## Betting on Sports (Part -1)

April 1, 2005

Can you bet on sports and make money? Let’s examine the question.

Attempt #1. If you knew for certain that North Carolina is going to win, then for every \$1 you bet on that win, you would get back \$5 (for a profit of \$4). (Those were the odds offered in mid-March 2005. For current odds on sporting and other events, see TradeSports.com web site. )

The flaw is obvious: how can you know for certain? Illinois is a good team too. Even though you favor North Carolina, you cannot really be sure. So, let’s try again…

Attempt #2: Suppose you are “flexible”. You figure that if any other team were to beat N.Carolina it would be Illinois. [You would not be alone, these two are the ‘favorites’.] Today, the odds on Illinois are similar to those on N.Carolina (put down \$1, get \$5 if they win). So, you can bet \$1 on each. Then, you lose one of the dollars, but get \$5 on the winning team. Spend \$2 and get \$5 back… excellent investment. You’ve increased your chances of winning, by backing two teams. In return, you are shooting for a lower maximum return.

Taking this further, instead of the top 2 teams, you can bet on the top 8 teams. Today, you could bet \$74 and get \$100 if any of the top 8 teams wins.

The same fundamental flaw still exists. While you have increased the odds in your favor, you still realize that there is a chance of an upset.

Attempt #3: Instead of simply saying that one of the top-8 will likely win, suppose we were to quantify it. Suppose we assume that one of the top-8 teams has an 80% likelihood of winning. (Roughly speaking, in ten years that are similar to this one, you expect only 2 years where a top-8 team does not win.)

This is quite an assumption, but if we accept it, would it then make sense to bet \$74 on the hope of getting \$100? “Decision theory” would say that the “expected value” of the bet was (\$100 x 80%=) \$80. So, paying anything less than \$80 for it works to your benefit.

Let’s examine this idea. Even if the odds are in your favor, what if you cannot afford even a 20% chance of losing \$74? If so, you are outside the scope of Decision theory. The recommendations assume that the event is something that will repeat over and over. You will have many, many chances to bet \$74. You can easily afford to lose any particular bet, and over the course of many such bets, there is an extremely high likelihood that you will come out on top. The likelihood of losing on a single bet is 20%. The likehood of losing even 50 of 100 such bets is tiny.

Attempt #4: Suppose you make 100 bets of 74 cents each, and with 80% chance that each will get you \$1. With a single bet, there was a 20% chance you would lose all your money and an 80% chance that you would get \$100. In the 100-bet scenario, it is very unlikely that you will be right every time. Also, it is even less likely that you will be wrong every time. Instead (after some calculation), here are the numbers: There is a 94% chance that you will end up with at least \$74; there is about a 5% chance I will lose a little and end up with between \$70 and \$73. It is highly unlikely (less than 1 in 10,000,000) that you will end up with less than \$50.

Summary: Well? Can you make money betting on sports? (“Should you”, is a separate question.)

Turns out that we have to assume a context:
Assumed Context: the amount being bet each time (i.e. on each “independent event”) is not substantial; it is small enough that such bets can be repeated many times over the “lifetime” of our test.

Well, within that context, can one make money betting on sports?

Turns out that the answer is nuanced:

It is highly likely, but not certain, that you can make money betting on sports if the odds are in your favor.

Wait a minute! The odds being in one’s favor is another way of saying that your estimate of the odds is better than (closer to reality than) the estimate “reflected” in the odds being offered by the bookies or “the market”.

This is a huge assumption.

Can your estimates be consistently better or is that just a dream? That is the subject of another post.

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