Sports Betting Is An Excellent Way To Lose Money

I have never, and maybe you, too, have never met any gambler who is not ahead overall, or at least even. Sure, every gambler will admit to losses here and there, but all of them are positive that, if you add up all the wins and losses, they are a little head, at worst about even. Or soon will be. And don’t forget, they will quickly remind you, of that one time they took home that enormous jackpot.

Anyway, they’re only doing it for the entertainment. Me, I don’t find it so enjoyable micturating away \$100 into the wind. But some find pleasure in it.

There are about a dozen major sportsbook apps, with many smaller popping up, and crapping out (thank you), all the time. Here’s one list. Ads for them are appearing everywhere, usually with a grizzled athlete doing a cameo. I think I saw Wayne Gretzky in one. I’d like to believe Gordie Howe would have punched in the mouth anybody who asked him to sell gambling.

Don’t do it. Don’t bet. But if you are determined, sports gambling is a terrific way to lose money. It’s also a good way to turn entertainment, i.e sports, into something which appears consequential and full of deep meaning. When instead it is just men playing a game.

Here are some basic calculations. These aren’t exactly unknown, but below I show you consequences of them I haven’t seen presented anywhere else.

How It Works

Right now, FanDuel lists these moneyline bets for which team will win the Super Bowl:

There are 14 as of this writing (Wednesday, 7 January, around 4 AM), but I can only screenshot the top (I have no idea why the screenshot is so blurry). They let you only bet one of these.

These are “moneyline” bets, which are simple. If you see “+x”, it means if you bet \$100 you win x: if you see “-x” it means you must bet x to win \$100. Bet \$100 on Seattle and you can win \$390 if the Seahawks win, for instance.

Moneylines aren’t probabilities, and to do any calculations about “fair” bets (see also the Powerball video), we need probabilities. We can recover them easily enough, and also learn about the vig, or vigorish, i.e. the cut FanDuel (or any sportsbook) takes.

Math alert! SKIP this section you want to get to The Meat.

Implied vig-probabilities are pv = x/(x+100) if the bet is “-x”, or pv = 100/(x+ 100) is the bet is “+x”. These are the implied, conditional probabilities with the vig. To recover the conditional probabilities without the vig, sum all pv and divide each by the sum. I.e. p_i = p_i/sum_i (pv_i), for each bet i in a particular gamble. You have to do the calculation over all possible bets in a gamble.

The vig is then sum_i (pv_i) – 1. Multiply by 100% to get the vig percentage.

All the probabilities, vig or vig removed, are conditional on the amounts bet and on whatever internal algorithms the sportsbook uses to set their moneylines. About those algorithms, more at the end.

Recall all probabilities of any kind, any where, any place, with no exceptions whatsoever ever, are conditional on the information or evidence assumed. No event “has” a probability. Probability only relates to information/evidence held or assumed.

The Meat

Taking into account all the moneylines at the time I made the calculation, we get an implied vig-probability of 20.4% the Seahawks win. The total vig-probability of all teams is 115.9%, which means FanDuel take is nearly 16% cut of the bets. This is huge.

The vig-removed implied probability, conditional on the bets and whatever internal formulas FanDuel is using to encourage betting, is found by dividing each vig-implied probability by the total vig-probability. This gives the Seahawks conditional probability of 17.6%.

That’s a pretty big difference, almost 3%, from the vig-implied probability of 20.4%. Maybe not so much for the individual gambler, but big for the company.

The next question is whether these are “fair” bets. A “fair” bet is one in which the cost is less than the amount you expect to win, and where the amount you expect to win is the moneyline (with return of the amount bet) times the implied conditional probability (not the vig-probability).

If you bet \$100 on Seattle, then if you win you get the \$390, plus your bet back, for a total of \$490. Which gives an expected amount won of 0.176 x \$490 = \$86.30 (the math shows this is the same expected payout for any of the 14 teams). This of course is much less than \$100, so the bet is not “fair”.

Understand that this is all “on average”. What the sportsbook takes in as profit on any particular gamble depends on how much they can attract to each bet, and so on.

Of course, who wins the Super bowl is only one kind of bet, whereas most bets are in two-team competitions. The math is the same, however.

At this moment of writing, FanDuel lists -620/+460 for the Rams-Panthers game on Saturday (the 10th). This means you must bet \$620 to win \$100, if you take the Rams, or you must bet \$100 to win \$460, if you take the Panthers. The vig-probabilities are 86% and 18%, respectively. Which summed gives 104%, which means the vig is 4%.

The conditional vig-removed probabilities are thus 83% and 17%. The expected amount won is \$96.18 (for either side). Which is also less than \$100, so the bet is not “fair”.

On average you will lose about 4% of your bet amounts, with vigs of 4%. Some bets as we saw have higher vigs, a few might be a tad lower. The vig will always be greater than 0.

Calibration

That “on average” only applies, however, if the FanDuel algorithm guarantees calibration. This basically means the conditional vig-removed probabilities line up with actual outcome frequencies.

I have no idea of FanDuel’s (or any sportsbook’s) internal metrics, but the hope bettors have is that the moneylines are not calibrated, and thus bettors can find an advantage. Rest assured FanDuel (and any bookie) knows of this, which is why they sometimes change payouts to encourage money to flow to one side or another of a gamble. The end result is likely going to be close to calibration. Which means you will lose, on average.

This also means no team has a probability of winning/losing/covering-the-spread, whatever. These are all internal conditional probabilities, and nothing more.

There lies the problem, and the hope. The moneylines are a combination of amounts bet, which are classic “revealed preferences”, and whatever internal algorithms to encourage betting the sportsbook uses. The probabilities are conditional on that information/evidence. The gambler might believe he has different evidence, which of course changes the probabilities for him.

For instance, the gamble is in college sports and the gambler has an in, and knows the game will be thrown, or he has hopes it will be. Same goes for any other kind of “inside knowledge” the gambler thinks he has. The conditional probability for the gambler is then different than the sportsbook’s. He can make money if the difference in probabilities is big enough and his information is accurate. Even here, sportsbooks are careful to limit amounts that can be gambled. Bookies are in business to win, and don’t like losing.

Cruelty

One survey (dividing through by all the distrust we have in surveys) says most gambles are at the \$50 mark, and that the average gambler bets a little over \$3,000 a year. Depressingly, most said they gamble to make some extra money. If they want to make extra, they should become a bookie. Alas, there are two known monopolies who discourage entry into this lucrative field.

With bets of \$50 and with \$3,000 total bet, that’s about 60 bets a year. Let’s see how that might play out for some average people.

The Other Side

Let’s see how “on average” gamblers play out. We’re just guessing here, since I don’t have any sportsbook inside statistics. Let’s suppose, though, that we have a lot of Average Joes who each makes 60 \$50 bets, taking the favorite half the time, and half the underdog. We’ll also suppose our Sportsbook is on the ball (thank you) and calibrates their moneylines.

We’ll use the -620/+460 for the Rams-Panthers game as our running example, with it’s lower-than-average 4% vig. Assuming calibration here means the Favorites win 83% of the time, and the Underdogs 17%. A \$50 winning bet on the Favorite brings in \$7.69 (in addition to the original \$50), whereas a winning \$50 bet on the Underdog brings in \$230 (in addition to the \$50). A losing bet brings out \$50. Right outta your wallet.

I’ve seen reports that sportsbook betting is now about \$1.5 Billion a year, and growing. With our 50,000 Joes each betting \$50 each for 60 times, we have \$150,000,000, or 10%, of the \$1.5 Billion. That 10% market share, which seems about right for one Sportsbook. But I’m just guessing. If you have better numbers, let me know.

The assumption is each Joe bets \$3,000; i.e. he has a pool of money he draws on, keeping his winnings separate. That’s not how everybody does it (some if they get any amount ahead, only bet that surplus), but this isn’t far wrong, either. Some will come away with more than \$3,000 at year’s end, and some less. Here’s what a picture of 50,000 Joes could look like, using our example numbers. This is the Sportsbook’s view.

The mean money won was –\$122.20, which is to say, a loss of one hundred twenty two bucks per Joe. The median money won was –\$160.20 (a loss!). One person lost \$2,021. Some did win. But only 41% won. Which means 59% lost. It’s not 50-50 because of the moneylines were not 50-50.

Some 17% didn’t lose anything and won as much as \$235 (the interval \$0–\$235). That \$235 or less is 75% of all Joes. Only about 4% of Joes won more than \$1,000 (on top of their bets). The most anybody won was \$2,474.90. It’s this guy that seduces the rest.

If Joe invested his money, perhaps in the bank, compounded annually at 4%, he’d have made \$120, which is better than 69% of the gamblers. And would have been 100% sure of not losing any money.

The Sportsbook raked in a gross profit of \$6,108,610. Which is not bad.

Now consider the guy who lost the two grand. This is bad, but it isn’t exactly devastating (for most). He kept one-third of his money at year’s end. He didn’t go bust. Which leaves him hope that next year he may be one of the winners. Which is bad, because as we’ve seen, it isn’t likely. And he didn’t lose it all at once.

Here are six typical Average Joes, and their changing Bank (amount won or lost) through time:

Joe 1 (J1) lost a few early bets, but stuck with it, and then hit a winning streak, which was loath to abandon. He ended up about even. Joe 2 started by losing, then almost hit even, which encouraged him (we might believe) to keep at it; and he even had a brief winning streak half way through. He never lost his optimism, but he did lose his money.

And you can paint similar pictures for the others. It’s hard to be consistently down, or up. There are always respites on the way down which give hope that just a few more bets will bring us back into the black. Even Joe 4 (J4) hoped he could keep streak flying, but was disappointed in the end.

It’s the nibbling away, with a few hits, that gets you. You never really see the end coming.

Conclusion: Sportsbook betting is a good way to lose money.

Video

This has additional information.

Here are the various ways to support this work:

• Subscribe at Substack (paid or free)
• Cash App: \$WilliamMBriggs
• Zelle: use email: matt@wmbriggs.com
• Buy me a coffee
• Paypal
• Other credit card subscription or single donations
• Hire me
• Subscribe at YouTube
• PASS POSTS ON TO OTHERS