Final polling and betting data

The implied probability of a No vote based on bookmakers odds up to 7pm on the 17th of September and the opinion poll probabilities of a No outcome (eliminating the don’t knows) are shown in Figure 1 below. The odds on a No outcome shortened throughout the 17th. The final observation was taken at 7pm.

A number of opinion polls were  also published on the 17th. They tended to show the No campaign having a tiny lead over the Yes campaign. Once the standard errors and the possible impact of the undecided voters are taken into account, there would seem to be little to choose between the likelihood of a Yes or No outcome. Yet this contradicts the bookmakers assessment of the odds, with the implied probability of a No vote now creeping up to 80 per cent.

Figure 1: Opinion Poll and Betting Market Implied Probability of a No vote


Sources: What Scotland Thinks,, own calculations

A betting market on the share of Yes votes in the referendum is also open. The distribution of these is shown in Figure 2. The most likely range of Yes votes is 45-49 per cent. The chance of an outcome above 50 per cent (a Yes win) is 0.15, which is consistent with the overall odds of a Yes outcome, which can be deduced from Figure 1. However, the implied probability of Yes outcomes in the 35 to 44 per cent range is over 0.4, higher than the probability of a Yes win.

Figure 2: Likely Yes Vote Percentage


Sources:, own calculations (omitting overlapping intervals)

Nevertheless, taken together, the evidence from the betting odds is suggestive is of a No victory with a majority of between between 2 per cent and 10 per cent.

Finally, a market has developed in the local authorities most likely to vote No. These are mainly dominated by the more affluent areas, those close to the Scottish-English border and interestingly, Orkney and Shetland, which are located close to Scotland’s main oil fields.   These are closely followed by Edinburgh, Scotland’s capital city. Clearly a Yes outcome where Edinburgh votes No would also pose significant political challenges.

Those areas least likely to vote No include Scotland’s more depressed former industrial cities – Dundee and Glasgow. These are joined by a group of authorities in central Scotland and the Western Isles (Na h-Eileanan Siar), which has always had close ties with Scottish nationalism.

Figure 3: Area Most Likely to Vote No

Area Most Likely NoSources:, own calculations

The probabilities implicit in the betting odds provide an interesting set of predictions for the outcomes of the referendum. But they are just predictions: nothing more, nothing less. What will be fascinating in the post-referendum analysis is how they perform compared with the opinion polls. This referendum has produced a wealth of data and a unique challenge to both methods of foretelling the outcome.

About David Bell

David Bell FRSE is Professor of Economics at the University of Stirling. He graduated in economics and statistics at the University of Aberdeen and in econometrics at the London School of Economics. He has worked at the Universities of St Andrews, Strathclyde, Warwick and Glasgow. His research is mainly in labour economics, fiscal decentralization and the economics of long-term care. He has been budget adviser to the Scottish Parliament Finance Committee. He is PI for the Healthy AGing In Scotland project (HAGIS).
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