Chapter 1: Odds and Probabilities
SPORTS BETTING 101:
ODDS AND PROBABILITIES
This chapter is intended for those of you who are excited about getting into the great world of sports betting, but don’t know where to start. Here is a key phrase that you absolutely need to understand when you are done reading this chapter: “It’s all about the odds.” You will see what I mean as we go along.
Before you place your very first bet, you need to have the basics down. It all starts with understanding the odds that bookies are showing to you. What do they mean? How do I know how much I can win when betting on a certain team? We will also discuss the two most common types of odds: decimal odds and American odds. Then, I will show you the very important relationship between odds and probabilities. Finally, the #1 mistake made by rookie/inexperienced/amateur gamblers will be unveiled.

DECIMAL ODDS
In order to make the concepts easier to understand, I will use the closing lines (i.e. just prior to the start of the game) in decimal format from the sportsbook Pinnacle on Super Bowl LI played February 5, 2017 at NRG Stadium in Houston, Texas:

Money line 
Spread 
Totals 
New England Patriots 
1.719 
3 2.090 
Over 57 2.000 
Atlanta Falcons 
2.260 
+3 1.833 
Under 57 1.909 
1.1 MONEY LINE
Let’s start with the money line: you are simply betting on which team is going to win the game. Period. The numbers are used to determine how much you can earn when betting a certain amount of money. All you need to do is multiply the amount you are willing to risk by the corresponding money line to figure out the potential return (which includes your initial bet).
For example, the money line on the Patriots was 1.719. If you wanted to bet 60$ on the Patriots to win the game “straight up”, your potential return would have been 60$ * 1.719 = 103.14$. In other words, you were risking 60$ trying to win a 43.14$ net profit (103.14$  60$).
How about the case of another gambler willing to risk the same 60$ amount, but this time on the Falcons to win? Since the money line was 2.260, the potential return was 60$ * 2.260 = 135.60$, which is the equivalent of a net profit of 135.60$  60$ = 75.60$.
Let’s recap: a person risking 60$ on the Patriots was looking at a potential 43.14$ profit, while a similar bet on the Falcons was yielding a potential 75.60$ profit. The higher return on the Falcons is simply an indication of them being viewed as the underdogs (i.e. the least likely team to win the game), while the Patriots were established as the favorites.
1.2 SPREAD
We now turn our attention to the column called “Spread”. When betting the money line, you are trying to figure out which team is going to win the game. When betting the spread, the margin of victory is what matters. You may lose your bet even though your team won the game, just like you could win your bet despite your team losing the match.
In the example above, the spread on the Patriots looked like this: 3 2.090. Just focus on the 3 for now. The minus sign indicates you need to look at the final score and deduct three points from the Patriots’ score. If they still beat the Falcons after subtracting those three points, you win the bet. The final score from that game turned out to be 3428 in favor of New England (in overtime). After making the 3point adjustment, the final score became 3128 for New England so a spread bet on the Patriots was a winner.
In plain words, betting the Patriots 3 means you expect them to win by more than 3 points. If they win by a 3point margin exactly, your bet is refunded. If they win by 12 point(s) or if they lose the game, your money is gone.
Recall how the line showed up as Patriots 3 2.090. I have already explained the 3 part. What about the 2.090? This figure, just like the money line, dictates how much you can win based on the risk amount. It works exactly the same way as the money line: multiply the amount you are willing to risk by this number and you end up with your potential return. So if you wanted to bet the Patriots “against the spread” at 3 for 200$, your potential return would have been 200$ * 2.09 = 418$ (i.e. a 218$ net profit).
Betting the spread on the Falcons functions in a similar way. Remember the line was Falcons +3 1.833. The +3 part means you need to add three points to the Falcons’ score to verify if your bet was a winner or not. It basically means you are going to win your bet either if the Falcons win the game (by any margin) or if they lose by less than three points. Again, your bet gets refunded if they lose by a 3point deficit exactly. Your money is gone if Atlanta loses by 4+ points. This time your potential return can be calculated by using the 1.833 figure.
Generally speaking, when the spread on a given team is “–x” it means they have to win by more than “x” points for your bet to win. Such a team is therefore established as the favorite. On the other hand, a spread of “+x” on a given team means they have to either lose by less than “x” points or win the game for your bet to be declared a winner. In this case, we are talking about the underdog.
1.3 TOTALS
The last column of the table concerns “totals”. Nothing complicated here. We are betting whether the total number of points scored by both teams combined will exceed a certain number or not. In the PatriotsFalcons example, the line was set at 57. If you believed more than 57 points would be scored in this game, you needed to bet the “over”: as you can see, the potential return on such a bet could have been calculated by using the 2.000 number. If you expected less than 57 points to be scored, you needed to bet the “under” with the associated 1.909 multiplier. Had exactly 57 points been scored during Super Bowl LI, all bets on totals would have been refunded.
Congratulations! You should now be able to understand odds on any sporting event in decimal format! It’s also important to understand American odds: below you will find a crash course on the topic.

AMERICAN ODDS
The following table is the analog of the previous one, but shown in American format:

Money line 
Spread 
Totals 
New England Patriots 
139 
3 +109 
Over 57 +100 
Atlanta Falcons 
+126 
+3 120 
Under 57 110 
As you can see, the money line on the Patriots was 139. It means you needed to risk 139$ if you wished to earn a 100$ profit (i.e. a return of 139$ + 100$ = 239$). What if you want to bet an amount that differs from 139$; how do you calculate the potential return? Here is how to convert negative American odds into decimal odds:
x in American odds is identical to (x+100)/x in decimal odds.
In the New England example, it means 139 becomes (139+100)/139 = 239/139 = 1.719 in decimal odds, which is the exact same number we saw in the first table!
Let’s move on to the Falcons money line: +126. It means risking 100$ yields a 126$ potential profit (i.e. a return of 100$ + 126$ = 226$). Let me show you how to convert positive American odds into decimal odds:
+x in American odds is identical to (x+100)/100 in decimal odds.
The formula above implies that +126 in American format becomes (126+100)/100 = 226/100 = 2.260 in decimal format. That’s exactly what we had previously.

RELATIONSHIP BETWEEN ODDS AND PROBABILITIES
Suppose you believe Team A has a 60% chance of beating Team B and the money line is as follows:

Money line 
Team A 
1.588 (American: 170) 
Team B 
2.600 (American: +160) 
Should you bet Team A or Team B? Or should you stay away from that game? Remember the important quote: “It’s all about the odds.” In order to answer this vital question, you need to calculate each team’s implied win probability:
Team’s implied win probability = 1 / team’s money line in decimal format
Following the above formula, Team A’s implied win probability stands at 1/1.588 = 0.630 = 63.0%, whereas Team B’s sits at 1/2.600 = 0.385 = 38.5%.
Let’s summarize everything in a table to help you visualize:

Money line 
Implied win probability 
Your estimation 
Team A 
1.588 
63.0% 
60% 
Team B 
2.600 
38.5% 
40% 
Here is the essential rule:
Bet any team for which your estimation of their win probability exceeds the bookie’s implied win probability
In the example above, you believe Team A holds a 60% chance of winning the game which is less than the casino’s 63.0% implied win probability so you shouldn’t bet on this team. However, your 40% estimation with respect to Team B is greater than the bookmaker’s 38.5% figure, in which case you should consider betting Team B. This is what experienced bettors call a “positive expected value play”. In abbreviated form, you will hear them say it is a “+EV bet” or a “value bet”.
Note: I am not going to discuss how to come up with estimated probabilities here. How did we obtain the 60% number? It is the most critical and difficult part when betting on sports. If you don’t come up with reliable numbers, you will lose money in the long run.
The sum of your estimated win percentages always equals one (or 100%); if Team A has a 60% chance of beating Team B, then Team B necessarily has a 40% chance of coming on top. However, notice how the sum of the bookie’s implied win probabilities does not equal 100%: 63.0% + 38.5% = 101.5%. That’s where they get their edge over gamblers and is their source of revenue. It is often called the “vigorish”, which is their commission for operating a sportsbook.
Suppose two evenly matched teams face each other on a neutral court, such that you believe each team holds a 50% chance of winning the match. Most bookies will offer the following odds:

Money line (American) 
Money line (decimal) 
Team A 
110 
1.909 
Team B 
110 
1.909 
Imagine for a moment that a grand total of 110 000$ was wagered by several bettors on Team A, while 110 000$ was also wagered on Team B (i.e. we have “balanced action”). From the bookie’s perspective, if Team A wins the game it will pocket the 110 000$ wagered on Team B, while netting a 100 000$ loss on Team A’s bets for a total net profit of 110 000$  100 000$ = +10 000$. As you can easily see, the bookmaker will also gain 10 000$ if Team B wins. In other words, no matter which teams wins the game, the bookie wins!
The vigorish is also the cause for staying away from certain games. Let’s use one last time the example where we believed Team A had a 60% chance of winning, but this time assuming a 62% estimation:

Money line 
Implied win probability 
Your estimation 
Team A 
1.588 
63.0% 
62% 
Team B 
2.600 
38.5% 
38% 
Our estimation is now lower than the casino’s implied win probability for each of the two teams. Therefore, you shouldn’t bet this game at all.

THE #1 ROOKIE MISTAKE
This one drives me nuts. You see it happening several times a day around the world. An amateur gambler looks at the day’s matchups and goes “I’m sure Team A is going to win this game because bla bla bla. Therefore, let me log in my sportsbook account and bet on them.” That is a very wrong approach to sports betting and a sure fire way to be a loser.
Why? Because that person broke the golden rule: “It’s all about the odds.” How can you possibly make the decision to bet a specific team without even knowing what the odds are? “I don’t care what the odds are; Team A is going to win, I can guarantee you that.” Please, don’t ever be that guy and I want to make sure you have the right mindset to avoid such a detrimental line of reasoning.
No team is ever “guaranteed to win” unless you are pitting professionals against 7year old kids. In any sensible league, the worst team still has at least a tiny chance of beating the top team. Whenever someone claims a team is a lock to win, ask him if he is willing to risk 10,000$ to win 1$. See how he is going to quickly back down. He is likely to respond that you are exaggerating. But the funny part is he just contradicted himself because he previously claimed he didn’t care what the odds were, but he now says no to 10,000 to 1.
He might defend himself by saying he didn’t care about the odds, as long as they were “reasonable”. But what is the definition of reasonable? I agree that 10,000 to 1 was a stretch (you’ll probably never see such odds), but I was just using an extreme example to make my point. Are 107 to 1 odds acceptable? How about 12.7 to 1? Where’s the threshold?
Just keep in mind the following quote: just because you are betting on a certain team, it doesn’t mean you believe they will win. As a matter of fact, most of the bets placed by savvy sports bettors are on teams they don’t believe will win. And yet, they turn out to be winners year in and year out.
How does that happen? Because they bet on underdogs the majority of the time. As a very general rule, the public prefers betting favorites because it feels more comfortable and yields a success rate above 50%. But it doesn’t mean you end up with more money in your pockets at the end of the year since you are risking more money than you can potentially earn.
Let’s consider a very concrete example. When you roll a dice, each number from 1 to 6 has one chance out of six of showing up. Now, if I asked you “do you believe we’ll get number 3 on the next roll of the dice?” your answer will probably be “no” because it’s more likely that any of the other five options will appear.
That being said, if I offered you to bet on “Will we get number 3 on the next roll of the dice?” the fair decimal odds would be “Yes” at 6.0 versus “No” at 1.2. If someone was crazy enough to offer you odds on “Yes” at 6.5, you have to take it even though you don’t firmly believe it is a likely outcome! It’s still a good bet.
If that crazy someone accepted to play this game on four rolls of the dice, it is possible that you lose on all four occasions. You might feel like you did something stupid, when in fact you made a smart move. Don’t focus on short term results too much. If you keep making clever bets, you will make money in the long run. If, instead of accepting to play the little dice game only four times, the crazy person was willing to play it 1000 times, it’s almost impossible that you will end up a loser. The probabilities are hugely in your favor. Long term success is what you should focus on.
The same kind of argument applies to sports betting. Suppose the whole world knows Team A is much superior to Team B. Let’s say they have an 80% chance of winning. If the money line on Team B exceeds 5.0 (1 / 0.20), the appropriate decision is to bet on them. So, for example, if the line is 6.3 I’m going to pound on Team B even though I don’t believe they will win (since my bestguess claims they only have a 20% win probability). Don’t try to find excuses to go against that by saying things like “Team A lost its previous game, they will be focused and playing like mad men and will destroy Team B” or any other nonsense arguments to force you into a bet that is not good to the long term health of your bankroll.
Odds are what matters the most. If you stick to betting teams for which the odds provide a positive expected return, you will do just fine. The key is finding and recognizing such opportunities; I will do my best to provide you with the best insight possible in that regard. It all starts in the next chapter and the following ones. Now that you’ve got the basics down and the right mindset, you are ready to take the next step towards your winning goals.
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