Investing in Betting: The 2014 World Cup

Overview 

 

The Merriam-Webster Dictionary defines a bet as “something that is laid, staked, or pledged typically between two parties on the outcome of a contest or a contingent issue”. Merriam Webster defines an investment as “the outlay of money usually for income or profit”.

 

The point of this blog is to explain how betting using strictly statistical analysis, being completely objective analysis, is investing. When a person removes personal bias from the equation and focuses solely on the numbers, that is the objective data, betting becomes investing. It is not only the expectation of breaking even, but with the expectation that my money is actually better invested a sports betting market, compared to the NASDAQ or DOW Jones. The betting strategies I suggest begin further down.

 

I am no math genius, but my faith remains in the validity of objective prediction making, based in statistical analysis. In all its forms, math can be thought of as the language of logical/quantitative reasoning.

 

This blog is based in several concepts that I have come to better understand as a result of reading articles written by Nate Silver, the statistician who has and continues to revolutionize how most people thinks about Statistics. He and his team at fivethirtyeight.com have created a formula that outlines the statistical odds for each game in the World Cup. When I refer to the “objective odds” or “objective data” throughout the rest of this post, it will be in reference to this model.[1]

 

Math, specifically statistical analysis, is at the core of the betting world. It is easiest to understand the relevant statistical concepts by using an example. With context, these principles and formulas become much easier to grasp.

 

Suppose that I have a bingo-style ball machine that contains 10 ping pong balls, numbered one through ten. It costs 10$ to play, and each time you pick the number correctly, you win 90$ (your original 10$ plus 80$ of pure profit). The allure of the game is obvious, but over the long haul, you will lose one dollar for every dollar you bet. The equation is known as solving for the expected value (EV).

E.V(of bet)=Probability(of winning)*Payout(of winning) –Cost(of bet)

For the above example: E.V(of a 10$ bet)= (1/10)*(90$) – 10 = -1$. Thus, the expected value based on percentage= -10%

The expected value equation applied to the example above tells us that, on average, we lost 1$ for every 10$ we spend. If I bet on a sports event based purely on subjective evidence (such as betting on my favorite team because they’ve looked good when I’ve watched them), my expected value is only slightly better than the example above: I lose about 1$ for every 11$ I spend. This is how “the house” (or the institution accepting your bet) makes its money. This is how people slowly but surely throw away money on sports betting.

 

When someone uses completely objective data however, being a hoard of relevant statistical information, the odds change. By using statistical analysis, we can actually flip the odds in our favor. This is right about the time when people begin to call me crazy, so go ahead. So let me explain myself a bit further by showing that it is not only possible, but very probable that a person can make a profit from betting on sports.

 

Further posts will do more to explain the logic behind this argument, such as the State of the Blog post I hope to have written in the next couple days, but for now let’s turn to a final example. If betting on sports is to be thought of as an investment, then let’s look towards the realm of economic investing. The following is a direct example that I am borrowing from Nate Silver’s book The Signal and the Noise.

When a novice investor starts off, an experienced investor might offer them a piece of advice in the form of a heuristic, or a generalized statement of “truth”. This heuristic is often stated as “Nobody beats the stock market”, meaning that in the long run, it is always better to invest in an index fund rather than by picking stocks. We know that this is a catch-all statement that actually bends the truth, for there are people who make their careers by betting, and succeeding, in investing better than index funds.

The above heuristic that “nobody beats the stock market” is meant to deter novice investors, because the vast majority of them do not beat the stock market.

For the novice sports better, who bets solely based on “their gut”, let me give you my own heuristic: YOU WILL LOSE MONEY BETTING ON SPORTS, and probably pretty quickly. But to say that “nobody makes money by betting on sports” is the same fallacy as the saying that refers to how no one beats the stock market. Just because something is difficult doesn’t mean that thing is impossible. The fact is that making a profit by betting on sports can be done, and per usual, it’s math (and thus logic) that is the driving force.

 

Investment Strategies for Betting on the World Cup

Instead of simply continuing my attempt to convince you in words, I will do so with real-life sports predictions. The World Cup begins tomorrow, and luckily Nate Silver (and his employees at fivethirtyeight.com) have already defined some intricate odds for every single game of the group stage. Taking these odds as the most objective out there, I have compared them to the odds on several sports betting websites[2]. Using average value, I have offered four “investment strategies” for someone betting on the world cup. If the heuristic about betting on sports is right, then I should lose about 1$ to every 11$ I spend. Let’s see what happens. My bet is that the profit I will (hypothetically) earn this month is greater than the profit I could make investing in the DOW or NASDAQ.

 

Imagine that you have 10,000$ that you wish to invest. I have laid out several approaches for betting on this year’s world cup, which would be chosen based on how much risk you are willing to bear.

 

** IMPORTANT FOR UNDERSTANDING THE APPROACHES: The “multiplier” refers to the payout of a winning bet. For instance, imagine that I am betting 1,000$ on Germany to beat Portugal, with a multiplier equaling 2.22. If Germany wins, I will receive (2.22*1,000)=2,220 dollars, 1,120 of which is pure profit. **

 

The Safe Approach: Bet early, Bet a lot

 

This strategy only takes into account bets with an Expected Value of 10% or greater. Using this approach, all bets are placed before the first match tomorrow.

 

This strategy puts to use what is perhaps the most fundamental principle in Statistics: the Law of Large Numbers. This law says that the more samples you take, the more representative of reality your sample will be in comparison to the true population. For example: if I flip a coin 10 times, there’s a good chance that the distribution will not be 50%-50%, meaning it’s very likely that I will get >=60% heads or >=60% tails. If I take 10,000 samples however, it would be very unlikely to get >=60% heads or tails.

 

I weighted the bets based on the difference between the odds provided by the betting website, and fivethirtyeight’s odds. For instance, lets imagine that the multiplier for betting on the USA to beat Ghana is 2.0, and the multiplier for the USA to beat Portugal is 4.0. The way to calculate the website’s probability is simply to divide 1 by the multiplier. So: the odds for the USA to beat Ghana would be (1/2)=50%, and the odds for the USA to beat Portugal would be (1/4)=25%.

 

Continuing with this example, imagine that Nate Silver’s team predicted the U.S. to have a 70% of beating Ghana, and a 35% chance of beating Portugal. If this were the case, based on what I have named “The Safe Approach”, I would bet twice as much money on the USA vs. Ghana game. Why? Because the difference between the objective odds and the website’s odds is twice is great. (see below)

 

For USA vs. Ghana: 70%(objective)-50%(online)=20%

For USA vs. Portugal: 35%(objective)-25%(online)=10%

 

The following is a table detailing the bets made using this approach

Teams or Question Bet Description fivethirtyeight Prediction % $ Bet Multiplier Expected Value (% profit Expected) $ Won?
Brazil vs. Croatia Brazil wins 91% 270 1.322 20.3%
Uruguay vs. Costa Rica Costa Rica wins 19% 133 8.740 66.1%
England vs. Italy England wins 43% 191 3.110 33.7%
Ivory Coast vs. Japan Ivory Coast wins 47% 168 2.670 25.5%
France vs. Honduras Honduras wins 12% 78 13.180 58.2%
Argentina vs. Bosnia&Herz. Bosnia&Herz wins 15% 64 8.800 32.0%
Germany vs. Portugal German wins 63% 316 2.220 39.9%
Ghana vs. USA USA wins 38% 82 3.000 14.0%
Brazil vs. Mexico Brazil wins 86% 194 1.333 14.7%
Australia vs. Netherlands Australia wins 15% 83 9.740 46.1%
Tie 24% 76 5.080 21.9%
Spain vs. Chile Chile wins 31% 222 5.430 68.3%
Cameroon vs. Croatia Cameroon wins 28% 75 4.210 17.9%
Italy vs. Costa Rica Costa Rica wins 26% 281 9.950 158.7%
Tie 30% 143 4.570 37.1%
Switzerland vs. France France wins 54% 100 2.070 11.8%
Argentina vs. Iran Iran wins 7% 39 20.840 45.9%
Tie 16% 40 7.280 16.5%
Germany vs. Ghana Ghana wins 11% 22 10.260 12.9%
USA vs. Portugal USA wins 32% 233 5.320 70.2%
Tie 29% 52 3.840 11.4%
Netherlands vs. Chile Chile wins 48% 256 2.990 43.5%
Costa Rica vs. England Costa Rica wins 20% 101 7.000 40.0%
Italy vs. Uruguay Uruguay wins 44% 137 2.760 21.4%
Japan vs. Columbia Columbia wins 60% 134 1.909 14.5%
Bosnia&Herz. vs. Iran Iran wins 19% 41 6.000 14.0%
Portugal vs. Ghana Ghana wins 29% 119 4.500 30.5%
Will Brazil win the group? Yes 95.20% 195 1.189 13.19%
Brazil points: Over/Under( 7.5)? Over 68.87% 374 2.1 44.63%
Cameroon points: Over/Under (2.5)? Over 57.72% 186 2.12 22.37%
Will Chile win the group? Yes 34.60% 216 4.48 55.01%
Will Netherlands advance from the group? No 56.60% 218 2.26 27.92%
Will Chile advance from the group? Yes 69.70% 263 1.826 27.27%
Spain points: Over/Under (6.5)? Under 59.71% 125 1.901 13.51%
Australia points: Over/Under (0.5)? Over 66.18% 129 1.699 12.44%
Will Spain win the group? No 52.40% 160 2.31 21.04%
Will Japan advance from the group? No 70.10% 249 1.787 25.27%
Will Italy win the group? No 79.80% 202 1.463 16.75%
Will Italy advance from the group? No 53.40% 331 2.89 54.33%
Will Costa Rica advance from the group? Yes 30.00% 334 9.07 172.10%
Costa Rica points: Over/Under (0.5) Over 87.41% 323 1.448 26.57%
Will Switzerland advance from the group? No 54.00% 172 2.26 22.04%
Honduras points: Over/Under (1.5)? Over 57.72% 234 2.25 29.87%
Will Argentina win group? No 26.50% 126 5.17 37.01%
Iran points: Over/Under (1.5) Over 57.73% 136 2 15.46%
Will Germany win the group? Yes 68.50% 158 1.68 15.08%
Will Portugal win the group? No 87.20% 245 1.364 18.94%
Will Portugal advance from group? No 56.30% 363 2.8 57.64%
Will USA advance from group? Yes 34.50% 171 4.03 39.04%
Will Belgium win the group No 51.90% 106 2.18 13.14%
Will Brazil win the world cup? Yes 45.292% 335 3.81 72.56%
Will Brazil reach the final? Yes 56.527% 282 2.47 39.62%
Group Stage: 1st Brazil, 2nd Cameroon Yes 22.29% 113 6.3 40.43%
Group Stage: 1st Chile, 2nd Spain Yes 20.79% 159 8.5 76.72%
Group D: 1st Uruguay, 2nd Costa Rica Yes 2.90% 8 41 18.90%
Group Stage: 1st England, 2nd Uruguay Yes 15.26% 34 7.5 14.45%
Group Stage: 1st England, 2nd Costa Rica Yes 6.33% 85 66 317.78%
Group Stage: 1st Costa Rica, 2nd England Yes 3.97% 60 186 638.42%
Group Stage: 1st Costa Rica, 2nd Uruguay Yes 4% 58 141 464.00%
Group Stage: 1st France, 2nd Honduras Yes 7.78% 36 17.5 36.15%
Group Stage: 1st Germany, 2nd USA Yes 18.68% 122 8.5 58.78%
Group Stage: 1st USA, 2nd Germany Yes 6.35% 43 25.5 61.93%

 

 

The Slight-Moderate Risk Approach: Tweaking the Safe Approach by weighting differently based on Average Value

 

In this approach, we are betting on the exact same games as in the Safe Approach, but are tweaking the amount of money we are investing in each game. Again, we make all of our bets before the World Cup begins.

 

Let’s return to the hypothetical example I used in the safe approach. The expected value of the USA to beat Ghana is: Probability(of winning)*multiplier-1.

USA vs. Ghana comes to: (.7*2)-1=.4=40%.

The same equation is used in the Portugal scenario, simply by plugging in the applicable numbers

USA vs. Portugal comes to: (.35*4)-1=.4=40%.

So based on the same information as used in the “Safe Approach” example, we would weight our picks differently, wagering an equal amount of money on each of the games.

 

The following table outlines the bets that are made by implementing this approach.

Teams or Question Bet Description fivethirtyeight Prediction % Multiplier Expected Value (% profit Expected) $ Bet $ Won/Lost
Brazil vs. Croatia Brazil wins 91% 1.322 20.3% 56
Uruguay vs. Costa Rica Costa Rica wins 19% 8.740 66.1% 183
England vs. Italy England wins 43% 3.110 33.7% 94
Ivory Coast vs. Japan Ivory Coast wins 47% 2.670 25.5% 71
France vs. Honduras Honduras wins 12% 13.180 58.2% 161
Argentina vs. Bosnia&Herz. Bosnia&Herz wins 15% 8.800 32.0% 89
Germany vs. Portugal Germany wins 63% 2.220 39.9% 111
Ghana vs. USA USA wins 38% 3.000 14.0% 39
Brazil vs. Mexico Brazil wins 86% 1.333 14.7% 41
Australia vs. Netherlands Australia wins 15% 9.740 46.1% 128
Tie 24% 5.080 21.9% 61
Spain vs. Chile Chile wins 31% 5.430 68.3% 189
Cameroon vs. Croatia Cameroon wins 28% 4.210 17.9% 50
Italy vs. Costa Rica Costa Rica wins 26% 9.950 158.7% 440
Tie 30% 4.570 37.1% 103
Switzerland vs. France France wins 54% 2.070 11.8% 33
Argentina vs. Iran Iran wins 7% 20.840 45.9% 127
Tie 16% 7.280 16.5% 46
Germany vs. Ghana Ghana wins 11% 10.260 12.9% 36
USA vs. Portugal USA wins 32% 5.320 70.2% 195
Tie 29% 3.840 11.4% 31
Netherlands vs. Chile Chile wins 48% 2.990 43.5% 121
Costa Rica vs. England Costa Rica wins 20% 7.000 40.0% 111
Italy vs. Uruguay Uruguay wins 44% 2.760 21.4% 59
Japan vs. Columbia Columbia wins 60% 1.909 14.5% 40
Bosnia&Herz. vs. Iran Iran wins 19% 6.000 14.0% 39
Portugal vs. Ghana Ghana wins 29% 4.500 30.5% 85
Will Brazil win the group? Yes 95.20% 1.189 13.19% 37
Brazil points: Over/Under( 7.5)? Over 68.87% 2.1 44.63% 124
Cameroon points: Over/Under (2.5)? Over 57.72% 2.12 22.37% 62
Will Chile win the group? Yes 34.60% 4.48 55.01% 153
Will Netherlands advance from the group? No 56.60% 2.26 27.92% 77
Will Chile advance from the group? Yes 69.70% 1.826 27.27% 76
Spain points: Over/Under (6.5)? Under 59.71% 1.901 13.51% 37
Australia points: Over/Under (0.5)? Over 66.18% 1.699 12.44% 34
Will Spain win the group? No 52.40% 2.31 21.04% 58
Will Japan advance from the group? No 70.10% 1.787 25.27% 70
Will Italy win the group? No 79.80% 1.463 16.75% 46
Will Italy advance from the group? No 53.40% 2.89 54.33% 151
Will Costa Rica advance from the group? Yes 30.00% 9.07 172.10% 477
Costa Rica points: Over/Under (0.5) Over 87.41% 1.448 26.57% 74
Will Switzerland advance from the group? No 54.00% 2.26 22.04% 61
Honduras points: Over/Under (1.5)? Over 57.72% 2.25 29.87% 83
Will Argentina win group? No 26.50% 5.17 37.01% 103
Iran points: Over/Under (1.5) Over 57.73% 2 15.46% 43
Will Germany win the group? Yes 68.50% 1.68 15.08% 42
Will Portugal win the group? No 87.20% 1.364 18.94% 53
Will Portugal advance from group? No 56.30% 2.8 57.64% 160
Will USA advance from group? Yes 34.50% 4.03 39.04% 108
Will Belgium win the group No 51.90% 2.18 13.14% 36
Will Brazil win the world cup? Yes 45.292% 3.81 72.56% 201
Will Brazil reach the final? Yes 56.527% 2.47 39.62% 110
Group Stage: 1st Brazil, 2nd Cameroon Yes 22.29% 6.3 40.43% 112
Group Stage: 1st Chile, 2nd Spain Yes 20.79% 8.5 76.72% 213
Group D: 1st Uruguay, 2nd Costa Rica Yes 2.90% 41 18.90% 52
Group Stage: 1st England, 2nd Uruguay Yes 15.26% 7.5 14.45% 40
Group Stage: 1st England, 2nd Costa Rica Yes 6.33% 66 317.78% 881
Group Stage: 1st Costa Rica, 2nd England Yes 3.97% 186 638.42% 1770
Group Stage: 1st Costa Rica, 2nd Uruguay Yes 4% 141 464.00% 1286
Group Stage: 1st France, 2nd Honduras Yes 7.78% 17.5 36.15% 100
Group Stage: 1st Germany, 2nd USA Yes 18.68% 8.5 58.78% 163
Group Stage: 1st USA, 2nd Germany Yes 6.35% 25.5 61.93% 172

 

The Continuous Approach: Moderate Risk

This method, unlike the previous two, does not involve wagering the entire 10,000$ at the beginning of the tournament. Rather, a person implementing the continuous Approach would wait until the day of the match to make a bet. This approach is only for betting on the outcome of individual games, rather than prop bets.

 

For any bet with an expected value exceeding 10%, this approach would encourage 1,000$ on that game. Because this method requires up-to-date betting/odds, there is no Excel tab explaining it. Each day of the World Cup, I will post a hypothetical bet based on this approach a few hours before games begin.

 

To make it less risky, one could weight their bet based on the Expected Value. Say the Expected Value % of Brazil is 20%, I would bet 200$ vs. if it were 40%, I would bet 400$ and so forth. I will make daily bets using this version of the method as well, updating my hypothetical “current bankroll” based on the outcomes of the games.

 

The High Risk (but Sort of Safe) Approach

 

This method begins by weighting in the same manner as the safe approach. The Reason it is more risky though is that it only takes into account the bets weighted among the top 10.

 

The table on the following page explains the bets you would make based on this approach.

 

Bet description $ Placed Multiplier % Profit based on Expected Value Probability of winning the bet based on objective data
Germany beats Portugal 1000$ 2.22 39.9% 63%
Brazil points in Group Stage: Over 7.5 1000$ 2.1 44.63% 68.87%
Italy: Doesn’t advance past group stage 1000$ 2.89 54.33% 53.4%
Costa Rica: Advances past group stage 1000$ 9.07 172.10% 30.0%
Costa Rica: Over 0.5 points 1000$ 1.448

 

26.57% 87.41%
Portugal: Doesn’t advance past group stage 1000$ 2.8 56.3%

 

57.64%
Brazil wins the World Cup 1000$ 3.81 72.56% 45.29%
Brazil reaches the World Cup Final 1000$ 2.47

 

39.62% 56.527%
Costa Rica beats Italy 1000$ 9.95 158.7% 26%
Brazil beats Costa Rica 1000$ 1.322 20.3% 91%

 

Costa Rica or Bust: Extreme risk

This strategy consists of betting only on a handful of games and propositional bets (called “props”) with the highest expected value.

 

I found that there were five bets I could make with an expected value exceeding 100%, and all of them involved Costa Rica being undervalued in the betting market. This also relates to Italy being overvalued in the market. I will explain at another time how markets can be bets can be over/undervalued based on fan bias. This occurs when one team’s fans flood the betting market relative to another team, as may be at the root of Italy overvalued “stock” and Costa Rica’s undervalued “stock”. Recognize this is the riskiest of all the strategies: Very large risk, with an even greater possible reward.

 

Bet description $ Placed Multiplier % Profit Expected Value Probability of winning based on 538
Costa Rica beats Italy 2,000$ 9.95 158.7% 26.0%
Costa Rica to advance from group 2,000$ 9.07 172.1% 30.0%
Cost Rica 1st in group, England 2nd 2,000$ 186 638.42% 3.97%
England 1st in group, Costa Rica 2nd 2,000$ 66 317.8% 6.33%
Costa Rica 1st in group, Uruguay 2nd 2,000$ 141 464.0% 4.0%

 

This may seem like pure insanity. Again, this is definitely not the way to make a low-risk investment. There is quite obviously a sizeable chance you lose every penny you bet. But the payout is staggering: 10,000$ could net you more than 400,000$ of profit. Even if Costa Rica can simply advance to the group stage, without any of the other scenarios occurring (which would be unlikely at that point), you will have made in excess of 8,000$ of pure profit. If any of the three bottom scenarios unfold, your 10,000$ investment will net you at least 130,000$ in pure profit. This is the highest risk, highest reward of the approaches.

 

 

The Sane Person’s Lottery: All or Nothing (XXXXXtreme risk)

 

If you really wanted to go for the biggest haul (and wouldn’t miss your 10,000$ a whole lot), you would bet your entire stash of 10,000$ on Costa Rica to get 1st and England to get 2nd in group D. Why? Because this bet has the highest % profit expected (exceeding 600%), and thus is the best value bet I found. The objective odds put the likelihood of winning this bet at 3.97% (found by applying some basic stats techniques to the odds on fivethirtyeight, which was the same way that objective odds were calculated for all the prop bets). 3.97% surely doesn’t look too hot, but if it’s your lucky year, your 10,000$ bet could earn you 1.85 million $ of profit. Not bad.

Another way of going of implementing the all or nothing approach would be to make a single bet based on “The Safe Approach”. The optimal bet based on that approach would be to bet against Portugal advancing past the group stage. This would net you 18,000$ of profit, and Silver’s odds have the probability of Portugal missing out on advancing at 56.3%.

 

Going Forward

 

I realize that there are a ton of predictions floating about these pages, so I hope it is not too confusing. I wanted to make sure I posted this prior to the beginning of the World Cup so may have sacrificed some neatness, both in style, grammar, and sentence structure. That being said, here’s my take on the investment strategies above.

If you are willing to bear quite a bit of risk, I would most likely suggest the second version of the Continuous Approach.

If you want to ensure that you will win money though, if you want to make sure that your profits exceed what could have been made investing in Index funds, then I would suggest either the Safe, Slight-Moderate Approach, or a combination of both.

If you are a Costa Rican millionaire, I think you know what needs to be done.

 

In regard to updating both versions of the “continuous approach”, I plan on posting my hypothetical wagers (based on both versions) each day before the day’s games. Further, I plan to update the results of how all of the approaches are doing after each team has played at least one game (in about a week from now). I will also post the price of the NASDAQ and DOW Jones at the time of the opening match so that on the final day, we can compare hypothetical profits.

 

I trust in the validity of these approaches because I trust in the thoroughness of Nate Silver, and the power or reason/rationalization that is utilized in Statistical analysis. If anyone wants to make a real-life bet with me, here is my proposition: Over the next three weeks, the aggregate profit of investing in “The Safe Approach” and “The Slight-Moderate Approach” (5,000 hypothetical dollars in each) will be greater than the aggregate profits one could make investing the same ratio in the NASDAQ and DOW Jones.

 

There’s Nate Silver, and then there’s Ziv’s Gold, and gold is quite the safe investment.

I’m apologize for the cockiness, but it’s time to show the world that just because an investment strategy works outside the box, doesn’t mean it isn’t valid.

“You Play to win the Game!” ~Herm Edwards

 

 

[1] The link to the model: http://fivethirtyeight.com/interactives/world-cup/

[2] sbrforum.com is a great website that allows a sports betting investor to compare the odds on different sports betting websites, in order to discover the optimal odds.

This entry was published on June 12, 2014 at 2:03 am and is filed under Uncategorized. Bookmark the permalink. Follow any comments here with the RSS feed for this post.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

Follow

Get every new post delivered to your Inbox.

%d bloggers like this: