In sports betting, the hook is paying additional vig to get half a point. In laymen terms, it’s risking a larger amount of money to win the same amount of money to move the spread .5 points in the bettors favor. For example, if wagering on a 3.5 point favorite and buying the hook the spread will now be 3 points. But to gain this advantage the bettor will have to risk $120 to win $100 (120/100) instead of $110 to win $100 (110/100). Thus, the price of the hook was $10 but obtained the bettor a more favorable spread.

A good rule of thumb is that any change to a bet offered will be to the advantage of the party who who takes the bet. This rule applies not just to sports betting but to casino table games generally. An example is the insurance bet in blackjack which reduces variance of outcome but is expected positive value for the dealer.

However, it is possible to determine the value of the hook using a sufficiently large data set of college football games [1]. Using the population of games, the likelihood of the hook influencing the bet’s outcome can be calculated which can then be used to determine the value of the hook.

A prior post covered college football spreads and explained the spread error [2] and looked at it as an average and standard deviation. For the purposes of this analysis, it’s helpful to look at a histogram of the spread errors. This visual shows that more than half the spread errors are worth more than a touchdown but the largest histogram bin is zero to the first point so we know many games are close and a point can matter.

 

To determine the exact value of the hook, each game must be simulated with the an adjustment to the spread. First for the favorite. Below are 20 data points which recalculate the outcome with the spread changed by half-point increments from .5 to 10 points and the percentage of games that change. The visual is a clear linear line from 0% at zero points to 25% of games at 10 points.

 

Looking at the incremental change, we see the value of the incremental half-point is within a narrow 1%-1.7% range. This implies that while the first half-point is slightly more valuable (1.7%) than the average over the first 20 half-points (1.2%) the actual number of games that are impacted by the hook is very small. We can safely assume that the hook will impact less than 2% of bets.

 

Popular advise is to buy the the hook for single score spreads (i.e., -3.5, -7.5) where a half-point is the difference between a single score such as a field goal or touchdown. To understand single score spreads and single score games, the following bar chart is game margins with single score games in red [3].

Clearly, we can see that these single score game margins are more common than other type of game margins. Games are 2.5 to 3.5 times more likely to end in a 3 or 7 point margin than 2, 4, 6 or 8 points.

The following visual shows that by odds, games with a 2.5-3.5 and 6.5-7.5 point spread are indeed more likely to be impacted [4] by a half-point adjustment with those spreads highlighted in red.

In fact, games with a spread of 2.5-3.5 and 6.5-7.5 are impacted by a half-point in 9% of bets while the average for the entire population is 4.7% of games. And this statistic answers the original question as to the value of the hook. For spreads of 2.5-3.5 and 6.5-7.5, the value of the hook is roughly 4.5% of the bet [5] while for all other games the hook is worth roughly 1.8% of the bet [6]. 

 

[1] The data set referenced is a 4,718 college football games from 2014-2018 with a spread and outcome.

[2] The spread error is defined as the difference between the spread and the actual game outcome. For example, if the spread is -7 points and the favorite wins by 8, the error would be 1. Alternatively, if the spread is -7 and the favorite loses by 1 the error would be 8.

[3] Single score game is a game result with the winning team margin of victory equal to the two most common scoring events in football, a touchdown plus extra point (7 points) and a field goal (3).

[4] Impacted is defined as a bet outcome which would be changed by a half-point adjustment. Earlier it was noted that a half-point change would cause the favorite to cover in less than 2% of games. However, impacted also includes games where the underdog would now cover as well as games where neither team would cover but a push would now occur. This explains the differential between the ~2% and ~4.5% between the two metrics.

[5] This calculation is approximately half the value of the likelihood of the half-point impacting the game. Importantly you must assume that you have no special insight into the outcome and thus there is a 50% chance your bet will be wrong and the half-point will be irrelevant.

[6] This is lower than the general average as you must remove the higher likelihood odds of 2.5-3.5 and 6.5-7.5 then recalculate the percentage of games impacted which becomes 3.6% compared to 4.7%.

This post attempts to use some statistics, figures and plots to assess team performance against college football spreads.

The histogram of season performance of teams against the spread for college football for seasons 2014-2018 [1] is a normal distribution with x% of teams season performance between 25% and 75% [2].

To see whether a team’s season performance vs the spread carries from one season to the next, the visual below shows the current and prior year performance vs the spread as a scatter plot. No pattern emerges, with 43% of teams declining year over year and 45% of teams improving year over year. The remaining 8% were constant year over year.

 

 

Looking at the same data differently, the next visual places each team into a quadrant based 50% as the divider. Counting each data point as a percentage of the population, we see that only 13% of teams with a better than 50% performance against the spread in one year perform better than 50% the next year. Additionally, a team with a performance of better than 50% performance in a year is much more likely to under perform the next year than continue a over 50% performance.

 

 

 

Statistics / Notes

[1] Each data point is a teams season performance against the spread calculated as a percent (games covering spread / total games). In the 2014-2018 timeframe there are 708 teams in the population with at minimum 10 games that included a spread in the season.

[2] In the population 708 games, 673 had a season performance of between 25% and 75%.

 

 

This post attempts to use some statistics, figures and plots to assess the accuracy of college football totals.

First, a few points of context and summary statistics.

• Totals are an attempt to handicap the combined score of the game. As such, the game total is set by assigning the game a number which represents the aggregate score of both teams. Bettors are then allowed to place a wager on that number but selecting the side (over/under) they wish to wager on. [1]
• The median total in college football is 56 points [2]
• In the population, 48% of bets results in an over, 51% in an under and 1% in a push. [3]

The histogram of totals is a normal distribution.

In the graph below, blue represent over bets and green represent under bets. The correlation between the total and the actual total score is .43 with an average error of 12.7 points [4] and average error standard deviation of 9.9 [5].

In the graph below, we can see very little relationship between the total and whether it results in an over or under. But to see this more clearly, the following chart are 25 groupings of a range of totals [6] with the average percentage of games with an over result in blue. The dotted lines are +/- 5% of the average, we see only 1 bucket is outside the +/- 5% range and there is no relationship between total and the likelihood of the outcome.

And the same chart for under results, again only 1 bucket outside the +/- 5% range and no visual relationship.

 

Statistics / Notes

[1] A total bet of 75, with a wager of over, would win if the combined score of the two teams is 76 points or more. Conversely an under wager would win if the combined score of the two teams is 74 points or more. An exactly combined score of 75 would result in a push (i.e., the money is returned to the bettor).

[2] Of the 4,637 games with a total between 2014 and 2018, 2,270 had a total less than 56 and 2,268 had a total greater than 56. The remaining 99 games had a total of 56.

[3] Of the 4,637 games, 2,207 results in an over (2,207/4,637 = .475), 2,361 in an under (2,361/4,637 = .509), and 69 in a push (69/4,637 = .014).

[4] Average error is defined as the average difference between the total and the actual total score. For example, if the total is 70 points and the actual total score is 65 the error would be 5 points.

[5] The standard deviation of the error as defined in [4] is 9.99.

[6] Each grouping has roughly similar numbers of games, roughly 200, and were created using ntile function of SQL. The total shown on the x-axis represents the average total for the grouping. For example, the first group is comprised of totals from 31 to 42.5 with an average total of 37.2, contains 200 games and 49% resulted in an over.

This post attempts to use some statistics, figures and plots to assess the accuracy of college football spreads.

First, a few points of context and summary statistics.

• Spreads are an attempt to handicap the game. As such, the points spread or line is set by assigning the favored team a negative number which represents the points that team is expected to win by [1]
• The median spread in college football is 11 points, however the median spread for games after week 4 which represents the majority of conference play is 9.5 points
• The spread accurately predicted the winner in 75% of games [2]
• Even excluding games with a team favored by 30 or more [3], favorites win 73% of games [4]

 

We can see from the spreads histogram that the distribution is right skewed. Those below the median the spread correctly predicted the outcome 62% and above the median correctly predicted the outcome 88% [5].

On a more technical note, the spread to margin of victory correlation is -.73 which can be seen in the plot below by the line of best fit. The scatter plot is also color coded blue/red with blue representing games which the spread correctly predicted the outcome and red the opposite. The average error is 12.7 [6] and the average error standard deviation is 9.9 [7].

The average error has no relationship to the size of the spread, which can be seen visually below. The chart is comprised of 50 dots, each representing 100 games with an average spread on the x-asis and the average error [6] for that bucket on the y-axis. As the spreads are larger the average error stays within the +/- 1 point band of the populations average. Stated differently, larger spreads are no more inaccurate than smaller spreads.

Looking at 10 buckets of spreads with equal number of games, we see more evidence of the predictive power of points spreads.

Spread Bracket	Win Percent (Favorite)
-1 to -3	49%
-3 to -4	61%
-4 to -6.5	62%
-6.5 to -8	66%
-8 to -11	72%
-11 to -14	76%
-14 to -17.5	86%
-17.5 to -22.5	88%
-22.5 to -30	94%
-30 to -62.5	98%

 

Statistics / Notes

[1] Example Team A -7, Team A is expected to win by 7 points and Team B +7, Team B is expected to lose by 7 points

[2] Favorites won 3,600 of 4,787 games in the five year time frame 2014-2018

[3] Teams favored by 30 points or more win 98% of their games and represent a lot of FBS – FCS match-ups

[4] Favorites won 3,131 of 4,309 games in which the spread was less than 30 points

[5] Of the 2,383 games with a points spread of less than 11, the favorite won 1,480 (1,480/2,383 = .62), of the 2,327 games with a points spread of more than 11, the favorite won 2,055 (2,055/2,327 = .88). The 77 games with a points spread of 11 were excluded.

[6] Average error is defined as the average difference between the spread and the actual game outcome. For example, if the spread is -7 points and the favorite wins by 8, the error would be 1. Alternatively, if the spread is -7 and the favorite loses by 1 the error would be 8.

[7] The standard deviation of the error as defined in [6] is 9.97.

 

How accurate are NHL odds? To assess this, we review roughly 7,000 individual outcomes over several seasons to understand the predictive power of the odds given to individual NHL games.

By bucketing each team’s odds in each match-up into 25 buckets with each bucket containing roughly 275 games we can look at the range of odds in the bucket, the average odds in the bucket, and the percentage of games in each bucket that won (i.e., win percentage).

As a reminder, the most common NHL bet is a moneyline bet where a wager is placed on a team to win and the odds placed based on the required risk to win a unit. For example, a team favored might be -210 which requires $210 to be risked to win $100, while an underdog might be +150 which requires $100 risked to win $150.

The general trend is that the higher the odds (lower the number) the more likely the team is to win. However, it doesn’t move in lockstep with each bucket. But of the 578 games with the team favored by -200 or more the teams won 66% and of the 203 games with the team favored by +200 or less the underdog won only 34% of the games.

Odds Range	Average Odds	Win Percentage
-400 to -220	-258	68%
-220 to -200	-206	64%
-200 to -175	-182	68%
-175 to -165	-169	61%
-165 to -155	-160	63%
-155 to -150	-152	57%
-150 to -140	-144	58%
-140 to -135	-138	62%
-135 to -130	-132	53%
-130 to -125	-126	52%
-125 to -115	-120	51%
-115 to -110	-115	48%
-110 to -110	-110	51%
-110 to -105	-105	50%
-105 to 105	89	50%
105 to 110	106	48%
110 to 115	112	44%
115 to 120	118	42%
120 to 130	124	40%
130 to 135	132	44%
135 to 145	140	38%
145 to 155	149	39%
155 to 170	161	32%
170 to 180	173	35%
180 to 320	216	33%

 

 2018 Season

During the 2018 season, Nebraska was favored in 6 games, underdogs in 6 and went 7-5 against the spread. Of the 4 games they won, 4 were games where they were favored. They also lost 2 games in which they were favored.

 

Opponent	Date	Spread	Outcome	Cover	Last 5	Last 10
Colorado	9/8/2018	Neb-3	5 point loss	No, 8 points	1-3-1	3-6-1
Troy	9/15/2018	Neb-10.5	5 point loss	No, 16.5 points	1-4	3-6-1
Michigan	9/22/2018	Neb+18	46 point loss	No, 28 points	1-4	2-7-1
Purdue	9/29/2018	Neb+3	14 point loss	No, 11 points	0-5	2-7-1
Wisconsin	10/5/2018	Neb+18.5	17 point loss	Yes, 1.5 Points	1-4	3-6-1
Northwestern	10/13/2018	Neb+3.5	3 point loss	Yes, 0.5 Points	2-3	3-6-1
Minnesota	10/20/2018	Neb-4.5	25 point win	Yes, 20.4 Points	3-2	4-6
Bethune Cookman	10/27/2018	Neb-47.5	36 point win	No, 11.5 points	3-2	4-6
Ohio State	11/3/2018	Neb+17.5	5 point loss	Yes, 12.5 points	4-1	4-6
Illinois	11/10/2018	Neb-17	19 point win	Yes, 2 points	4-1	6-4
Michigan State	11/17/2018	Neb-1	3 point win	Yes, 2 points	4-1	7-3
Iowa	11/24/2018	Neb+7.5	3 point loss	Yes, 4.5 points	4-1	7-3

2017 Season

During the 2017 season, Nebraska was favored in 4 games, underdogs in 8 and went 4-7-1 against the spread. Of the 4 games they won, 3 were games where they were favored. They also lost a game in which they were favored.

Opponent	Date	Spread	Outcome	Cover	Last 5	Last 10
Arkansas State	9/2/2017	Neb-14.5	7 point win	No, 7.5 points	2-3	4-6
Oregon	9/9/2017	Neb+10.5	7 point loss	Yes, 3.5 points	2-3	5-5
Northern Illinois	9/16/2017	Neb-10.5	4 point loss	No, 14.5 points	1-4	4-6
Rutgers	9/23/2017	Neb-12	10 point win	No, 2 points	1-4	4-6
Illinois	9/29/2017	Neb-6	22 point win	Yes, 16 points	2-3	4-6
Wisconsin	10/7/2017	Neb+12.5	21 point loss	No, 8.5 points	2-3	4-6
Ohio State	10/14/2017	Neb+24	42 point loss	No, 18 points	1-4	3-7
Purdue	10/28/2017	Neb+3.5	1 point win	Yes, 4.5 points	2-3	3-7
North- western	11/4/2017	Neb+7	7 point loss	Push	2-2-1	3-6-1
Minnesota	11/11/2017	Neb+2	33 point loss	No, 31 points	1-3-1	3-6-1
Penn State	11/18/2017	Neb+27	12 point loss	Yes, 15 points	2-2-1	4-5-1
Iowa	11/24/2017	Neb+5	42 point loss	No, 37 points	2-2-1	3-6-1

2016 Season

During the 2016 season, Nebraska was favored in 9 games, underdogs in 4 and went 7-5-1 against the spread. Of the 9 games they won, 9 were games where they were favored. They lost no games in which they were favored.

Opponent	Date	Spread	Outcome	Cover	Last 5	Last 10
Fresno State	9/3/2016	Neb-29	33 Point Win	Yes, 4 Points	4-1	6-4
Wyoming	9/10/2016	Neb-25	35 Point Win	Yes, 10 Points	4-1	7-3
Oregon	9/17/2016	Neb-3	3 Point Win	Push	3-1-1	6-3-1
North- Western	9/24/2016	Neb-9	11 Point Win	Yes, 2 Points	4-0-1	6-3-1
Illinois	10/1/2016	Neb-20.5	15 Point Win	No, 5.5 Points	3-1-1	6-3-1
Indiana	10/15/2016	Neb-3.5	5 Point Win	Yes, 1.5 Points	3-1-1	7-2-1
Purdue	10/22/2016	Neb-24.5	13 Point Win	No, 11.5 Points	2-2-1	6-3-1
Wisconsin	10/29/2016	Neb+9.5	6 Point Loss	Yes, 3.5 Points	3-2	6-3-1
Ohio State	11/5/2016	Neb+17.5	59 Point Loss	No, 41.5 Points	2-3	6-3-1
Minnesota	11/12/2016	Neb-6.5	7 Point Win	Yes, 0.5 Points	3-2	6-3-1
Maryland	11/19/2016	Neb-13	21 Point Win	Yes, 8 Points	3-2	6-3-1
Iowa	11/25/2016	Neb+3	30 Point Loss	No, 27 Points	3-2	5-4-1
Tennessee	12/30/2016	Neb+9.5	14 Point Loss	No, 4.5 Points	2-3	5-5

2015 Season

During the 2015 season, Nebraska was favored in 7 games, underdogs in 5, a pick’em in 1 and went 7-6 against the spread. Of the 6 games they won, 3 were games where they were favored and 1 was a pick’em. They lost 4 games in which they were favored.

Opponent	Date	Spread	Outcome	Cover	Last 5	Last 10
BYU	9/5/2015	Neb-5	5 Point Loss	No, 10 Points
South Alabama	9/12/2015	Neb-27.5	39 Point Win	Yes, 11.5 Points
Miami	9/19/2015	Neb+3.5	3 Point Loss	Yes, 0.5 Points
Southern Miss	9/26/2015	Neb-20.5	8 Point Win	No, 12.5 Points
Illinois	10/3/2015	Neb-3.5	1 Point Loss	No, 4.5 Points	2-3
Wisconsin	10/10/2015	Neb+2.5	2 Point Loss	Yes, 0.5 Points	3-2
Minnesota	10/17/2015	Pick’em	23 Point Win	Yes, 23 Points	3-2
North- Western	10/24/2015	Neb-7	2 Point Loss	No, 9 Points	2-3
Purdue	10/31/2015	Neb-8	10 Point Loss	No, 18 Points	2-3
Michigan State	11/7/2015	Neb+4	1 Point Win	Yes, 5 Points	3-2	5-5
Rutgers	11/14/2015	Neb-7.5	17 Point Win	Yes, 9.5 Points	3-2	6-4
Iowa	11/27/2015	Neb+2.5	8 Point Loss	No, 5.5 Points	2-3	5-5
UCLA	12/26/2015	Neb+5	8 Point Win	Yes, 13 Points	3-2	5-5

How accurate are NFL spreads? To understand that, we can review some basic statistics regarding 1,536 regular season NFL games from 2012 to 2017. The median spread of these games was 4, the median outcome was 27-17. Of those games, the favorite won 66% of the games, which is somewhat lower than college basketball.

The median variance against the spread was 8, but as you can see below the variance ranged from many games less than 5 points (i.e., very accurate spreads) to games off by more than 30 points (i.e., very inaccurate spreads).

So how accurate are NFL spreads? Pretty accurate but not perfect.