By Gary Best of Compu Pick
The question of whether or not buying the half-point is a good strategy and at what numbers has been debated since the advent of the wager itself.
Some considered it a “sucker” bet that would only hurt you in the long run. While others swore by it, saying it turned their ties to winners on a consistent basis. Most players, however, weren’t sure one way or the other and just stayed away from the wager altogether.
Then just about the time people started coming up with rules explaining when buying the half-point was profitable, the NFL Competition Committee came along and instituted the two-point conversion and threw the debate back into the depths of chaos.
Since then it seems no one has taken the time to analyze the effects of the two-point conversion on scoring in the NFL. Until now.
This report will discuss some of the interesting effects of the 2-point conversion on margins of victory, the lines themselves, the occurrences of “pushes” and lastly our strategy for buying the half-point. The data used in this report covers every regular season game from 1983-1999.
The old rules have changed.
What is Buying the Half-Point?
Most sportsbooks will allow you to move the line by a half point in either direction at a cost of increased vig (i.e., decreased winnings). Typically, since a standard football wager is at –110 ($110 to win $100), a half point can be purchased at new odds of –120 ($120 to win $100). So if you could wager $110 to win $100 on a team getting 7 points, you would be able to move the line to 7.5 but would have to wager $120 to win the same $100. Your probability of winning has increased, but so has the amount of money you stand to lose if you don’t.
There are some additional restrictions when you’re buying to get on or off of a line of 3. Since such a large proportion of games are won by exactly 3 points, you must pay –130 ($130 to win $100) to move off 3 to 2.5 or 3.5 and from 2.5 and 3.5 onto 3. Some sportsbooks will even go so far as to disallow buying the half-point at these numbers entirely. As we shall see, this is not a bad idea.
What is Significant About the 2-Point Conversion?
Since the 2-point conversion became an option at the start of the 1994 season, teams have used it to turn two field goals and a touchdown into 14 points. More importantly, teams have used it to tie the score. As a result, games are now more likely to be won by exactly a field goal, a touchdown or a combination of the two.
The Old Rules
Before we discuss the different effects of the two-point conversion, it probably makes sense to first examine the world that existed in 1993.
In this world, the most common winning margin was 3, much like today. But the other most often occurring margins of victory were, in order, 7, 4, 6, 10 and 14. These are the traditional “key numbers” and 45% of games would be decided by one of these margins.
It turns out that the only place where buying the half-point was profitable was around 3. So if the line was 3, it would have been mildly profitable in the long term to buy yourself up to 3.5 or down to 2.5. Similarly if the line was at 2.5 or 3.5 you could profitably buy yourself onto 3. A move off of 3 would have added 3.1% to your expected ROI while a move onto 3 would have added 2.0%. This is at the increased odds of –130.
At every other line it would have been to your disadvantage to buy the half-point. So if you weren’t buying it, don’t feel like you missed out.
That was then; this is now. Let’s take a look at the effects of the two-point conversion.
Effect on Margins of Victory
The graph below illustrates that the percentage of games that were won by 3, 7 or 10 points has increased in the last 6 seasons compared to the previous 11. It should be no surprise that the number 3 is still the most frequent margin of victory. About 16% of all games since 1994 have been won by 3 points.
Also please notice that the percentage of games that have been won by 4 or 6 points, traditional key numbers, has decreased since 1994. The percentage of games won by 14 points remains unchanged. So while the same key numbers are important, their order has changed. Their new order, in descending percentage of occurrence, is now 3, 7, 10, 6, 4, and 14. Note that 10 has passed both 6 and 4 in frequency. One of these margins of victory occurred in 47% of all games since 1994.
Effect on Lines
For various reasons, even the distribution of the closing line itself has changed as the graph below illustrates. A closing line of 3 is over 3% more likely since 1994. It doesn’t sound like much, but this shows an increase of almost 1/3. Notice also that a closing line of 7 is almost 1% more likely as well. The occurrence of lines of 10 and 14 has not changed appreciably.
Different factors go into the closing line as opposed to the opening line. The opening line is most likely determined by Las Vegas Sports Consultants headed by Roxy Roxborough and is only available to a few select wiseguys. Whereas the closing line reflects adjustments made to the line as money comes in on a game throughout the week and is not finalized until game time. It is usually in a sportsbook manager’s best interest to have equal amounts of money bet on both teams so that they show a predictable profit no matter which one covers the spread. They do this by moving the line to attract more wagers to the team that is not being bet as heavily.
So what this chart shows is not necessarily an increase in opening lines of 3, but an increased resistance to moving the line off of 3. The worst situation for a bookmaker to be in is to have bets out on both sides of a key number. If the game is won by exactly 3 points, it’s possible that he could lose all bets on both sides and push (tie; all bets are refunded) all bets in the middle. This is called getting “middled”. A sportsbook manager who gets middled too often because of poor line movement will not be burdened by his job for too long.
To avoid getting middled, sportsbook managers will think twice about increasing or decreasing the line past key numbers. They will move the line onto the key number, but will avoid going past it. From our graph it can be seen that this resistance has increased since 1994.
Effect on Pushes
A “push” is when the game is won exactly by the line. It’s as if the game never took place and all bets at that line are refunded. This is central to our study of the half-point because when you buy a half-point, the most you can do is convert a loss to a push or a push to a win. You cannot change a loss to a win without buying a full point, which is beyond the scope of this report.
As illustrated by the chart below, the number of pushes has skyrocketed since 1994 as a result of both the increased occurrences of key-number margins of victory and the higher likelihood of having a similar closing line. The percentage of games with closing lines at 7 and 10 that pushed has increased almost 10%. Those with lines at 14 have increased over 3% while those at 3 have increased almost 1%.
The graph also shows large increases around 5 and 12, but note on the Margin of Victory chart that there are not many of these games to start with so a single push can drastically affect the statistics.
In general, 2.0% of games pushed from 1983-93 while 3.0% of games pushed from 1994-98. Based on this data, a game played after the two-point conversion was instituted is one-and-a-half times as likely to push as one played before.
The New Rules
So what do all these effects mean?
Well they do point out a consistent trend since the implementation of the 2-point conversion in 1994. First of all, the frequency of games won by the key numbers 3, 7 and 10 has increased. Secondly, there are more closing lines equal to those key numbers. Lastly, there are many more pushes at those key numbers. All this would lead us to believe that it may now be worth it to buy the half-point at 3, 7 and 10.
But that’s only half-right.
As would be expected, it is now even more profitable for us to avoid pushing by buying the half-point to get off of 3, 7 and 10. We see a 4.8% increase to our expected ROI buying to get off of 3 and whopping 11.2% and 12.7% increases to get off 7 and 10 respectively. It must be pointed out that compared to the small increases in the occurrences of 7 and 10 in our MOV and Lines charts, the actual long-term gains may not be as sizable. However, it should still be worthwhile to buy the half-point at these numbers.
However, while it is profitable to buy the half-point to get off these key numbers, the same cannot be said about paying to get onto them. It turns out that around 3 is still the only place where it is profitable to buy onto a key number, showing a mild 1.5% increase to your ROI. Notice that this percentage increase has actually decreased since 1993 when it was 2.0%. However, due to the especially large increases in the occurrences of a closing line of 3, this should probably be more profitable in the long term.
Our sample size at 14 is not statistically significant so it’s hard to say if it would be profitable to buy the half-point there. There have only been 14 games since 1994 with a closing line of exactly 14 but 1 of them did push. Based on that extremely limited sample set, you would show a 5% increase to your ROI buying to get off of 14. But since neither the occurrences of a 14-point MOV nor line has increased, this wager should probably be avoided.
In summary, the two-point conversion has had many effects on the scoring of NFL games. It has changed the distribution of the margins of victory, increased a line’s resistance to moving past certain key numbers and has also caused many more games to push against the spread. Combining these factors together makes for a profitable betting opportunity that did not exist prior to 1994. To maximize your profit, you should buy the half-point to get onto or off of 3 and to get off of 7 and 10.