Football season is finally here, and sports bettors are gearing up just as anxiously as the players. Maybe even more so. When thinking about your own betting strategy, this is the best time of year to ask yourself some fundamental questions to help you gain the biggest advantage. One of those questions is: When is it best to buy points against the spread? Or, maybe you want to ask it backwards: When is it best to sell points to get a bigger potential payout? These days there are so many options to bet alternate lines, it can be difficult and confusing to choose.
While I want to help my fellow bettors, I’m not the guy who can tell you which way you’ll get a bigger edge when pricing out alternate lines. What I can tell you is that calculating those edges is only step one in deciding which way to bet. Step two is calculating how much of an impact your bet is most likely to have on your overall bankroll. Once you do that, you may not want to bet the line with the biggest edge after all.
So how do you do step two, and why is there a difference between edge (or ROI) and bankroll growth? Because, in order to figure out how much bankroll growth you’ll average on a certain line, you have to factor in the amount of money you can reasonably bet on that line. That’s where the Kelly Criterion comes in, since it calculates the percentage of your bankroll you can wager for a given edge and odds so that you get most expected growth (EG) of your roll. Even if you never bet “full Kelly,” this calculation is important because, if you’re smart enough to bet a certain fraction of Kelly (1/3, 1/4, whatever you choose), then you’ll still be betting different amounts on different lines depending on their edges and their odds.
If you’re a huge math person, what this means is that what you really want to know when comparing alternate lines is the maximum expected growth (MEG) for each one. Luckily, it turns out there’s a very simple formula to approximate it.
MEG = edge2/(2*odds)
This “edge squared over twice odds” amount is typically very small, because it calculates the median change to your total bankroll from just one bet. So I’ll use a financial term called basis points (or 1/100 of a percent) to crunch those numbers. Since a 3% edge at standard -110 odds yields about five basis points of EG, each basis point is precious when talking about growing your bankroll the quickest.
If you like to keep the math simple, just think of the answer this way: If you have a 3% edge on a -110 line, then betting 1% of your bankroll (or one unit) is pretty reasonable. But, if you had that same edge on a -200 line, it would be just about as reasonable to bet 2% of your bankroll. When you do, you’re earning that edge on twice as much money, and your expected profit will be even higher. To see this concept in action, let’s look at an example from the Week 1 NFL slate and use the MEG to decide whether to buy (or sell) points for the game.
Say, for example, the Los Angeles Rams are getting 2.5 points against Buffalo at a price of -110. You estimate they have a 54% chance of covering, so you calculate your edge like so:
edge = b * p – q
edge = b * p – (1-p)
edge = 0.91 * 0.54 – 0.46
edge = 0.031 or 3.1%
Where:
b = net fractional odds of the bet (for American odds +200 → +200/100 = 2, -200 → -100/-200 = 0.5)
p = probability that the bet wins
q = probability that the bet loses, or 1 - p
That’s a pretty good line! But then you look at all the alternate lines, too. The ones you’re most interested in are buying points up to +7.5 and selling them down to -2.5. For the sake of our example, let’s say the Rams have a 68.5% chance to cover +7.5, and by line shopping on your favorite app you find the best odds for the bet are -200. You also calculate they have a 34% chance to win by a field goal or more, and for that -2.5 line you can get +200 odds. We can calculate the edges on those alt lines too, and compare them to the painted number:
edge on +7.5 = 0.5 * 0.685 – 0.315
edge = 0.0275 or 2.75%
edge on -2.5 = 2 * 0.34 – 0.66
edge = 0.02 or 2%
When you go to choose one of these three bets, then the answer is obvious, right? The +2.5 line has the biggest edge, so it must be the best bet. Case closed. On the other hand, you haven’t accounted for the MEG yet. Armed with our simple “edge squared over twice odds” formula, let’s take another look at those lines and see which one makes the most sense. For the Rams +2.5 line, we’d get:
MEG (+2.5) = edge2/(2*odds)
MEG (+2.5) = 0.0312/(2*0.91)
MEG (+2.5) = 0.00096/1.82
MEG (+2.5) = 0.00053, or 5.3 basis points
Similarly, for the +7.5 line, we’d get:
MEG (+7.5) = edge2/(2*odds)
MEG (+7.5) = 0.02752/(2*0.5)
MEG (+7.5) = 0.00076/1
MEG (+7.5) = 0.00076, or 7.6 basis points
And, for the -2.5 line, we’d get:
MEG (-2.5) = edge2/(2*odds)
MEG (-2.5) = 0.022/(2*2)
MEG (-2.5) = 0.0004/4
MEG (-2.5) = 0.0001, or 1 basis point
Now which line looks the best? It’s clearly +7.5, because, while its edge is slightly smaller than the edge on Rams +2.5, its odds are much shorter. Therefore, it’s less risky, so you can stake more on it and get a higher overall expectation. Rams -2.5 comes in a distant third place, even though it rates pretty close to the other two merely on the basis of its edge. In fact, given its longer odds, you’d need to estimate more than a 5.5% edge for it to have a higher MEG than you get for the +7.5 line. Do you see why?
The improvement in EG you get by buying points here may seem small, but successful sports betting usually comes down to finding small advantages and making the most of them. In cases like these, where the odds on alternate lines are significantly different, the way you make the most of that spot is to buy points only if it increases your MEG. This is true even if it decreases your edge a little.