The unique scoring structure of American football — three points for a field goal and six points for a touchdown before the extra point, which is worth one point, so long as a team decides not to try for a two-point play — clumps scoring differentials around certain key numbers. That makes betting on the NFL different from wagering on other sporting events: The key numbers should almost always dictate your approach to wagering on weekly point spreads.

Since 2015 — when the NFL moved extra-point attempts back from what was essentially a 20-yard field goal to a more difficult 33-yard attempt —** **15 percent of regular season games have ended with a scoring margin of exactly three points. That might sound small, but it represents the most frequent outcome by a significant amount. Nine percent of games finished with a differential of seven points, and seven percent of games were decided by six. Together, those margins have accounted for nearly a third of all games.

Of further interest to sports bettors is how often particular point spreads ended exactly on the number: with a three-point favorite winning by three points, for example. The push rate for a game with a point spread of three is nine percent; not surprisingly, that’s the highest push rate for any point spread other than 14, which has less than one-tenth the sample size. (In other words, far fewer games start with a point spread of 14.)

This type of information is critical to determining line value in the NFL, because it helps you determine the worth of acquiring an extra half point on a bet — which could turn a push into a win. (Sportsbooks allow bettors to “buy a half-point” — paying worse odds for the chance to move a point spread from -3 to -2½, from +7 to +7½, and so on.)

If this sounds confusing, don’t worry: Here’s a quick primer how you should approach several key numbers on the point spread. (Sportsbooks, of course, also offer odds on every quarter, every half and so on; these rules do not apply to those smaller-scale time frames.)

How to play a point spread of 3 and 7

If the point spread is three, you’ll want to either play the favorite at -2½ or the underdog at +3½, as both options give you the benefit of turning a push into a win in the event of a three-point final margin. (For beginners: Assume the Philadelphia Eagles are favored by three points against the Washington Commanders, and win the game, 27-24. Underdog bettors who took the Commanders would win if they had made the bet at +3.5, since the final margin was 3 points; Eagles backers who had Philadelphia at -2½ would also win. Anyone who had a three-point spread would push, meaning the stake would be returned with no profit or loss.)

Ideally, you can find a rogue or stale line of -2½ or +3½ at -110 odds (wager $110 to win $100), giving you an edge over the house. Here’s why. The true value of a -2½ or +3½ line when the consensus line is ±3 -110 is -130. (Avert your eyes if you hate math: that number is derived by factoring in the original implied probability at -110, 52.4 percent, and adding half the push frequency.) Thus, it becomes profitable to move off the three-point spread by playing the favorite at -2½ or the underdog at +3½, if the price better than -130.

Point spreads of seven should be played in a similar fashion. If moving off a 7-point spread at -110 odds, you need to find either the favorite at -6½ or the underdog at +7½, either at a price of -124 or better. This also illustrates that not all half points are created equal; the half-point adjustment on a 3-point spread has greater value. Why? It all depends on how often you expect the final margin to land exactly on the number in question. The higher the possibility of a particular outcome, the more valuable the extra half-point becomes.

How to play a point spread of 4 or 5

Games with point spreads of -4, -4½, -5 and -5½ have ended with a score differential of exactly five or six just 13 times in the past eight seasons. In other words, you are probably better off going with an alternate line rather than one of those point spreads. The benefit of an alternate line is acquiring a more lucrative price.

Let’s go back to a real world example. If the line for the Buffalo Bills in a game against the Miami Dolphins is -4 -110 and you can find an alternate spread of -6½ at +120 odds or better — meaning a profit of at least $120 for every $100 wagered — that’s a more profitable play. The chances of the Bills winning by exactly five or six — a win at -4½ but a loss at -6½ — aren’t high enough to cancel out the bigger winnings if they cover the larger spread. If you find a -5 or -5½ -110 spread as the main or consensus line, then you should want an alternate line of -6½ at prices of +109 and +104, respectively.

If the underdog is getting 4, 4½, 5 or 5½ points, you can usually stick with those, knowing the game is more likely to end with a differential of three points than it is with six.

How to play a point spread of 6

If you are debating a line of -6 -110 and can’t find -6½ at -102 odds or better, take a look at the money line bet, which only requires your chosen team to win, by any margin. Teams with a closing point spread of -6 have gone 60-30-1 straight up since 2015, equating to a 66.5 win rate. The break even price for such a win rate is -200, so a moneyline bet at less than -200 odds could be appealing.

Interested in taking the underdog at +6 -110? Then you probably want to investigate the prices for +7½. If you find an oddsmaker offering that alternate spread at -150 odds or better, it is worth considering.

There are other point spreads, of course. Week 2 of this season featured a few favorites of nine or more points, which adds a level of complexity to your decision-making. Those are big numbers, and you have to be sure the team strengths are as lopsided as they look on paper. If not, in taking the favorite you are giving away two key numbers, three and seven, plus the possibility of a third in a 10-point margin.

You could also stay away from those situations — no one says you have to bet every game — and focus on games in which you believe you gain an advantage by exploiting the most frequent key numbers of three and seven. In general, the takeaway should be this: Always make sure you have a key number covered in your favor, usually by grabbing the extra point or half-point that would convert a loss or a push into a win.

*Illustration by Lily LK for The Washington Post.*