At some point, every sports bettor must learn to overcome short term variance.  Most new bettors think that they understand that there will be ups and downs - it is gambling after all, right?  What they fail to account for is how volatile betting on sports can be, especially on a short timeline. 

Think about it this way.  Assuming standard -110 pricing, each individual bet has the potential for a +90.9% gain and a -100% loss.  These are huge swings!  There are very few risks we take in life (especially with money) with that kind of volatility.

Many amateurs struggle with the fact that if they are expecting to win 55% of their wagers (more than enough to consistently turn a profit), the wins and losses will never come in a predictable pattern.  More on this later.

How to Beat Variance & Minimize Risk

Overcoming variance is simple in theory.  You just need to maintain your expected winning percentage, increase your number of wagers, and avoid going bust by spreading your risk carefully. 

Maintaining Expected Win Rates 

As I said, overcoming variance is simple in theory.  It’s much harder in practice.  Maintaining your expected win rate is not something you are know exactly at any given point in time.  It is in flux, however, over enough time you can establish a baseline estimate.  How much time it takes is up for debate, however, once you hit 200 bets in a sport you can make an assumption that you will be able to maintain that win rate.

Increasing Number of Bets

The best way to understand how increasing your number of wagers decreases variance is by using Monte Carlo simulations to show how hypothetical betting scenarios play out over time.  For our simulations we used an expected win rate of 55% and standard -110 pricing on each game.

To illustrate this point, we ran five simulations using the same variables except for number of bets placed.  For simplicity we risked $110 to win $100 on each game.  Straighter, less jagged graph lines indicate less risk/variance.  

Sports Betting Variance by Number of Bets

At just 10 simulated bets, not only are there big jumps up and down but, even with each game given a 55% probability of winning, in this case the end result was an overall loss.

 With 50 bets we still see a wide variety of results.  There are many peaks and valleys, indicating both winning and losing streaks.

 Increasing the sample to 200 bets, we see things start to even out and follow a more linear path.

 At 1,000 bets in our simulation we really don’t see a huge difference from 200 but, again, the path is showing less volatility.

 

Once we bump the number of bets to 5,000, you can see how much variance has been taken out  of the path.  There are still peaks and valleys of course, but over time they end up being very small bumps.

 

Spreading Risk (Knowing How Much to Bet Per Game) 

When you are dealing in a high variance market like sports betting, you absolutely must manage risk properly.  This is probably the single biggest failing of most bettors.

Your starting point should always be how much money in total you are willing to lose betting on sports.  It should never be an open-ended amount and you should never start with an idea of how much you want to bet per game or how much money you want to make.

Once you’ve established a starting bankroll, there are two money management strategies to consider: Flat Betting and Kelly Betting.  We only recommend these two strategies or some small variation of them.  

We urge you to stay away from Martigale (sequence) betting techniques or other scams that will only result in an eventual collapse of your bankroll.  We will deconstruct this style of betting in a future article.

Flat Betting

Flat betting is wagering the same amount on every game.  We recommend starting at 1% of your bankroll.  Most bettors are taken by surprise at this recommendation.  After all, you would need a $10,000 starting bankroll to bet $100 per game.  Remember, this is a starting point and one that is based on minimizing risk.  It also establishes self-control, something many bettors struggle with.

After you have consistently bet at 1% for a time, you may want to increase your flat bet amount to 2-5%, but we do not recommend going much higher than that.  Your ultimate goal here is to be able to ride out bad streaks and not go completely bust.

Kelly Betting

Kelly betting is based on the Kelly criterion, a formula used for calculating optimal bet size to maximize growth.  There are many online tools for this, but the math is simple enough that you can make the calculations yourself.  The crucial element here is your expected win rate.  

We always advise clients to estimate a low win rate because Kelly betting will destroy your bankroll if you estimate a higher win percentage than you actually achieve.

To calculate your Kelly bet size (K), you need three variables, all in decimal format:

a = To Win Odds
b = Expected Win Rate
c =  Expected Loss Rate 

You will need to calculate your “To Win Odds” (a) by using the following variables:

x = To Win Amount
y = Risk Amount 

To Win Odds Forumula

Kelly Bet Size Formula

Example:

Your expected win rate is 55%, making your expected loss rate 45%.  Your bet odds are -110 (risking $110 to win $100).

For a we take 100 / 110 = 0.909 

That gives us all of our variables and our final formula.

a = 0.909
b = 0.55
c = 0.45 

 The resulting recommended bet fraction is 0.055, or 5.5% of your bankroll.

We should note here that Kelly betting is used to maximize growth, but it does come with a high risk if your estimated win rate is off or you run into a long losing streak.  In order to mitigate some of that risk, we would advise you to start with a half-Kelly approach, taking 5.5% of your bankroll and cutting it in half for each bet. 

Mental Obstacles to Conquer in Order to Better Understand Variance in Sports Betting

Knowing how most amateur bettors misuse and misunderstand probability will go a long way in helping solidify the concepts above in your mind.

The Gambler's Fallacy

The first mental obstacle to overcome is the gambler’s fallacy.  This is the assumption that past outcomes have an influence on future events.  For example, if you flip a coin heads 10 times in a row, there is still only a 50% chance the 11th flip will be tails.  However, if you ask most novice gamblers, they’d be willing to bet a much larger amount on tails for that 11th flip, even though the expected outcome for both heads and tails is exactly the same (50%).

In a Monte Carlo simulation, we used a sample of 100 games, betting $110 to win $100 on each, giving every game 55% probability of winning.  In this example, we ended up with an overall record of 57-43 (57%) and a profit of $970.  That’s a great return, however, there was a point in the simulation where five games in a row lost.  At this point in the simulation we were down -$280 from where we started, but were still able to finish with a 8.82% return on investment (ROI).

Black Swan Events

This brings us to another mental obstacle for understanding variance: underestimating the occurrence of low-probability events.  In the scenario above, there was only a 1.85% chance (0.45^5) of losing five consecutive games.  How could this happen!?  You need to realize that these types of streaks are a regular occurrence and will inevitably happen to you if you are betting on sports - no matter how good you are! 

To drive this message home, we ran 30 more simulations with the exact same parameters.  27 of the 30 results had at least 4 losses in a row, while one had as many as 9 (an event with a roughly 0.08% probability)!  It is only in hindsight that we can’t believe a low probability event happened to us, but it is foolish to believe low probability events will never happen (in probability theory, these are referred to as black swan events). 

Are You Up to the Challenge?

Winning money betting on sports is difficult thanks in large part to short term variance.  The majority of bettors give up or go bust before they even really get started.  We have covered a lot of ground here, but we feel these ideas are of paramount importance to anyone who is serious about making money on sports betting.