oil exporters.
For 2020, they estimate Saudi Arabia fiscal break-even to be 83.6 and the external break-even to be 55.3. So this part appears to be true.
I've been unable to verify that Russia's fiscal break-even is "less than half of that". There are many claims to that effect in the media, originating from Russian state-owned media, but I don't see anyone explaining where they got this figure. Knowing what we know about Russia's opaque budget, I'm extremely skeptical of this claim. Note that the FT article above mentions $100 as an estimate for Russian's fiscal break-even. According to http://graphics.wsj.com/oil-producers-break-even-prices/ , Russia's fiscal break-even price is $72. That's not less than half.
I'm guessing that Russian propagandists are trying to compare Saudi fiscal break-even with some other, totally different statistic for Russia, such as the cost of production. (See, for example, http://graphics.wsj.com/oil-barrel-breakdown/ ).
Russia has suffered a very humiliating defeat in the oil price war (see, for example, https://www.bloomberg.com/news/articles/2020-04-13/putin-makes-painful-climbdown-as-he-sues-for-peace-in-oil-war ). You can expect the army of paid Kremlebots to pomulgate all sorts of falsehoods in an effort to make Russia's defeat appear less humiliating that it actually was.
