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.
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. 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%|
|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%|
|Switzerland vs. France||France wins||54%||100||2.070||11.8%|
|Argentina vs. Iran||Iran wins||7%||39||20.840||45.9%|
|Germany vs. Ghana||Ghana wins||11%||22||10.260||12.9%|
|USA vs. Portugal||USA wins||32%||233||5.320||70.2%|
|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|
|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|
|Switzerland vs. France||France wins||54%||2.070||11.8%||33|
|Argentina vs. Iran||Iran wins||7%||20.840||45.9%||127|
|Germany vs. Ghana||Ghana wins||11%||10.260||12.9%||36|
|USA vs. Portugal||USA wins||32%||5.320||70.2%||195|
|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$||1.448
|Portugal: Doesn’t advance past group stage||1000$||2.8||56.3%
|Brazil wins the World Cup||1000$||3.81||72.56%||45.29%|
|Brazil reaches the World Cup Final||1000$||2.47
|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%.
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
 The link to the model: http://fivethirtyeight.com/interactives/world-cup/
 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.