Indeed, the scale of ballot box stuffing employed to achieve Putin’s stellar result eclipses the levels of fraud seen in all previous Russian elections, both presidential and parliamentary.

Novaya Europe used a method devised by mathematician Sergey Shpilkin to estimate the share of “irregular” votes cast in the election, based on data for 97% of votes published by the Central Election Commission (CEC) and collected by Telegram channel Nevybory.

According to the CEC, after processing 97% of paper ballots, 74.5 million people took part in the election, 64.7 million of whom voted for Putin. This figure does not include online voting.

The initial estimates using the Shpilkin method put the number of irregular votes at 31.6 million. However, as this election was so unabashedly rigged, even the models developed to assess the scale of electoral fraud in unfair elections cannot be applied.

In fair elections, plotting turnout against the number of votes for the winning candidate in individual polling stations will produce a scatter plot that forms a discernible oval-shaped cloud. This shape can be used as a reference point by which to assess fraud levels in unfair elections, something it has been possible to do in all federal elections in Russia until now. If ballot box stuffing has occurred, both turnout and the winner’s share of the vote will increase, causing the cloud to grow a tail and to become shaped like a comet.

This may be evidence not only of direct fraud, such as ballot box stuffing, but also of other strategies such as forcing public sector employees to vote, which blur the cloud and interfere with proper psephological analysis.

Almost all votes for Putin fall into an area where the share of votes cast for him increases with turnout, while for the other candidates (especially Vladislav Davankov, who is seen by many as the closest the ballot had to an anti-war candidate) this pattern is reversed.

The graph also shows a “grid” with integer values of turnout and vote share, which indicate that the final tally was rigged, as in most cases the vote share and turnout numbers are non-integer figures.

Another reason for such irregular distribution is the widespread use of online voting, especially in Moscow, where election expert Pyotr Zhizhin estimates 71% of voters cast their ballots online.

Due to extremely high turnout rates for online voters (over 90%), this data has been analysed separately to that from polling stations. However, uncoupling online voting from paper voting in Moscow is not possible, as most of those who voted in the capital did so online, thus decreasing turnout rates on the ground. Consequently, a separate cloud of results for Moscow is visible on our graph.

Indeed, to make the most rigorous assessment of the scale of voter fraud, Moscow is best excluded from the calculations altogether. This reduces the initial estimate of 31.6 million fake votes to 22 million, or 35% of all paper ballots. That estimate is likely to be low anyway as it doesn’t take into account online voting fraud or votes cast under Russian military occupation in Ukrainian territories where the election was held.

If we assume that all the votes we consider fake were the result of ballot box stuffing and exclude them from the calculations, that would put Putin’s real result at around 81%. However, other fraudulent practices may have been employed, such as counting votes for other candidates for Putin. This would bring Putin’s share of the vote down to 57% or even lower depending on the scale of the fraud and the methods used to achieve it, which cannot be accurately assessed.

Incidents of voter fraud at polling stations in Moscow also show certain peculiarities, once again having to do with online voting. Analyst Maxim Gongalsky told Novaya Europe that due to the large number of online voters, ballot box stuffing in Putin’s favour could not be done on a large scale sin the capital since relatively few Muscovites decided not to vote, meaning that mass ballot box stuffing would result in turnouts of over 100%.

Another advantage of this tactic for the authorities is that the Shpilkin method is unable to mathematically detect the fraud as voter turnout remains unaffected.

With that in mind, Gongalsky proposed splitting the Moscow results into two distributions, one corresponding to a fair outcome and the other to a rigged one. Such calculations would put Putin’s share of the Moscow vote at 68% instead of 76% and increase Davankov’s result to 17%. Consequently, at least 150,000 offline votes in Moscow must have been fake.

Our own calculations confirm strategies to bolster Putin’s result at the expense of Davankov on a federal level, with our graph showing that Davankov outperformed both other alternative candidates, Slutsky and Kharitonov, at polling stations with a turnout of under 70%. At higher turnout percentiles, the ratio changes, which led to communist candidate Kharitonov taking second place overall in the official results.

In addition, the graph shows peaks at figures divisible by 10, which usually indicates final tally rigging. The Shpilkin graph also shows that the discrepancy between Putin’s real and adjusted results starts at 70%.

The number of votes added by rewriting final tallies (expressed on the graph as peaks) can be estimated separately. Our calculations show that about 5.9 million votes were added in Putin’s favour through voting report manipulation (the Shpilkin method already takes into account some of these anomalies).

The anomalies in the data indicate that 5,900 polling stations (6.7%) could have simply reported the desired results that the authorities had handed down to them.

During all three days of the election we saw evidence that this was the case: for example, on the first day of voting, all 136 polling stations in the city of Stary Oskol in the western Belgorod region reported a turnout of 47%; the same incident occurred in a district in the Tula region in central Russia, where 16 out of 21 polling stations reported identical turnouts.

Statistical methods are unable to identify a number of other serious issues that affect election outcomes in Russia just as much as ballot box stuffing. These include the unequal access opposition candidates are given to campaign resources, state control of the media, voter coercion, and many other undemocratic features as detailed by the voter rights NGO Golos. Ultimately, this means that neither polls nor statistical analysis can accurately reflect the preferences of Russian voters in this election.

Infographics: Alexander Bogachyov