52.4 – such an odd number. Where does that come from? Let me take you back to algebra class.
While we are on the subject, I’ll show how to calculate the winning percentage needed to profit given ANY line. I’ll also show how to work backwards and find an appropriate line given a team’s chance to win.
Finding the Break Even Point for Spread Bets
The line for the common point spread is -110. It looks something like this on a sportsbook site:
Team One -7 (-110)
Team Two +7 (-110)
This means Team One is favored by 7 points and that you must lay $110 to make $100 profit.
The reason the line is -110 and not even money is because all bookmakers charge a “vig” or “juice”, typically 10%. This is a 10% commission on all bets.
If spread bets were even money bets, we would only need a percentage greater than 50% to profit. How can we figure out the percentage we need if we are making -110 bets? Let’s do some simple calculations.
Calculations to Get 52.4%
Every time we win a spread bet, we are earning $100 in profit. Our winnings can be represented by 100 times the variable x, where x stands for the percentage of bets we win.
Winnings = 100x
Each time we lose a bet we are losing $110, because this is the amount we must wager to earn $100. Our losses can be represented by 110 times the percentage of bets we lose.
Since we are already using x to represent the percentage we win, we can use 1-x to represent the percentage of bets we lose. Remember that all percentages must add up to 1. So if we win 60% of our bets, or 0.6, then we must lose 40% of our bets, or .4 Ties/pushes are always excluded from the calculations since they do not affect the final profit.
Losses = 110(1-x)
We now have an equation for winnings and an equation for losses. If we subtract our losses from our winnings we will get total profit.
Profit = 100x-110(1-x)
Now that we have this formula, we can plug the number 0 into “Profit” and solve for x to find the percentage we must win to achieve 0 profit, our break even point.
At this point we can easily plug this into our calculators or use the ever-powerful WolframAlpha to solve. You could always solve it algebraically by hand but that takes longer and is not necessary in the days of calculators.
Plugging this equation into WolframAlpha, it tells me that x=11/21. What is 11/21 as a percentage? It is 52.38% which rounds up to 52.4%. Bingo!
Using a General Formula to Find % for ANY Line
Now that we have this formula, we can generalize it to find the break-even point for ANY line, not just -110.
Our current equation is 0=100x-110(1-x), right? The 100 is in there because that the amount we win with each correct pick. The 110 is in there because that is how much we lose with each incorrect pick. Let’s replace 100 with W (for amount won) and replace 110 with L (for amount lost).
General Formula to Find Break-Even Point: 0=Wx-L(1-x)
Now we can plug in numbers from ANY line that Vegas sets and solve to find x. Let’s do an example. Pretend you are someone who always buys an extra half-point in NFL games, turning your lines from -110 to -130. When you win a bet, you still win $100, but you now lose $130 when you make an incorrect pick.
Let’s plug that in: 0=100x-130(1-x) and then solve for x using WolframAlpha. I got that x=13/23 or 56.52%. Now you know that the break-even point is up to 56.5% from always buying that extra half-point.
One more example: say a moneyline bettor loves betting underdogs in the +200 to +300 range. He figures the average line for his bets is +240. Now the bet size is only $100, which is what he stands to lose. His winnings will be $240 on each win.
Plugging this in, we get 0=240x-100(1-x) and determine that the bettor needs to hit his +240 bets at a rate higher than 29.4% to profit.
Working Backwards: Finding the Appropriate Line
We are all trying to find value, but how do you know when you’ve found it? If the bet is even money, it’s simple. The team you think will win is more valuable in an even money bet, obviously.
We already know about value for -110 bets. If a team has greater than a 52.4% chance of covering the spread, they have value.
What if a team has a line of -200? Are they valuable if they have a 55% chance of winning? A 60% chance? A 70% chance? What will it take?
Up until this point we have been using lines/odds to calculate the win percentage needed to profit. Now we are going to do the opposite. We will be using expected win percentages to find whether the Vegas odds are accurate or are too low, which means value is present.
Remember our general formula from earlier? 0=Wx-L(1-x). Keep it handy. We’ll be using it.
Finding Value by Working Backwards
Alright! Let’s do an example so we can see what goes where in our formula. Imagine you are intrigued by an upcoming game. I’ll use this past Thursday’s Jags-Titans matchup.
Before you check the Vegas lines, you do a ton of research/handicapping and conclude that the Titans have a 60% chance to win this football game. In your eyes, Tennessee is the favorite. Favorites have negative odds, meaning one typically bets the line to win $100.
Since the chance of winning (60%) and the amount you could win ($100) are each known, these can be plugged into the formula.
This leaves us with only one unknown variable: L. Remember that L stands for the amount we would lose with an incorrect bet. For a favorite, L is the line. Using WolframAlpha, we can solve for L, finding that L=150.
This is great! It means that a team who wins 60% of the time will break even with a line of -150. Now we can check the posted moneyline for the game, knowing that anything more favorable than -150 means the Titans have value but anything less favorable than -150 means they are overpriced by Vegas.
Checking the odds, we see:
Since the Titans are -210, we should probably stay away from them since we only give them a 60% chance to win. This means that -210 is a -EV line. Since the Titans are overpriced in our eyes, we could always check the Jaguars’ line to see if they have value. If we give the Titans a 60% chance to win, then we must give the Jaguars a 40% chance (excluding ties, like always).
We can plug 40% into our formula for x and plug 100 in for L, because with underdogs we typically only bet $100 to win the line.
That gives us: 0 = W*0.4-100(1-0.4) which allows us to easily solve for W, or the amount we stand to win. Remember, for an underdog W is the line.
WolframAlpha says that W=150 which means anything more favorable than +150 odds gives the Jags value. Since the Jaguars are listed at +175, we would want to jump all over that line since we valued them at +150.
Why Would I Handicap Before I Check Lines
If you check the lines first, you risk falling for the spread storyline. Handicapping is much less biased when the Vegas spread is not in the back of your mind. If you see a large spread in the NFL, like -13, it is difficult to avoid thinking, “they are definitely going to win”. In reality, the team might only have an 80% or 90% chance to win that game.
Become comfortable at handicapping before checking the spreads and your pick game should improve by leaps and bounds. As your ability to accurately handicap improves, your chances of spotting glaring discrepancies in the spread will increase. This is being proactive rather than simply reacting to what Vegas determines.
Use this information to find value, filter out bad bets, and maximize profits across all sports, not just the NFL.