Sports Betting Lessons: Value Betting
Sports Betting Lessons
By Professor MJ
This form of sports gambling is the one I privilege the most, personally.
In order to clearly understand the concepts in this article, you need to be comfortable with American odds. If you are not, I have got an easy solution that won’t take more than two minutes of your time: first read Section 2 of the “How to Understand Odds, Point Spreads and Probabilities” article. It is not complicated. Otherwise, you will quickly feel lost.
If you asked me to summarize in one sentence what value betting is about, it would go like this:
We quickly discussed the topic in the article entitled “How to Understand Odds, Point Spreads and Probabilities”. Recall the critical rule:
As opposed to arbitrage betting where we are betting both teams from a given match, we will now bet only one team and hope for the best. Some strict rules will determine when to place such bets.
For the sake of this article, a team’s win probability will be estimated by looking at the various lines posted in different bookmakers. Another avenue would be to come up with your own estimation based on statistical models and/or your judgement. We are not going to cover this subject in this article (perhaps in a future one?) because there is so much to be said.
2. A Simple Example
There is no better way to explain a concept than by looking at a concrete example. Let’s start with a very simple one:
As you can see, all bookmakers have the same -140 +120 odds, except the last one that has -165 +145. If you managed to grasp the content from my “Arbitrage Betting” article, you know you have an arbitrage opportunity in front of you. As a matter of fact, you could potentially bet Team A with Bookie #5 (at +145 odds) and bet Team B at any of the other four sportsbooks (at -140 odds), while locking a guaranteed profit if you strategically select the amounts wagered on each side. That would be fine, and I wouldn’t blame you for doing so.
Personally, I would go the “value betting” route, though. What does that mean? In the fictitious example above, the clear consensus seems to be Team A at +120 and Team B at -140. You can easily tell that Bookie #5 is way off base and is offering odds (+145) which are much higher on Team A than any of its competitors (+120). To me, that’s a clear signal that Team A at +145 is a good bet.
It does not look appealing, in this specific example, to do arbitrage by also betting Team B at -140; this line is certainly not a bargain since four bookies have posted the exact same line! So why would you waste your money on it?
Therefore, my recommendation is to only bet Team A at +145 and trust the fact that it represents a profitable bet. Sure, Team A might end up losing the game. In the long run, though, you will come out a winner if you place a large number of value bets like this one.
3. A More Complex Example (How to Detect Value Bets)
In the example above, it was pretty obvious that the -140 line on Team B was not a bargain, while the +145 odds on Team A was indeed a steal. Is there a pragmatic way of determining whether we have a value bet or not in less obvious cases? Here are detailed instructions that explain how to find +EV plays by looking at lines posted by several bookies.
Once again I will use an example in order to illustrate the concept; otherwise things will get very tricky and won’t be as clear:
Notice that there isn’t an arbitrage opportunity here. The best line on Team A is +128, while Bookie #2 offers the best odds on Team B at -130. As you learned in the “Arbitrage Betting” article, since the number associated with the “plus” sign (128) is NOT greater than the number associated with the “minus” sign (130), you cannot do arbitrage. Does that mean you should move on to the next game? Not necessarily.
It is possible that either the +128 line on Team A or the -130 line on Team B yields positive expected value. Which of the two seems the most off-track?
Let’s focus on the various lines on Team A (presented in ascending order): +110, +125, +127, +128 and +128. As you can see, the +128 line does not seem like an outlier at all since two different bookies have posted this exact line, and another one is extremely close (+127).
All right, so let’s turn our attention to the lines on Team B: -130, -138, -143, -145 and -147. This time, we observe a certain gap between the best line (-130) and the second-best line (-138). We should investigate further to verify if betting Team B at -130 is a smart idea or not.
3.1 True Odds
This subsection is very important. You should pay close attention to it and make sure you fully understand how it works. It may not be the sexiest portion of the article, but it is extremely relevant. I invite you to read it several times, if necessary.
For the sake of checking whether the -130 line is a bargain or not, we need to compute “true odds”. This term refers to odds that would be posted if bookmakers were not taking any commission (i.e. no vigorish), for example Team A -170 versus Team B +170 (both numbers are the same, except for the sign in front of them). Casinos wouldn’t make much money (if any) if they did that.
Let’s go back to the example above. As you can see, Bookie #1 posted the following lines: Team A +127 versus Team B -147. If this sportsbook was kind enough to remove its vigorish, what would be fair lines (or “true odds”)? You might be tempted to answer Team A +137 versus Team B -137 because 137 is the number in-between 127 and 147. But that is incorrect.
Step #1: Convert American odds into decimal odds.
If you don’t remember how to do it, please go back to the article “How to Understand Odds, Point Spreads and Probabilities” (section #2 about American odds). In the current example: Team A at 2.27 (= [100+127] / 100) versus Team B at 1.68 (= [100+147] / 147).
Step #2: Obtain the implied probabilities.
As seen in “How to Understand Odds, Point Spreads and Probabilities”, a team’s implied win probability is equal to 1 divided by its money line in decimal format. For Team A we get 1 / 2.27 = 0.4405, while for Team B we obtain 1 / 1.68 = 0.5952.
Step #3: Find the fair/true probabilities
The odds posted by Bookie #1 imply that Team A has a 44.05% chance of winning, while Team B has a 59.52% win probability. The sum equals 103.57%, which is greater than 100% because of the commission taken by the bookmaker. If you want to come up with true probabilities, you need to divide each team’s implied probability by their sum.
For Team A we get 44.05 / 103.57 = 42.53%; for Team B we come up with 59.52 / 103.57 = 57.47%. The sum now equals 100% so we know these win probabilities are fair. The conclusion here is that Bookie #1’s odds basically claim Team A has a 42.53% chance of winning the game, whereas Team B holds a 57.47% chance of coming on top.
Step #4: Convert back into American odds
How do you go from a probability to its corresponding American odds?
- If the win probability, p, is 50% or less: American odds = +100 * (1 – p) / p
- If the win probability, p, is over 50%: American odds = -100 * p / (1 – p)
Let’s apply the above formulas to the true probabilities above:
- Team A: p = 0.4253. Since it is less than 50%, use the first formula: American odds = +100 * (1 – 0.4253) / 0.4253 = +100 * 0.5747 / 0.4253 = +135.
- Team B: p = 0.5747. Since it is over 50%, use the second formula: American odds = -100 * 0.5747 / (1 – 0.5747) = -100 * 0.5747 / 0.4253 = -135.
In other words, true odds are Team A +135 versus Team B -135.
3.2 Do We Have a Value Bet?
Now that I’ve taught you how to calculate true odds, let’s go back to the original question associated with the example above: does the -130 line on Team B with Bookie #2 offer value (i.e. has a positive expected value)?
The potential bargain concerns odds posted by Bookie #2: we are going to calculate true probabilities from each bookmaker, except #2. We use the exact same procedure as the one decribed in the preceding subsection.
Team A’s true chances of beating its opponent are 42.54%, 42.89%, 43.07% and 42.70% according to sportsbooks #1, #3, #4 and #5, respectively. The average turns out to be 42.80%. As for Team B, we get an average of 57.20% (which, naturally, is 100% - 42.80%).
If you transform into American odds: Team A +134 versus Team B -134. Those are what we call the “fair odds” or “true odds”.
Generally speaking, if the line on a given team is greater than its fair odds, then you have a value bet (or +EV bet); therefore, you should bet this team.
Here is the final conclusion in the case of the example above. If you believe odds posted by bookies 1-3-4-5 are truly representative of the relative strength between teams A and B, then you should bet any line above +134 on Team A and any line better than -134 on Team B.
Since the -130 line posted by Bookie #2 is indeed higher than -134, then you should place a wager on Team B at -130 because it does provide value. You can see it more easily in decimal format: -130 corresponds to 1.77, whereas -134 corresponds to 1.75 (1.77 is indeed greater than 1.75).
4. How to Calculate Return on Investment (ROI)
As I often say, you should view yourself as a sports investor, rather than a sports gambler. You are investing in good sport bets that you believe are underrated. Investors in financial markets, like the stock market, talk about ROI all the time; how much is my money generating per year? 5%? 10%?
As serious sports investors, we also wish to determine how much we can expect to earn from a given bet. In the example from the previous section, how much money can we anticipate to make, on average, from placing a $100 bet on Team B at -130? Remember that we found the following true probabilities: Team A at 42.8% versus Team B at 57.2%.
First, let’s find out the potential return of a $100 bet at -130 odds, which is the equivalent of 1.7692 in decimal odds. Potential return = $100 * 1.7692 = $176.92. Alternatively, we could say that the potential net profit of such wager is $76.92 ($176.92 minus the original stake of $100).
To summarize, we have a 57.2% chance of winning $76.92 (if Team B wins the match) and a 42.8% chance of losing $100 (if Team B loses the match).
The ROI is obtained through the following couple of key formulas:
- EXPECTED VALUE = (Potential net profit * Win probability) – (Potential loss * Loss probability)
- ROI = Expected value / Risk amount
In this case, we get:
Expected value = ($76.92 * 57.2%) – ($100 * 42.8%) = +$1.20
ROI = +$1.20 / $100 = 0.012 = +1.2%
Here is the proper way to interpret this ROI figure: a $100 bet at -130 on Team B should earn you, ON AVERAGE, a net profit of $1.20.
Of course, if you do place such a bet, you will either lose $100 or increase your bankroll by $76.92. There is no way you can make a $1.20 profit on that game. But what the ROI is telling you is that if you had the opportunity to place such a bet one million times (from playing these two teams one million times under the exact same conditions), you would end up with a net profit representing close to 1.2% of the total amount wagered on all of those games.
As you can see, the -130 bet was nothing to write home about; a 1.2% ROI is not spectacular!
5. Arbitrage or Value Betting?
5.1 My Personal Preference Versus Yours
I want to dig a little deeper on this topic because that’s a question I get asked often. Recall the very simple example at the beginning of this chapter where all bookies posted -140 +120 lines, except one sportsbook that offered -165 +145? As seen earlier, you could either elect to do arbitrage (betting both teams, one at -140 and the other at +145) to lock a guaranteed profit, or you could take the value betting path by placing a wager only on the +145 line because it’s way off base.
I mentioned I would personally go the value betting route because the -140 line is not offering any value. If you were to calculate its ROI, it would be negative. I don’t like placing bets that I know take money out of my pocket, on average. There is only one valid reason why you might consider doing arbitrage here: to reduce risk.
When you do arbitrage and you don’t screw up (see the pitfalls detailed in Section 5 of the “Arbitrage Betting” article), your bankroll steadily increases. But when you stick to value betting, your bankroll will see fairly big spikes going up and down. If you lose sleep because you are worrying too much about your bets, then you should either reduce your betting amounts, or focus exclusively on arbitrage betting.
5.2 The Coin Flip Story - Keep it in Mind!
When you lose value bets, you will curse yourself for not hedging with a bet on the opponent. In the simple example, assume you hesitated for a while between doing arbitrage or value betting before you finally settled on value, which means you only bet the +145 line. If that team loses, you will be upset that you didn’t hedge with a bet on their opponent at -140. But that’s part of the game and you need to remember that you will make more money in the long run if you avoid “bad” lines that do not provide value.
Whenever you find yourself angry because you lost a value bet when you could have secured a little profit by doing arbitrage, bring back to your mind the following little story. You probably agree that if we flip a coin, then fair odds would be “heads” +100 and “tails” +100. Both outcomes are equally likely. Now, let’s say Crazy Man offers the following lines: “heads” +105 and “tails” -102. Betting “heads” undoubtedly provides good value because you earn more money when you win compared to the amount you squander when the bet loses, despite the win probability being fixed at 50%.
You could do arbitrage and bet both sides with a guaranteed profit, but why bet “tails” when it is unquestionably a bad bet? In the short term, doing value betting by sticking to “heads” might incur some losses if you get unlucky, but you’ve got to trust the process and understand that in the long run that is the way to go to maximize your profits!
When you get +105 odds on a coin flip, you hold a small edge over Crazy Man, much like casinos have a small advantage over roulette players. Do all gamblers leaving a casino go home with losses? No. Some get lucky and win some dough. But if a guy places flat $100 bets while playing roulette for 1000 hours I’m willing to bet my house he will be in the red at the end of the session. I could even include the furniture in the deal.
5.3 Cases Where Arbitrage Betting is Better than Value Betting
I just want to make sure one thing is clear, though: I’m not saying arbitrage betting should be avoided all the time. In some cases, it turns out to be the best option. Here is a quick illustration:
Bookie #1 has the best line on Team B at -170, while Bookie #5 offers the highest odds on Team A at +180. As you are now familiar with the concept, you probably quickly detected an arbitrage opportunity. Would you be better off only placing a bet on Team B at -170? Or only on Team A at +180?
The -170 line on Team B looks like a bargain considering the next-best odds on this team are -185 (i.e. a 15-cent difference). However, the +180 line on Team A seems as good a bargain because the next-best odds on them turn out to be +165, which also yields a 15-cent difference. In this situation, I would do arbitrage.
5.4 How to Maximize Your Profits
Therefore, the general rule I advocate is to do value betting, unless both sides of the arbitrage bet are equally good and you cannot clearly tell which one represents a true bargain. To me, that’s the way to maximize your profits. But if you feel more comfortable slowly growing your bankroll thanks to a mix of arbitrage betting and cashing bonuses, then that’s perfectly acceptable too. Whatever strategy fits your personality and your risk tolerance level the best!