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Expected Value

Expected Value and Bankroll GrowthAn effective money management strategy is essential for any long-term wagering success.  Without it we can be assured of a few things.  First, and this is the best case scenario, we will earn money, but not as much as we should.  In short, we won’t maximize our potential.  The other scenario, we lose money when we shouldn’t or at a faster rate than we should.  Both of these options are unacceptable to the professional investor.  We don’t leave things to chance, or hope for luck.  So how is it we find and implement the proper money management formula?

A proper strategy must accomplish two goals.  First, it must allow us to maximize our winnings.  If we have a bankroll of $1000 and we win $100 that’s a 10% increase.  But if we have the same opportunity when we have a $2000 bankroll and we still only earn $100 then we’ve only had a 5% increase.  Any good formula should solve this problem.  Second, it must protect against losses.  This is usually the clearest sign between a professional investor and a gambler.  When the gambler goes on a losing streak he becomes emotional and bets even more money on the next game.  This is called chasing the money and it’s a guaranteed way to go broke.  The correct procedure is to bet less at that point because your roll is smaller.  We have to look at percentages instead of dollar amounts.

The way to achieve both of these goals is to use a proportional betting system.  This means we bet more when we have more and less when we have less. Throughout the years many have tried to develop systems but only one can be recognized as the best, the Kelly criterion. This system was originally described by J.L Kelly Jr. in a 1956 issue of the Bell System Technical Journal.  Edward O. Thorp later demonstrated its practical use in a 1961 address to the American Mathematical Society.  He later included its use in two books he authored, Beat the Dealer (gambling) and Beat the Market (investing).

A rigorous mathematical proof of the formula can be seen in many places.  This includes the books he has written along with Wikipedia and many other articles.  We won’t go into the actual formula here, but we do encourage you to view it for yourself. We have a calculator so you can see how it works.  The formula was originally applied to individual events.  When that happens it’s very straightforward.  However, for our uses we had to change it slightly.  What must be kept in mind is that the majority of the time we will have multiple bets open at once.  This is due to games being played at the same time, an unavoidable circumstance.  We can’t bet the same as a single bet, all the bets combined would leave us with too much exposure.  Also, the formula applied to the stock market doesn’t translate exactly to our market.  When buying and selling a stock even in the event of a loss you don’t lose everything, you sell the stock for some money.  In sports investing there are no fractions, only an outright win or loss.  Keeping these differences in mind we tweaked the formula so that it still offered all its original and intended advantages while applying directly to our field.

When looked at mathematically, the advantages of proportional betting are hard to argue with.  As opposed to other ways, such as the flat bet, we can easily see the difference.  Even critics of the Kelly Formula rarely argue against proportional betting, only against the actual numbers this formula uses.  The main problem they have is their objection to being able to accurately predict the win percentage.  We solve this problem be applying our formulas to many past years data and arriving at an accurate winning percentage estimate.  Even though this formula wasn’t initially intended for handicapping sports, we make it work for us.  It would be a shame to take something as rare as a true and consistent formula for handicapping the winners and hamper it with an ineffective money management system. Explore the advantages a proportional betting system gives you.


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