Betting Math, Probabilities & The Book’s Real Motive

On Sunday (January 22nd, 2023), I received a lot of similar questions regarding why the prices on the NFL Divisional Playoff games seemed off given the market action.

1) Why was the book at -6…the highest price of the week if they were so overextended with Cincinnati liability against Buffalo?

2) Why was the book “only” at -3.5 for San Francisco if they were so overextended with San Francisco liability against Dallas?

The biggest horseshit myth of the bookmaking business, that is repeated year after year by the talking heads in the media, is that as a bookmaker you want to get equal action on each side of the market. Thereby, you profit from the vig. Sounds good, and the math checks out, but that’s not what real bookmakers are trying to do.

Your goal as a bookmaker is to get your clientele to bet as much money as possible on prices that are -EV (negative expected values). What is expected value? Simply put, betting something that carries a negative expected value (“-EV”) means you are wagering on something that has an expectation to provide you a negative return on investment over the long-term. Your goal is always to bet +EV wagers. The “+EV” means positive expected value. The expectation being that using +EV wagers will provide you a positive return on investment over the long-term.

Now back to our friendly bookmaker. Your goal as a good bookmaker is not equal action. It is to have -EV prices hanging on BOTH sides of the market (sides and totals). You don’t care if 100% of the money is on Team A -5 or on Team B +5…if both sides are -EV, you are golden! You, as the bookmaker, might lose that specific market, for that day, but over the long-term you will make a fortune if all the bets you book are -EV prices for the bettors placing them. It’s simple math. It’s the same math that if you as a bettor only wager on +EV angles and situations, you might lose today, tomorrow and the next day, but over the long-term you will grind a fortune.

It is tough to have a market priced where both sides are -EV. In most cases, just due to the math of it, you have markets where one side is -EV and the other side is +EV. It’s just a matter of degree as to the value, or lack thereof, on one side of the wager versus the other. As a bookmaker, you would be quite happy with 99% of the money on the -EV side, and 1% on the +EV side. The preceding sentence is a perfect situation, and it is about as far away from “a book wants 50/50 action on each side” as you can get in a market, yet the book would LOVE it!

What does this mean for this past Sunday? If you take a deep dive into the prices…

Buffalo opened -4 and ended up at -6, despite Cincinnati getting the majority of the money in that market. Why would the book do that? Is it because they are stupid and decided it is time to give away money? Is it because the book miscalculated? Unlikely, given how a sports betting market works and how the book gleans information from the sharp and public bettors in the market to sharpen the number. Why not lower it to Buffalo -3 to try and draw Buffalo money to get to that Holy Gail of 50/50 money split every book supposedly wants? It is because the bookmaker sees Cincinnati +6 as a -EV wager and Buffalo -6 as, at worst, a small +EV wager. So, why drop the price to -3 and perhaps make Buffalo a BIG +EV wager in the process? You don’t want to dissuade bettors from betting negative values by making the price worse to awful for them…you want to suck them in. It’s really the theory behind the Book Position.

So, we have a perfect market…we are booking good volume on -EV Cincinnati at +6, and we aren’t taking in a ton of money on the small +EV side of Buffalo -6. Perfect for the bookmaker!

As a bookmaker you want to give bettors on the side with the heaviest volume the WORST negative expected value price you can that will not dissuade the sheep from betting. The more money bettors place at a -EV price means the more dollars your inherent edge will grind out of those bettors. At the same time, sharp money knows the value side of the wager is Buffalo but likely not as much a value at -6 as it was at -4, so they don’t bet it heavy. If -6 were an amazing value then sharp money would hit it hard enough to force books to go to -6.5 so they can push back sharps and attract even more public money on the -EV side (i.e. Cincinnati now +6.5). “Wow! Cincy up to +6.5…it’s a lock…I can’t pass that up,” says John Q. Public.

It’s the same theory with Dallas and San Francisco. San Francisco opened at -4 and closed at -3.5. Everyone was betting San Francisco, so why not go to San Francisco -4.5 or -5? It’s because you are painting a masterpiece as a bookmaker where you can give San Francisco bettors a very attractive -3.5 price (which is why people see this as “only” -3.5…because it seems so low and so good) while at the same time not giving sharp money such a juicy +EV price of +4.5 or +5 (or better) that they hammer you on the other side (in this case Dallas).

So what can we deduce? If nothing more…because the book has San Francisco liability and Cincinnati liability, yet the lines are getting more attractive for both teams, it likely means the book is not scared of that money on either team because they see San Francisco -3.5 and Cincinnati +6 as -EV wagers…so bet away Mr. Public!

Does it mean both wagers win? Of course not…and we eventually saw NEITHER wager won. However, that will not dissuade the book from doing the exact same thing this weekend? It’s the Law of Large Numbers! Unlike casual sports bettors who panic if they can’t win 80% of their bets, the book knows if they can hit just 50% of the -EV sides, thanks to vig, they will make a FORTUNE! If they can hit more of the -EV sides than 50%…now we are really making money!!!

The public won Sunday on the -EV sides, but on Saturday the public went 0-2 on the -EV sides (Kansas City and public dog NY Giants). The book went 2-2 on the weekend with -EV sides…and gets the benefit of vig!

So, TSP wrote this up because he was telling us to HAMMER Buffalo and Dallas? No, TSP wrote this to inform you on how bookmakers operate…real bookmakers who practice the art of bookmaking…not this pussy bullshit you find at DraftKings, BetRivers, PointsBet, FanDuel, William Hill (WH is a disgrace), etc.

I was not predicting what was going to happen. I was just deducing that the value sides on Sunday WERE NOT Cincinnati nor San Francisco. Which then leads me to believe that Buffalo and Dallas ARE the value sides or at worst, the less -EV side.

Side note: I changed the percentages in the math section below to 53% and 47% because it shows how even a 53% probability (I used 55% in the initial article) can provide an edge in a parlay.

What does all of the above mean? If the assessment is correct and let’s pretend Buffalo and Dallas are the value sides, however minor, then each team has at least a 53% chance of covering the spread. Not a “Lock of the Year”, 85% chance of winning, but a long-term positive grinding 53% chance.

If you really want some math…

The chance of two 53% probability outcomes occurring together (meaning Buffalo and Dallas BOTH cover) is 28.09%.

The chance of two 47% probability outcomes occurring together (meaning Cincinnati and San Francisco BOTH cover) is 22.09%.

The chance of one 53% probability hitting (Buffalo or Dallas covering) and one 47% probability hitting (Cincinnati or San Francisco covering) is 24.91% in each combo (Buffalo and San Francisco or Cincinnati and Dallas)

So, here’s what we have for probabilities of the possible outcomes…

Buffalo and Dallas cover 28.09% chance

Buffalo and San Francisco cover 24.75% chance

Cincinnati and Dallas cover 24.75% chance

Cincinnati and San Francisco cover 22.09% chance

A two team spread parlay pays out at +264. A payout/moneyline of +264 implies a 27.47% chance of the outcome occurring.

Do you see what I see? A Buffalo -6 and Dallas +3.5 parlay will pay +264 and implies I have only a 27.47% chance of hitting this parlay…BUT…I know because of the math I did above and knowing the value sides that I actually have a 28.09% chance of hitting this parlay. So, the book is paying me out as though my chances are 27.47% of winning, but my chances are 0.62% higher at a 28.09% implied probability of winning this parlay!

Yes, my friends…this is value. Anytime the chance of something occurring is greater than implied probability calculated by the book, and displayed as the bet price/odds for that wager…you have value on your side. My chance of winning this two team parlay is hardly 90%…in fact it is only 28.09%, which means there is a WHOPPING 71.91% chance I DO NOT WIN this parlay. However, because the +264 payout is based on only a 27.47% implied probability, I am making out on this deal thanks to my actual 28.09% chance of winning! The tiny 0.62% difference represents the probability edge I have over the house and how I will grind my long-term profits on a wagering situation like this one.

If I always bet when the percentages favor me in the way displayed above, I will never lose in the long run. Short run…sure I will lose, maybe even badly from time to time…long run…the math always wins!

As we saw for the above example, the parlay didn’t win, but that’s gambling. There was almost a 72% chance I wouldn’t hit the parlay…and that’s where she fell.

HOWEVER…even though the bet lost, we did get some inside information from the book based on how they treated the teams in these markets and what they did with the prices? Are you ready?? It’s going to mean more reading, but it will provide you a little angle to use in future wager assessment/handicapping.

The inside information the book gave us through their price moves relates to how they rate these teams.

The book was not scared of all that Cincinnati money nor the San Francisco money, despite the liability to both teams. It tells us that the book views these teams as overvalued by the gambling public. Hence why these teams were seen as -EV by the book. Overvalued teams win all the time, every single day. However, over the long run, betting against the overvalued teams will generate a profit.

What does this mean moving forward? It means that there is a good chance, given these overvalued and heavily bet teams won, that these teams will be even more overvalued in the week ahead.

Does this automatically mean that Philadelphia and Kansas City are undervalued and the bet to make? Not necessarily. We need to do the same assessment for those two teams as well.

With Philadelphia, the public was HAMMERING the NY Giants and the book moved Philly from -7.5 to -8 despite all this action. It tells us the book was not worried about the Giants money and the Eagles were undervalued, with the Giants being overvalued…hence why the book didn’t mind making the Giants price better from +7.5 to +8.

With Kansas City we can’t get much of a read because unlike the other three games, the money was on Kansas City and the line moved with Kansas City, not against Kansas City like the other three games this weekend. So, nothing really to easily go on for assessment. The Mahomes injury also complicates this read given he is a key player.

When we look at the market action this week, we now see the money leaning to Philadelphia, but a lot of that money was booked at -1.5 and -2…not the current -2.5 price. Most of that money was sharp money too. So, perhaps our deduction on Philly being undervalued and San Fran overvalued was on target because as soon as the game opened, sharp money jumped on Philly and the book realized they made the price too much against San Francisco and thereby moved up from Philly -1 to -2.5.

What about Cincy/KC? There is little sharp money involvement so far, the bulk of the money is public money hammering Cincinnati. The line has moved from KC -2 to Cincy -1.5 with this action! The Mahomes injury possibility complicates the read here. However, we could assume that at some point Kansas City will be a value. Why? Well at some point every side of a wager becomes a value. However, for our purpose, we know Cincinnati was overvalued in its last game, then they upset the Bills, plus the Mahomes angle is likely making an overvalued team (Cincy) even more overvalued as the public overcompensates for the Mahomes injury. Given the book knew the public love for Cincinnati after the Sunday action against Buffalo, and it knew of the Mahomes injury prior to Cincinnati even playing on Sunday, the book likely was not going to set a price that opened with Cincinnati as anywhere near a value given the circumstances. So, since the book knew of the Mahomes issue when setting the opening price, we can assume Cincinnati +2 was not a value, and so Cincinnati -1.5 is definitely not a value.

Again, the above does not mean Cincinnati is a 95% guaranteed lock winner, but likely Kansas City +1.5 is a value proposition with a long-term win rate of 53%.

Yes, I am making some assumptions with the above, but seeing as we can’t predict the future, everything with gambling is an assumption in an effort to calculate the probability of an outcome and thereby locate the optimal price.

The above form of deduction isn’t going to print you money nor give you some incredible lock wagers moving forward. Just a little tool to have in your pocket for quick assessment of future games based on actions by the bookmaker given market & price dynamics of past games. Same theory works for totals as well. It works for any sport too.

Good luck!