Using simulations to demonstrate the merit of closing line value
28 April, 2020

In our article about survivorship bias, we demonstrated that some unskilled tipsters would - in the short to medium term - achieve impressive results if the sample was large enough. Because the sample consists exclusively of unskilled tipsters, the only possible driver of impressive tipping histories is dumb luck.

Precisely because it is possible that tipping histories with impressive yields are the product of nothing but luck, we concluded the article explaining closing line value by recommending that you focus on tipsters who provide you with their closing line value numbers.

To refresh your memory, we have made a similar simulation to the one from the article outlining closing line value.

Below we have made a simulation of 1000 tipsters devoid of any predictive abilities, randomly making 200 tips at odds 1.96 for outcomes with a 50% chance of winning.

The graphs of the four most successful tipsters in the sample are displayed in a way they could have been on a tip-selling website.

We have also enabled you to make changes to this simulation as you please.

Tips per tipster
Decimal odds
Probability, %

In this article we will expand on the simulation above and also simulate the closing prices for the various tips. This will enable us to produce not only the actual profits and yields for the various tipsters, but also the closing line value numbers.

We trust that, after having seen how the closing line value and actual profit/yield numbers interact for a population made up entirely of unskilled punters, you will agree that the closing line value is an invaluable indicator for assessing the quality of tipsters.

To be able to run such a simulation, we need to establish some basis for how odds are likely to differ between the time a tipster makes a tip and the time the event is closed for betting. In other words: a basis for simulating the odds difference between a tipster’s tip and Pinnacle’s closing odds.

To get such a basis we have used an archive of Pinnacle’s MLB and NBA moneyline odds between the second half of 2017 and early 2020. To make the odds more consistent, we have removed Pinnacle’s margin from the odds, in accordance with the formula we always use for removing the margin, which can be found in this article.

Tipsters are likely to launch their tips at different times, but most tips are not launched at the opening price. As we don’t have a good way of estimating when the average tipster normally launches the tips, we have made an arbitrary estimate. In our simulation we will assume that the tips are being launched eight hours before the start of the event.

Our sample consists of 9003 matches. We would have preferred a much larger sample, but as we only need it to simulate closing prices, we still think it is a sufficient sample to get the job done.

If you want to see the maths we have used to get a sample for the odds changes, please click expand/collapse below. However, if you are not interested in seeing this you can just read on.

Click to expand/collapse an example of the calculations we have applied:

As the simulation at the start of this article revolved around tipsters randomly choosing between one of two outcomes priced at odds 1.96, we have applied the various odds changes of our sample to odds of 1.96-1.96. The likelihood for the various odds changes are shown in the table below:

Click to expand/collapse the table containing to see the sample of odds changes:

We will now make another version of the simulation from the start of the article. This time we will also simulate closing odds for all of the tipsters’ tips. This enables us to calculate average closing odds and the closing line value.

The sort by filter, allows you to choose if you want to display the tipsters with the best results for actual profit or closing line value.

The results by filter, gives you the possibility to choose if you want the result of the tips simulation using 50-50 as the likelihood for the tip winning or losing or if you want this likelihood determined by the simulated closing odds after the margin has been removed.

The blue graph indicates the tipster’s actual profit and the orange the closing line value profit.

Below we have displayed the graphs of the four tipsters with the best actual yields.

Tips per tipster
Sort by Actual profit Closing line value
Results by 50-50 Closing odds no margin

The four luckiest performers of our sample of 1000 unskilled tipsters, making 200 tips, have likely achieved impressive actual yields in the range of 15-20%. However, there are two other facts we find striking:

1) The closing line value for all four of these tipsters is negative

2) How smooth the graphs for closing line value are when compared with the graphs for actual profit

We have sorted the 1000 tipsters by actual yield and we know that our tipsters are not in possession of any predictive abilities. Sheer luck is therefore the only possible driver of their success, so poor performance if measured by the closing line value should not be a surprise.

The interesting question is, what if we ranked the 1000 tipsters by closing line value instead of actual yield? This would provide us with an overview of the performance of those tipsters who had the best luck in the closing odds part of the simulation and were assigned the shortest closing odds.

Below we have run the same simulation again; the only difference is that we are displaying the four tipsters lucky enough to obtain the best results when measured by closing line value.

Tips per tipster
Sort by Actual profit Closing line value
Results by 50-50 Closing odds no margin

Interestingly, we again find the same two things striking:

1) The closing line value for all four of these tipsters is negative

2) How smooth the graphs for graphs for closing line value are when compared with the graphs for actual profit

That the closing line values are negative again, even after we have sorted the tipsters by this parameter, is informative. It shows that it is exceedingly difficult for an unskilled tipster - to deliver impressive results on this criterion - through nothing but dumb luck. It also means that it is a far superior benchmark to apply if you want to avoid following unskilled tipsters - who have obtained their results through nothing but good fortune.

The smoothness of the closing line value graph when compared with the noisy actual profit - tells the same story. It clearly shows that in the short to intermediate term, the closing line value is far less likely to diverge from the range which is to be expected by a tipster’s skill than the actual profit.

A natural question based on the above is what precisely is the short to intermediate term? Or to put in another way, when is the sample large enough to make it unlikely that the driver behind a tipster’s impressive result is just luck? The answer to the question depends to a large degree on your definition of impressive results.

Arguably the most common way to answer this would be to introduce the concept of the p-value (probability value). Although we have nothing against using p-values to test the quality of tipsters, we believe it is only a viable avenue if you have some idea about the sample size of starting tipsters. Often this information is just not available to you.

This is why we have instead chosen to add a zero to our simulation and simulate 1000 tipsters making 2000 tips.

Tips per tipster
Sort by Actual profit Closing line value
Results by 50-50 Closing odds no margin

As you can see, after having pressed simulate above, it is far from impossible to achieve yields of 4, 5 or 6% even after 2000 tips. Clearly it is possible - for completely unskilled tipsters - to be lucky enough to produce good results for large samples of tips. Because of this, the merit of the closing line value should be obvious even when the tipster you are assessing has made a large sample of tips.

If you do not have access to a tipster’s closing line value numbers and you have to rely on his Actual profit and yield as the only yardstick, it is very easy to be tricked into following unskilled tipsters.

If you are still curious as to how large a sample should be for you to feel safe that a tipster is skilled, we recommend that you play a bit with the simulation above, inputting your own criteria. Remember that, depending on your processor power, there is a chance you will need to decrease the number of tipsters if you want to check for a large amount of tips.

In our opinion the simulations we have made in this article clearly highlight how important it is to have access to closing line value numbers. We would go as far as to say that even if they exist, very few tipsters are worth following unless you have access to their closing line value metrics. If you want to minimize the chances of following unskilled tipsters, closing line value is the answer!

The only viable objection we can see towards the importance of the closing line value - is that we have not demonstrated that Pinnacle’s closing odds are accurate. This is why we will gauge the accuracy of Pinnacle’s closing odds in a future article.



Please login to write comments