Understanding Variance in Sports Betting: Breaking Down Expected Value & How to Control Variance

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Matt ModiSeptember 7, 2022 at 04:34 AM

We’ve all been there. One of the most frustrating things in the world is a cold streak when you are betting on sports. It’s been three days, you are consistently beating the closing line, and yet you have nothing to show for it except lost bets and frustration.

This is called variance, which is one of the most important concepts in sports betting to understand.

Human nature can make it a difficult beast to accept, even if you do conceptually understand variance.

The definition of variance is the fact or quality of being different, divergent or inconsistent. At its core, variance essentially means inconsistency.

Inconsistency is also the nature of sports. In baseball, there are hitters in the Hall of Fame who hit at a .300 average, which means they don’t get a hit 70% of the time. Steph Curry, the greatest shooter in NBA history, shoots 42.8% from 3-point range. This means that he misses close to 60% of his 3-point attempts. 

Sports betting is similar, albeit not to that extreme. The best sports bettors in the world win at roughly a 55% rate. The way I like to explain variance, as well as Positive Expected Value (EV) betting in general, by using the example of a weighted coin. 

Normally, flipping a coin means there is a 50% chance that the coin lands on heads and a 50% chance it lands on tails. What this means is that if you flip a coin twice, there is a 25% chance that it lands on heads twice, a 50% chance that it lands on heads once and tails once, and a 25% chance that it lands on tails twice. 

Now, let’s pretend that you are flipping a weighted coin, that is actually weighted toward heads and lands at a 52% rate toward heads, and only 48% on tails. You are the only person that knows this, though, the person you are placing a bet with still thinks it’s 50/50. 

With this knowledge, you should bet on heads every time — every single time. The person you are placing the bet with is giving you 50/50 odds, but you know that heads is actually more likely to land at 52%. 

So, instead of the 25/50/25 table above, the probability distribution now looks like the one below.

This means that, even though heads was the better bet, there is a 23.04% chance that you would have lost both of your bets. Does that mean heads was actually the wrong bet, and moving forward you should bet tails? No, it actually just means you had bad luck or bad variance. 

Flipping a coin twice is fun and all, but let’s now look into significantly larger numbers. With the new OddsJam recommended filters, we tell new sports bettors to give it roughly 250 bets to really get a gauge of how things are going. So, using a binomial calculator on the internet, let’s go from two flips of a coin to 250, with the results below.

Understandably, this is probably a lot to look at, so I will define the important columns below.

Probability of success on a trial: This is asking for the percent chance the coin lands on heads, which, as we mentioned above, is 52%.

Number of trials: This is the number of times we are flipping the coin, or placing a Positive EV bet from the recommended filters. 

Number of successes (x): This is asking how many times we think it is going to land on heads. In this example, I input 125, which would be 50%. 

Now let’s get to the good stuff.

Cumulative probability: P(X>125): This is telling us the percent chance that it lands on heads more than 50% of the time. So, basically, there is roughly a 70% chance that, after 250 flips of a coin, you will have made money from this interaction. A 70% chance! That is pretty good. 

Cumulative probability: P(X<125): This is telling us the % chance that it lands on heads less than 50% of the time. This means that, even with the edge you have, there is roughly a 25% chance that you will have lost money from this series of 250 bets. 

So, 70% of you will have been very happy with your 250 Positive EV bets, but there is also an unfortunate 25% of you that will have lost money. That is how variance works, and in the 25% case, a horrible stretch of bad variance. That still doesn’t mean that betting on heads was a mistake, it just means that you had horrible luck. 

Now, let’s see what these numbers look like when increased from 250 to 1,000. 

Now, that 70% of individuals that profit goes up to 90%, and the 25% of individuals that lost money went down to roughly 10%. That still leaves an unlucky 10% who still managed to lose money even after 1,000 bets. But, with that said, what that also means is that if you give yourself enough time and sample size, you are statistically likely to end up in the green if you are sticking with Positive EV betting. 

Here are some OddsJam customer testimonials to show real-life examples of how variance works, but in the long run everything should still end up positive. 

This next one is fun to show. This individual has profited over $13K using OddsJam but just look at these swings of ups and downs. 

This user went through a six-week stretch where they were down in five of those six weeks. That was predictably not a fun stretch, but, luckily, the course corrected and the next three weeks were profitable, with two of them being big winnings weeks.

Overall, it is understandably easy to get frustrated and think everything is wrong and that life sucks when you are in the midst of one of these cold streaks. However, it is important to understand the nature of variance and that bad streaks are going to happen.

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