Over the years we often share insightful research with our readers that may help in the enjoyment, understanding of and profiting from the football experience. This week we address the issue of key numbers - numbers that occur most often in terms of NFL victory margins. 'Key numbers' are often misunderstood. Let's take a look at what we mean.
The number '3' is the most common margin of victory. But do you know to what extent and how often it occurs? The answer is that over 15% of all NFL games since 1981 have been decided by exactly 3 points. That's over 1 game in 7. Put another way, at least two games each week can be expected to be decided by exactly 3 points. That is by far clearly the most common margin in the NFL -- almost double the next most common margin, 7 (just under 8% of all games).
It is a frequent discussion as to whether a bettor should 'buy' the extra half-point in games involving 'key' numbers. For instance, if you wish to play an underdog that is currently listed at + 3 ½ you have the ability to get + 4 on that team by laying 6-5 (12 to 10) instead of the normal 11-10. Buying that extra half point increases your break even point from 52.38% (at 11-10) to 54.56% (at 6-5). Likewise, if a favorite is - 6 ½ you could buy the extra half-point and lay only - 6.
Most people are aware of the importance of the number '3' and impulsively answer 'yes' when questioned as to whether they should 'buy down' when playing a favorite a half-point away from a key number and that they should 'buy up' when playing a similarly situated underdog. But is this the correct thing to do? Should you lay the extra 'vig' to buy that half point? Or are you giving away too much? Let's examine the issue.
The proper question is not how often does a final margin result in 3, 7, 6 or other key numbers. Rather, the proper question is how often does a 3 ½ point favorite win by exactly 3? Or, how often does a 2 ½ point underdog lose by exactly 3 points? Those two questions concern the changing of potential losses into pushes. But you can also ask how often does a 3 point favorite win by exactly 3 points (so that buying down to - 2 ½ changes a push into a win)? Or how often does that 4 point underdog lose by exactly 4 points (so that buying to + 4 ½ turns that push into a win).
First, here are the top 10 key numbers. These ten numbers combine for over 60% of final margins in NFL games over the past 26 seasons. The numbers are listed with their frequency of occurrence.
3 - | 15.57% | 10 - | 6.07% | 4 - | 5.35% | 1 - | 4.31% | 17 - | 3.82% |
7 - | 7.95% | 6 - | 5.72% | 14 - | 4.78% | 2 - | 3.92% | 11 - | 3.40% |
We've studied the past 6 and the past 25 seasons to see how often games within a half-point of a key number fall on that key number. Note that while over 15% of all games land on 3, some of the games are won by the Underdog and in most of the games the line was other than 2 ½, 3 or 3 ½. That's what we're trying to analyze. In the following chart the first number represents for results for the past 6 seasons (2001 through 2006) and the second number represents 25 seasons' results (1982 through 2006).
Pointspread Range | # of Cases (A) | Critical # * | # of Cases (B) * | Pct. Of (B) / (A) |
½, 1 or 1 ½ | 111 / 465 | Land on 1 | 0 / 5 | 0.00 % / 1.08 % |
1 ½, 2 or 2 ½ | 163 / 806 | Land on 2 | 3 /24 | 1.84 % / 2.98 % |
2 ½, 3 or 3 ½ | 525 / 1695 | Land on 3 | 49 /156 | 9.33 % / 9.20 % |
3 ½, 4 or 4 ½ | 261 / 994 | Land on 4 | 8 / 23 | 3.07 % / 2.31 % |
5 ½, 6 or 6 ½ | 205 / 773 | Land on 6 | 6 / 21 | 2.93 % / 2.72 % |
6 ½, 7 or 7 ½ | 240 / 890 | Land on 7 | 14 / 41 | 5.83 % / 4.61 % |
9 ½, 10 or 10 ½ | 93 / 372 | Land on 10 | 8 / 22 | 8.60 % / 5.91 % |
13 ½, 14 or 14 ½ | 25 / 139 | Land on 14 | 1 / 4 | 4.00 % / 2.88 % |
* Only the # of cases when the FAVORITE wins by the specific margin
As you can see, with the exception of the key numbers '3', '7' and '10' the percentage of times the 'key pointspread' and the 'key result' coincide is quite small, 4 percent or less. For example, of the 205 times a team was favored by 5 ½, 6 or 6 ½ points between 2001 and 2006 that favored team won by exactly 6 points just 6 times, or 2.93% of the time. What does this mean? We'll have a follow-up discussion next week.
I will now add my own mathematical conclusion I came to from this analysis. When you pay for a half point you lose 9.09% more per loss than when you don't but it. If your book charges you (-125) from (-110) to move the line (like mine does) you are losing 13.6% more per losing bet. Now lets take an example of 11 games bet buying the hook. I am using 11 because 9% is the amount of times you can expect to be helped by buying the hook on games with lines around 3. In a group of 11 games you can expect 1 more winner buying the hook as opposed to not buying it. I am going to assume we are a successful gambler and would win 6 of our 11 bets without buying the hook. In this scenario we would be 6-4-1 on games with a line of 3 (1 push because 1 in 10 will land on 3) Our results from these bets would have been (+160) per $100 unit. By buying the hook we turn the push into a win and our record is 7-4, (+700) on the wins and (-500) on our 4 losses at -125 each. Net profit went up from (+160) to (+200) so it does pay off when paying for the hook on games with lines of 2.5,3 or 3.5. On games around the key number 7 we can expect 1 in 20 (5%) to be affected by buying the hook. Same scenario as above, except now our record without paying for the extra half point is now 11-8-1. 11 wins (+1100) and 8 losses (-880), $300 net won. We improve to 12-8 with the 1 changed result, (+1200) from the wins and (-1000) on our 8 losses at -125 each, net won $200. You can see it caused us to do worse when we paid for the half point off of 7. Conclusion...only buy the hook on games with lines of 2.5,3 and 3.5.