Sports Betting - A Numbers Game

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The act of sports betting is a numbers game. It is about theoddsmakers setting odds and about the sports bettor factoringprobabilities. We have written extensively on subjects suchas betting value, why we do not use moneyline bets, the problemswith parlays, shopping lines, the fallacy of blind trend analysisgiven the concept of regression, calculating moneyline breakeven percentages, etc, etc. Suffice to say, we are steeped inthe belief that understanding the mathematics of sports wageringis enormously important for one to have a legitimate probabilityof beating the odds over the long haul.

It makes our stomachs churn to see otherwise intelligent folksdisregard the significance of playing in a manner that can potentiallyincrease his or her chances of winning. For whatever reason, logicflies out the window for most when there is money to be won. Thishuman tendency fuels most of our articles and is also the inspirationfor this several part series entitled “What are the Odds?”This of course is Part 1. In as much, it makes sense to startwith the basics and also with a glaring example of poor probabilities.

Let's first take a quick look at the word probability.The dictionary definition is; the likelihood that a given eventwill occur. The statistical definition is slightly more complex,but basically carries the same meaning; A number expressingthe likelihood that a specific event will occur, expressed asthe ratio of the number of actual occurrences to the numberof possible occurrences. Proper interpretation of this wordis integral to the sports bettor, as it provides the frameworkby which to assess probability vs. posted odds.

In past articles, we have made such statements as; shoppinglines at five different sportsbooks vs. playing at just onesportsbook gives you a much higher probability of winning thanlosing. Or we will say; frequently playing (-200) and abovemoneyline favorites in baseball will decrease your probabilityof long term success. These statements do not imply that playingat only one sportsbook will keep you from winning or that itis impossible to win betting -200 favorites over the long haul.For us to say this would be entirely untrue.

The Surgeon General of all people has made the statement smokingcigarettes causes lung cancer. We hate to say it, but Mr. SurgeonGeneral could not be anymore incorrect. To say smoking cigarettescauses lung cancer would imply that everyone who smokes cigaretteswill get lung cancer. This is not true, as many people aroundthe globe smoke without getting lung cancer. What he shouldsay is; smoking cigarettes increases your probability of gettinglung cancer. Similarly, this is why we always attach the wordprobability to our concepts.

At times, however, we will have one of these theories refutedby a reader. Said reader usually illustrates their point byclaiming he or she has in fact beaten the number, or at leastknows someone who has, using a contrary method to which we havepresented as a low probability path to success. But this isnot at all surprising. Individual cases of defying odds arequite frequent, whereas the masses defying the odds are impossible.

For example, California has a state run gambling operationcalled *Superlotto. The idea is to pick 6 numbers and matchthem to six selected from 51 numbers. The risk is $1 and thepayout for matching 6 of 6 can often be well into eight-figures($10,000,000+). Picking six of six sounds like fairly decentodds given the payout … right? At the same time, a fiveteam parlay may seem appealing given its payout. But these arewhat we term sucker bets, as they suck in people’s moneyby dangling a proverbial gold carrot in front of their nose.The gold carrot being the low risk vs. potentially enormouspayout structure. These bets play on the human weakness of greed.

So what exactly are the odds of matching 6 of 6 numbers out51? Are the odds 1 in 100? 1 in 1,000? How about 1 in 10,000?No, all three of those guesses are wrong, as the odds of picking6 of 6 correct out of 51 come in at precisely 1 in 18,009,460.So perhaps it is less straightforward than it looks. The goodnews is that if you buy 100 tickets a week, you can expect towin the jackpot on average every 3,463 years. If you buy $25,000worth of tickets a week, you can expect on average to win aboutevery 14 years.

But the really astute lottery player prefers the pick 6 inTexas, as the odds are much better. That is, in Texas you picksix and only have to match them with 50 numbers—ratherthan 51 in California—for the same $1 buy in. So what arethe odds of winning in Texas? Instead of us busting the companyabacus on such a formula, we’ll refer back to an articlepublished in May of 2000 about the Texas Lottery on the MotleyFool web site.

“There are 50 possibilities for the first number, then49 possibilities for the second number, then 48 possibilitiesfor the third number, then 47 possibilities for the fourth number,then 46 possibilities for the fifth number, then 45 possibilitiesfor the sixth number. Now you get to find out how good yourcalculator is. If it doesn't fail on the calculation, you'llfind that 50*49*48*47*46*45 = 11,441,304,000.”

“This enormous number, then, is all the possible setsof 6 numbers, in a specific order. However, in the lottery,the numbers can be in any order. For instance, if 1 2 3 4 56 wins so does 4 1 3 6 5 2 and 2 6 5 1 4 3 and many others.If you have 6 numbers, the number of possible orders for themcan be counted in the same way as we counted the possible setsof winners. The first number can be one of the 6, the secondcan be one of the 5 left, and so on, so that 6 numbers can bein 6*5*4*3*2*1=720 possible orders. So the number of possiblewinning numbers for any given lottery pick is 11,441,304,000/ 720 = 15,890,700. Our odds of winning are one in about 16million.”

So what does all this mean in terms of probability? In California,we would need to have a jackpot of at least $18,009,460 to geteven odds on our $1 at risk in a Pick 6. In Texas, we need atleast $15,890,700 to have even odds on our $1 at risk. So ifthe jackpot rises above either of those thresholds, one couldpresumably say the lottery is a fair deal. That is, if you couldafford to buy 18,009,460 lottery tickets, you statisticallyshould grab a winner in there somewhere. Unfortunately, thisequation has left out two additional mathematical variablesthat need to be considered.

For matters of simplicity, we will totally ignore the factthat people winning the lottery rarely get the stated amount,but rather payments over 20 years or an option to take halfthe total amount all at once. But let’s suppose this ruledoes not exist. Sadly, the rule that does exist is taxes andthose cannot be dismissed; sure as death some would say. Basically,about 50% of the jackpot goes to Uncle Sam. This puts the dollarat risk equation in California’s Pick Six Superlotto to$18,009,460 / .50 = $36,018,920 for breakeven. But in orderto net $36,018,920 in cash, the payout would actually have tobe $72,037,840.

So our 18 million to one break-even point has been lifted toroughly 72 million to one. That is a 400% increase. In NFL terms,that is like a touchdown favorite moving up to -28. Or a -110favorite in baseball being priced at -440. Suffice to say, thesenew odds do not carry much long term value. The oft malignedsports gambling world offers much fairer odds to shoot at thanthese government sponsored rackets. The word hypocritical comesto mind. How can they simultaneously try to ban offshore gamingbecause it is detrimental to Americans when their gambling operationsare holding about 4 dollars for every one paid out. They areno different than any casino or sportsbook, except that thestate run lotteries offer absurdly high vigorish ... juice …house take if you will … or better yet, the “WhiteHouse” take as half the winnings go to Uncle Sam.

Oh … and based upon lottery history, it is very rare thatone person takes home all the loot. Only four times in Californiahistory has a single individual won more than $72,000,000. Moreoften than not, the jackpot is shared by several people. TheMotley Fool article quoted the average as 6 per jackpot in Texas.Theoritically, if the average jackpot is split into six pieces,it would need to be $432,227,040 to be an even return on $1at risk.

So the question then becomes; is the lottery a high probabilitymethod of earning money? We would say not and may in fact writean article about it (whoops, we just did!). But here is theproblem. The New York Times reported a New Jersey lady won thelottery jackpot not once, but two times already. And if we publishsuch an article, she may write us rebutting our silly conceptof the lottery being a sucker bet. After all, she along withseveral other folks have enjoyed terrific success playing lotto.Maybe we should hire this lady from New Jersey as a handicappingconsultant? Sounds like she knows what she is doing, havingbeaten the 72 million to 1 odds twice already.

We will be publishing another installment of “What arethe Odds" as soon as possible. We have a significant amountof tangible examples floating around that will in all hopesclarify common mathematical errors we all make when it comesto risking our hard earned money on ill advised methods of wagering.Good luck in the meantime and remember, logic is the best friendof a gambler.

*California has since changed their Superlotto Pick 6 to aSuperlotto-Plus Pick 5. And no, the Pick 5 is not a good beteither! Note that state records indicate California Lotteryticket sales have generated better than $40,039,388,667 overthe past eighteen years. The total payout during the same timespan has been $20,309,533,526. Subtract taxes from the prizemoney, and the ticket revenue to payout ratio climbs to about400% in favor of the house. Not surprisingly, that 400% houseedge correlates exactly to the calculations performed above.

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