Professor's Analysis of Scottish Independence Vote for Pre-vote trends


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After a series of articles in The Conversion [Article 1 and Article 2], Prof Bill Buchanan has now analysed the betting trends in relation to the final results, and has found that the betting market reflected the end result more than the opinion polls here.

The following is the text (see Blog for the full article).


Over the past few weeks I have being doing some analysis of the odds around the Scottish Independence Referendum, so let's now see how the predictions actually went.

The final bookies odds for a Yes were 1/5 (5-to-1 on), with a 4/1 No vote bet, and they were right, as the margin between Yes and No reflected the odds more than opinion polls were defining.

Largest moves towards Yes or No

The bookies predicted that Dundee was the favourite for the strongest Yes, and so it was. In second and third place was Clackmannanshire and Glasgow. Table 1 and Figure 1 outlines the results, where it can be see that the Top 3 for the largest Yes vote in percentage terms were actually Dundee, West Dunbartonshire and Glasgow, so the bookies actually got No 1 and No 3 correct. Clackmannanshire, which was the first to be announced, actually ended up in 12th place. In terms of change, Inverclyde, Renfrewshire, North Lanarkshire and South Ayrshire show the greatest changes towards a Yes, while Clackmannanshire, Angus and Moray showed a stronger move towards No, where Clackmannanshire, which was 2nd favourite for the highest No vote ended up in 12th place. The writing was on the wall straight after Clackmannanshire was announced, as it was a No majority for the 2nd favourite for a Yes.

If we assume anything between +3 and -3 is roughly correct, the bookies managed to predict the following: Dundee City, Glasgow, East Ayrshire, Falkirk, South Lanarkshire, West Lothian, Midlothian, Argyll & Bute, Aberdeen City, Edinburgh, East Dunbartonshire, East Lothian, East Renfrewshire, Shetland Islands, Highland, Dumfries & Galloway and Scottish Borders. So the bookies have predicted more than 50% for share (17 out of 32).

They underestimated the strength of the Yes vote for West Dunbartonshire (-9), North Lanarkshire (-11), North Ayrshire (-12), Fife (-7) and South Ayrshire (-12), and underestimated the strength of the No vote for Comhairle nan Eilean Siar (+6), Stirling (+10), Perth & Kinross (+6) and Orkney Islands (+6). Orkney, which was predicted to be in 26th place, actually end up with the strongest No vote.

Table 1: Actual result and predicted place from odds

Figure 1: Actual result and predicted place from odds (-ve shows stronger Yes than prediction, and +ve shows a stronger No than prediction).

So ... who won Punters or Bookies? Winner: Bookies.

Head over heart?

One thing that sticks out is the vote in Aberdeenshire, which was No 9 in most likely to vote for a Yes, but they ended-up at No 24. What seems to have happened is the Aberdeenshire is a strong SNP area, but, perhaps, the head ruled the heart ... where the relative affluence of the area overruled the strong independence focus. Angus and Moray too are strongly SNP, but have gone more with their head, as both areas too are fairly affluent. The bookies obviously predicted that the heart would rule the head in these areas, and that's why they didn't manage to predict them in the correct position.

For heart over head Dundee, Glasgow, and East Ayrshire were predictable; it was other West Coast areas which showed the great head over heart movement, including South Ayrshire moving from one of the least likely (No 31) to somewhere nearer the middle of the table. Renfrewshire and Inverclyde, though, stormed through the odds with massive heart over head turnaround.

East v West?

Scotland is changing as a nation, and the referendum vote perhaps highlights this in relation to the changes in the odds and the results. Table 2 should a rough split between North/South, West and East and tallies-up the scores for each. It can be seen that West scores -77 in changes, where many of the regions in the West produced stronger than predicted results, and the East scores a positive value of +69. The North/South also scores a positive with +8.

Table 2: East, West and North/South

There are generally different demographics between the east and west of Scotland, with a migration of population from west to east. Edinburgh, for example, now has a population of 487,500 (nearly 10% of the total population of Scotland), and is growing at a rate of 1% each year. It also has a fairly young population, with 23.8% aged 16 to 29 years (as apposed to an average of 18.3% over Scotland) . Midlothian, West Lothian and East Lothian have also been growing at a fairly fast rate, possibly due to the effect of a strong economy in Edinburgh, as apposed to failing populations in the West of Scotland.The areas of Moray and Angus have also seen growth due to the success of Aberdeen as a major Oil & Gas hub.

The different demographic is also highlighted with Glasgow has a life expectancy of 71.9 for males as apposed to Edinburgh where it is 77.2. This trend is not consistent, though, with areas such as East Dunbartonshire, appearing 26 out or 32, and having an average male life expectance of 79.4.

So who won in changing perception ... East or West? East Coast.

Odds variation

The odds over the last few weeks did not reflect the opinion polls, especially in the last week or so, where No stayed around 1/4 and Yes started drifting out to 3/1, even as the polls were narrowing the gap. As the polls over the past few days showed the difference between Yes and No narrowing, the bookies started to push the odds out for a Yes. Figure 2 shows the variation of the odds for a Yes vote. It can be seen that there were a good deal of variations over August and September, but the bookies ended up with a fairly consistent consensus.

As seen in Figure 3, the high point of the campaign (in terms of the Yes vote odds) was 7 Sept, where the average odds came into 2.78, followed by a drift out to 4.39 by 13 Sept, and a slight drift-in to 3.91, but the last two days showed a drift out. Generally the odds didn't quite mirror the opinion polls, which tended to narrow the gap over the week before the vote:

18 Sept: 4.52 (Out)
17 Sept: 4.23 (Out)
16 Sept: 3.91 (In)
15 Sept: 4.03 (In)
14 Sept: 4.19 (In)
13 Sept: 4.39 (Out)
12 Sept: 4.06 (Out)
11 Sept: 3.49 (Out)
10 Sept: 2.78 (Out)
09 Sept: 2.85 (Out)
08 Sept: 2.82 (Out)
07 Sept: 2.78 (In)

Figure 2: Variation of No odds

Figure 3: Yes odd for 30 days before poll

So ... who won ... Opinion Polls or Bookies? Winner: Bookies.

% Share of the Vote

The opinion polls were putting the difference between Yes and No within just a few points in the last few days. The bookies though were still predicting 45-50% for a Yes vote, and this is where it ended-up. In the end the bet for 45-45% was 2.1 (which is almost an even money bet). It can be seen from Figure 4 that the prediction was for the lower end as the odds for 40 to 45% are much lower than 50-55%:

40% or less6.840 to 45%3.545 - 50%2.150 - 55%5.1

Figure 4: Percentage share for Yes vote

So ... who won ... Opinion Polls or Bookies? Winner: Bookies.

Prediction on turn-out

The best bet of all was actually related to the how well the Scottish electorate did in turning-out. The actual turn-out was 83.9%, which few could have predicted, and the bookies got this right in terms of the favourite with 7/4, but it was an excellent bet, as there was a nearly 9% difference in the lower end of the bet:

>75% 7/4
70% - 75% 12/5
60% - 65% 5/2
65% - 70% 14/5
55%- 60% 23/5
55% 23/5

So ... who won ... Opinion Polls or Bookies? Winner: Bookies.


Do you want to see the odds the day before the election? Well we can look in the Wayback engine here.


What was surprising on the run-up to the vote was that the bookies were not reflecting the trends of the opinion polls. While the opinion polls were getting closer, the odds for a Yes were drifting out. One of them was going to be wrong, and it looks like the bookies where predicting the end result more accurately, and not going with the trends in the opinion polls. This perhaps shows that bookies understand the dynamics of human nature than targeted sampling.

The split between East and West cannot be ignored in terms of the prediction in how they would vote, with the West showing strong movement towards a Yes, and the East, generally, away from it. Perhaps the industries of finance and Oil & Gas on the East Coast are perceived at a high risk on a Yes Vote?

The full blog is here.

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Associated people

William Buchanan
Director of CDCS
+44 131 455 2759