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Ask the Wizard: Sports Betting

See also questions I've answered about sports other than football.

As a sports bettor, who likes to play underdogs, and who likes to shop around for lines, I know the value of finding each and every extra half point you can. In your typical NFL or NBA game, what is each half point worth to you? I know that a gambler at -110 on a fair line needs to hit 52.4% to break even. I know lines are dictated by the marketplace, but what would you say each half point is truly worth? If you could get a half point extra on the fair line of each game you bet would that make your break even point truly be 50%. Is there any way to calculate it? Thanks. — Chris from Chicago

As I show in my page in the NBA, when buying a half point the probability of a win is 51.01%, a loss is 47.01%, and a push is 1.98%, assuming the bettor never buys the half point off of a spread of 0 or -1, which he shouldn't do. If you only had to lay 110 for the extra half point, the expected return would be (0.5101 - 1.1×.4701)/1.1 = -0.64%. So, a free half point would not be enough to overcome the house edge.

Not that you asked, but if you lay 120, you can buy a half point at most sports books. If you were prepared to bet a game against the spread anyway, is the extra half point a good value? Laying 110, the house edge for a random picker is 4.45%, including ties. Laying 120, the house edge with the half point is 4.50%. So, buying a half point is marginally not worth the price.

The value of buying a half point in football depends a great deal on the point spread, because some margins of victory are much more likely than others. The only time it is worth buying the half point in the NFL is off of a point spread of 3. Unfortunately, the sports books know this too, and won’t let you do it off of 3, most of the time. February 17, 2009

What is the standard deviation of the difference between the final point differential between the two teams in an NFL game and the pointspread of that game? — Don from New York

For the benefit of other readers, let's look at an example from the last Super Bowl, to illustrate what you are asking. The Patriots were a 12-point favorite, but lost by 3. So the game finished 15 points away from the point spread. If I understand the question correctly, you are asking about the standard deviation of this difference. The mean difference was close to zero for each league studied. Here is what I get for the standard deviation:

        NFL              13.31 (based on 2000 to 2007 seasons) 
        College Football 15.72 (based on 1993 to 2007 seasons)
        NBA              11.39 (based on 1987 to 2003 seasons)      
So, the 2008 Super Bowl finished 15/13.31 = 1.13 standard deviations away from expectations. I'm ignoring the adjustment factor for a discrete distribution, to keep things as simple as possible. The probability of being 1.13 standard deviations or more from expectations, in either direction is 25.85%. This can be found in Excel, using the formula 2 × normsdist(-1.13). June 7, 2008

What is the probability of an NFL game ending in a tie? – Lee from Los Angeles
From the 1983 to 2007 seasons, there were 10 ties over 5,901 regular season games played. Rules dictate that a game can not end in a tie in the post-season. So that would make the probability, based on historical games, 0.17%, or about 1 in 590. January 13, 2008
Thanks for the great website! My father and I are having an argument about hedging bets and could really use your help! The particular situation involves a bet on the Super Bowl. Prior to the start of the season (my father can't remember the year) my uncle placed a bet that New England would win the Super Bowl. The bet paid 60 to 1. Just before the Super Bowl (in which New England was playing) my uncle hedged his bet (father can't remember the details) giving up the potential $6,000 pay day but guaranteeing a $3,000 one instead. I'm convinced that this was a sucker bet but my father won't listen to me. I'm arguing that by hedging in this spot he was giving up expected value and the smart bettor never does this. My father is arguing that it's fine to give up the expected value because of the money involved and the fact that this bet doesn't come up often, exactly the same as insuring your house. Of course, I argue that home ownership is inherently different than sports betting in that one can be avoided while the other really can't. What are your thoughts? Please help us settle this! – James from Oakville, Ontario
The Seventh of my Ten Commandments of Gambling is, "Thou shalt not hedge thy bets." However, in my remarks I add, "Exceptions can be made for insuring life-changing amounts of money." So if the surrender value of $3,000 is a life-changing amount of money to him, and if the probability of winning were not much more than 50%, then I wouldn't begrudge his decision. However, unless this was in 2002, the probability of New England winning was much higher than 50%. The other two years they played in the Super Bowl, 2004 and 2005, they were 7-point favorites. I would estimate the probability of winning either year was about 71%. A fair surrender value would have been 0.71 × $6100 (including his original bet back) = $4,331. The house edge on the offer, which was equivalent to an even money bet on the other team, was 29%-71% = 42%. So, if I'm right about the year, he made a very bad decision. He could have gotten much better odds on the open market by betting the other team on the money line. Whoever offered only $3,000 was either very ignorant of the game or took unfair advantage. Interestingly, New England won all three of their recent Super Bowls by three points. January 2, 2008
You have talked about your betting of the underdogs in the NFL. Did you simply bet the home underdog each time or was it more complicated than that? And most importantly, what line determined if it was a home dog...The early line or the line just before the game. Thanks. – Steve from Milwaukee
I don’t just blindly bet underdogs, even if I have to lay -105 only, which is the case this season at the Plaza in downtown Las Vegas. If I detect only a small advantage on a sports bet, I won't bet it. In sports I always assume a certain margin of error, because ultimately people play the game, not statistics. However, if I can find a better than the market line, or the side comes with the recommendation of a trusted handicapper, then I would be happy to make the bet. November 4, 2007
Other than the free sites, can you recommend a site where I can get professional sports handicapping for a monthly fee, or percent of win. – Danny M. from Santa Barbara
No. I do not endorse any touts. September 30, 2007
What is the maximum amount of money you can win on a college football wager in a Vegas casino without having to provide your personal information to the casino when you cash out your ticket? I'd like to know the amount I can win (per wager) and still have them pay me cash with no questions asked. – Harold from Monterey Park, CA
$10,000. A cash transaction of more than $10,000, whether in sports or not, will necessitate a CTR (cash transaction report). You may also ask to be paid in chips, although the same CTR would be generated if and when you cashed them in. March 5, 2007
With many online books offering halftime wagering, I'd love to know your opinion on "dutching". Sometimes it's obvious, but at what point would you consider betting the opposite of your game bet at halftime? Also, what amount would you consider if you found a favorable situation?
I assume by "dutching" you mean hedging. The sixth of my ten commandments of gambling is "Thou shalt not hedge thy bets." The only time I would make an exception is when the hedge bet itself has a positive expected value, or life changing amounts of money are at stake. December 26, 2006
In your answer to Edward from Placentia you say, "Square action on the money line tends to favor the favorite, creating value on the underdog." I'm not so sure this is usually the case. As you know, most small time gamblers like to risk a little to win a lot. This is achieved by betting the moneyline on the dog in these high profile games. While you were correct in your analyzation of the Super Bowl, I would urge you to look at this past NCAA Football championship game between USC and Texas. Tons of public money came in on Texas ML, while the spread stayed around 7. On gameday, both USC -185 and Texas +206 was available. I'm not really looking for an answer here, but I thought it might be something else for you to consider when betting sports in the future. Thanks for the great site! - Brad from Las Vegas
I'm afraid I don't know much about college basketball. However, I agree that gamblers prefer to get odds rather than lay them. Nevertheless, I still say that in the NFL square money usually falls behind the favorite. For this reason, in any given Super Bowl, the spread will not be in synch with the Money Line. As an example, the 2005 Super Bowl had a 7-point spread. Normally the money line on a 7-point favorite is -300. However, on New England it was around -250. My explanation is that Eagles fans were disproportionately betting the money line, while New England fans were giving up the 7 points, creating value for New England on the Money Line. April 19, 2006
All other things being equal, in particular temperature and pressure, can a kicker kick a ball further in low or high humidity?
Physics is not my strong subject so I asked two physics experts, my father and Andrew N., this question. Both agree the ball will go further if the humidity is high. Here is how Andrew N explained why.

Interesting question. I looked up a few bits of data on the internet, and it looks like the ball will go further on a humid day than on a dry day, everything else being equal. The two factors that are most relevant are: 1) the air density; and 2) air viscosity.

1) Air Density

Contrary to popular belief, humid air is lighter than dry air. This is because the water molecules take up the same space but weigh less than the O2/N2 mixture. Lighter air results in less buoyant force on the football because the football is displacing less mass. However, the density of dry air at 20 C and 700 kPa(*) is 8.33 kg/m3, and with 42.1% relative humidity at the same temperature and pressure the density is 8.32 kg/m3 according to the sources listed, a difference of about 1/10th of 1%. So this isn't going to effect the distance much.

(*) - 700 kPa is a high pressure, but it's the only data I could find. However, in engineering terms it's not much different from normal atmospheric pressure so I believe the properties listed in the data will be applicable to the situation at normal atmospheric pressure (101.325 kPa).

2) Air viscosity

Viscosity is the force that contributes to skin drag on the football. A lower viscosity will contribute less to drag, resulting in a longer flight. For dry air at 20 C and 700 kPa, the dynamic viscosity is 18.3 Pa*s, while for the air with 42.1% humidity the viscosity is only 17.8 Pa*s. This is a difference of about 3%, again not much but a little more significant than the effect of air density. However, humid air will still contribute to a slightly longer football flight.

To see if this makes sense in the real world, I found a golf website that has some data on golfball flight distance in dry and humid conditions:

As you can see, in humid air the golfball goes further, but only by a yard or two at most. So humid air definitely results in a longer projectile (golfball or football) flight, but the effect is very slight.

Andrew N

Data culled from:

wipos.p.lodz.pl/HighTech/example1.html (data on humid air at 20 C and 700 kPa)
physics.holsoft.nl/physics/ocmain.htm (calculators for humid air properties)

Wizard's comments: To add to the first point, Boyle's Law says that given the same temperature, the volume of gas is inversely proportional to the pressure. So given the same temperature and pressure the volume of gas will be constant, in other words the same number of molecules per unit area. The atomic weight of oxygen is 16, nitrogen is 14, and hydrogen is 2. So a water molecule (H2O) has an atomic weight of 18, while O2 and N2 are much heavier at 32 and 28 respectively. So when it is humid the lighter water molecules push the heavier O2 and N2 molecules out of the way, causing for less resistance for the football to cut through the air.

March 27, 2006

People have a misconception that sports betting limits in vegas are really high, which in my experience only applies to football and not always in that case. Could you tell me the approxamite limits in vegas sports books on the 4 major sports? Thank you for your time. -- Betsy from Malibu

I don't count hockey as a major sport because it gets very little action. I'm told that the Coast casinos have the highest limits. There is no maximum set in stone that I know of but they take large bets on a case by case basis. Here is what I think they would probably take on the average game.

NFL side: $50,000
NFL total: $5000
MLB money line: $10,000
MLB total: $2000
NBA side: $10,000
NBA total: $2,000
March 13, 2006

I am in an NFL squares pool and I have drawn very good numbers. 7 and 4 for pittsburgh and 4 and 0 for seattle. I was wondering what the probability is on me winning this year?

For my readers who may not understand the question, a Super Bowl pool has a 10 by 10 grid. Players will buy squares for a set amount each, writing the name of the buyer in each square. After all 100 squares have been purchased the rows and columns should be given headings randomly from 0 to 9. Kind of like a 10 by 10 multiplication table, only with the row and column headings randomly shuffled. Then the terminal digit of each team’s score will used to determine the winner. The reason for the shuffling is that some terminal digits are much more likely than others, as you will see below. For example, whoever ended up with the Seattle 0, Pittsburgh 1 square would have won the pool, because the final score was Seattle 10, Pittsburgh 21.

The following table shows the frequency of each combination in every NFL game from the 1983 to 2005 seasons. It should be noted that the 2-point conversion rule came along about 1998, which would have the effect of smoothing out the distribution a bit.

Terminal Digit in the NFL - Away by Home Total
Away Team Home Team Total
0 1 2 3 4 5 6 7 8 9
0 126 104 34 160 138 37 99 237 64 32 1031
1 73 40 17 41 103 21 36 117 67 31 546
2 25 15 1 20 30 9 13 33 9 12 167
3 194 69 33 66 102 40 102 132 43 40 821
4 122 133 27 78 108 27 48 215 59 35 852
5 32 12 12 21 21 9 13 36 22 5 183
6 91 47 17 75 57 7 28 57 25 39 443
7 217 115 35 135 195 47 65 125 69 47 1050
8 43 59 12 24 41 23 20 38 15 7 282
9 48 28 17 33 40 14 29 33 14 7 263
Total 971 622 205 653 835 234 453 1023 387 255 5638

The next table shows the probability of each combination based on the totals in the table above.

Terminal Digit in the NFL - Away by Home Probability
Away Team Home Team Total
0 1 2 3 4 5 6 7 8 9
0 0.0223 0.0184 0.006 0.0284 0.0245 0.0066 0.0176 0.042 0.0114 0.0057 0.1829
1 0.0129 0.0071 0.003 0.0073 0.0183 0.0037 0.0064 0.0208 0.0119 0.0055 0.0968
2 0.0044 0.0027 0.0002 0.0035 0.0053 0.0016 0.0023 0.0059 0.0016 0.0021 0.0296
3 0.0344 0.0122 0.0059 0.0117 0.0181 0.0071 0.0181 0.0234 0.0076 0.0071 0.1456
4 0.0216 0.0236 0.0048 0.0138 0.0192 0.0048 0.0085 0.0381 0.0105 0.0062 0.1511
5 0.0057 0.0021 0.0021 0.0037 0.0037 0.0016 0.0023 0.0064 0.0039 0.0009 0.0325
6 0.0161 0.0083 0.003 0.0133 0.0101 0.0012 0.005 0.0101 0.0044 0.0069 0.0786
7 0.0385 0.0204 0.0062 0.0239 0.0346 0.0083 0.0115 0.0222 0.0122 0.0083 0.1862
8 0.0076 0.0105 0.0021 0.0043 0.0073 0.0041 0.0035 0.0067 0.0027 0.0012 0.05
9 0.0085 0.005 0.003 0.0059 0.0071 0.0025 0.0051 0.0059 0.0025 0.0012 0.0466
Total 0.1722 0.1103 0.0364 0.1158 0.1481 0.0415 0.0803 0.1814 0.0686 0.0452 1

Although there is a ceremonial home team in the Super Bowl, I think we can ignore that. Let's also ignore everything about both teams and go strictly off of the historical averages above. Finally, let's ignore the fact that the Super Bowl can not end in a tie, which would make a match like 4/4 a little less likely to win. So let's take an average when the terminal digits are different. For example the probability of your Pittsburgh 7, Seattle 4 square would be the average of Away 7, Home 4; and Away 4, Home 7. Doing so results in the following probability for each of your squares.

Pitts 7, Sea 4: (0.0346+0.0381)/2 = 0.0364
Pitts 7, Sea 0: (0.0385+0.0420)/2 = 0.0403
Pitts 4, Sea 4: 0.0192
Pitts 4, Sea 0: (0.0216+0.0245)/2 = 0.0231

So your total probability of winning one of these is 11.90%. Considering you only covered 4% of the squares you made out well.

Although you didn't specifically ask, here is how often each terminal digit occured. It shows that overall from most the frequent the order is 7043168952.

Terminal Digit in the NFL - Away and Home Totals
Terminal
Digit
Away Team Home Team Total
0 1031 971 2002
1 546 622 1168
2 167 205 372
3 821 653 1474
4 852 835 1687
5 183 234 417
6 443 453 896
7 1050 1023 2073
8 282 387 669
9 263 255 518

Finally, here is the probability of each terminal digit.

Terminal Digit in the NFL - Away and Home Probabilities
Terminal
Digit
Away Team Home Team Total
0 0.1829 0.1722 0.1775
1 0.0968 0.1103 0.1036
2 0.0296 0.0364 0.033
3 0.1456 0.1158 0.1307
4 0.1511 0.1481 0.1496
5 0.0325 0.0415 0.037
6 0.0786 0.0803 0.0795
7 0.1862 0.1814 0.1838
8 0.05 0.0686 0.0593
9 0.0466 0.0452 0.0459

March 5, 2006

In two different sections on your site, you mention that in general it is better to bet on underdogs rather than favorites against the money line. However, as you point out in your Sports Betting Appendix 3, the money line house edge is LOWER when betting on the favorite. Isn't that a contradiction? Isn't it true for a bet of any type to seek out the lowest house edge? - Edward from Placentia

Good point. After giving it some thought I have decided to remove my sports betting appendix 3. It was based on the assumption that the fair line is exactly between the two money lines. For example, in the last Super Bowl the money lines were generally Seattle +160 and Pittsburgh -180. My appendix was based on the unrealistic assumption that the fair money lines would be +/- 170. In reality money lines are market driven. Square action on the money line tends to favor the favorite, creating value on the underdog. Assuming Pittsburgh, as a 4-point favorite, was fair historical data, a 4-point favorite has about a 61% chance of winning. That would make the fair money lines +156 on Seattle and -156 on Pittsburgh. To remind you, most casinos had the money lines at +160/-180. Of course Pittsburgh won the game this time, but historically speaking, I'm sure you would make out better betting underdogs over favorites on the money line. Feb. 11, 2006

Millennium Sports offers a 6-point 2-team teaser at even odds. I'd like to see the teaser page updated with these odds. Plus I'd like to see another table that states what percentage of individual bets you'd have to win to break even. I calculate the 2 team 6 point teaser witheven odds to be 75% to break even. A difficult task. Thanks - John from Herndon, VA

I just updated my Sport Betting Appendix 4 to include the Millennium teasers, as well as using more recent data. Here are is the house edge on teasers including the Millennium odds and whether the pick is on a team or the total.

Two Team 6-Point Teasers
Pays Team Total
-12012.85%18.12%
-1109.25%14.74%
Ev4.92%10.68%

Two Team 6.5-Point Teasers
Pays Team Total
-1105.85%10.41%
-1209.58%13.97%
-13012.74%16.98%

To answer your question, to beat the 6-point teaser you would need an overall probability of winning of greater than 50%, so per pick the probability of covering the tease would need to be the square root of 0.5, which equals 70.71%. To beat the 6.5-point teaser the probability per bet would be 52.38%, or 0.52380.5=72.37% per pick. Feb. 11, 2006

This year our "Football Bet Taker" upped the juice on over/under bets from 10% to 20%, and eliminated the 10% juice on parlays. So this year instead of making 2 separate o/u bets, I have been parlaying the 2 bets at a payoff of 2.5 to 1. Is this a good strategy to use? - Rob from St. Louis, Missouri

The expected return on the straight bets would be (0.5*1 + 0.5*(-1.2))/1.2 = -8.33%. The expected return on the parlay would be 0.25*2.5 + 0.75*-1 = -12.5%. However, if I were to only bet two games and want to win or go bust trying, then I would go with the parlay. More importantly, I would boycott this bookie out of principle, because I've never heard of having to lay -120 on straight bets before. Nov. 22, 2005

Your system for your NFL picks seems to be weighted too heavily towards the underdog. Only 8 out of 49 games have you picking the favorite. In one you pick a team on an even line. Is this a flaw in your system or are people more apt to pick favorites and your system is trying to take advantage of their tendency? I didn't do an analysis but it tends to be from my observation that few bets are won in the spread range without the team actually winning the game. - Ian from Boulder

Historically speaking underdogs are a better bet. Here are the results of every game played from the start of the 1983 season through week 10 of the 2005 season.

Favorite wins against spread: 2,554 games
Underdog wins against spread: 2,724 games
Game ends exactly on spread: 150 games

So on resolved bets, the underdogs have won 51.61% of the time. It is also well known that square bettors prefer to bet favorites, creating value on the underdogs. Nov. 22, 2005

I have always wanted to do some of my own NFL handicapping but I am having a hard time finding a site, hopefully free, to download historical data by team. Any suggestions? Downloadable files would be my preference since cutting and pasting off of a web page isn't real practical but I would be willing to do so if needed. Also, information such as weather and turf conditions would be a great help. - Ed from Indianapolis

Personally, I use the NFL Access database from Mr. NFL, which costs $99. If there is anything as good for less, I'm not aware of it. Nov. 2, 2005

Do you advise playing the money line or the spread on your NFL picks or does it not matter one way or another? - Aaron Kelly from New York

Regardless of the reason for making the bet, in general it is better to bet underdogs on the money line and favorites against the spread. Nov. 2, 2005
Wizard, I've got a question regarding my "true" winning percentage for NFL picks. I tell my friends that I have not had a losing season for the past 5 years (which is true), betting from Weeks 3-16 with an average of 2-3 picks per week. My thing is that I have a great feel for games and I bet substantially more in games where I believe the odds are in my favor. As an example, I have made 9 bets this year, 4 of which were $55, hitting 3 of those picks. I have made 3 $110 bets, winning 1 of those. But I loved two games in which I bet $330 on one, and $600 (even line), and won both. Absolutely, I'm 6 of 9 for 66% clip, but being that I hit on the games I was more sure about, it really signifies around an 80% clip (money wise). Does this make sense to you? I've roughly done this, it turned out, when I calculated it for the last 5 years (60-70% in picks, but ~80% when factoring how much money I wagered). Can you tell me an easy way to factor in the amount bet, and If i'm correct in my assumptions? Thank you very much. - Luke from Chicago
I have been thinking a lot about this lately. In my opinion a winning percentage should have an equal weighting per game. You should also have a separate statistic on your overall return of investment; however, any statistic should be backed up with a list of the side, date, line source, point spread, and the odds (usually -110). Another issue you don't bring up is what to do if you have to lay -120 off of a 3 or 7 point spread. It would be easier to attain a good win percentage if you loaded your picks with such bets. So I believe a return on investment figure should be kept even if flat betting. Another thing that bothers me about some other handicappers is they quote lines that are nowhere to be seen. I think it is okay to shop around a bit but quoted lines should be not difficult to find. I admit, I didn't do some of these things myself this season, because I didn't think of these things when I started. Next year, if I do this again, I will document my results as an investment as well. Oct. 26, 2005
Since you're doing football now I have a question about parlays. I recently placed a bet where I picked the over/under in each of the 4 quarters of the Steelers/Chargers MNF game and won. (Only quarters, no half or total.) Now the sportsbook won't pay because they say there's correlation -- that winning one quarter makes it more likely that I'll win another quarter. I believe each quarter of a game is mutually exclusive but they disagree. What does the Wizard think? - Phil from Chicago
First, whoever accepted this bet should honor it, on principle alone. A gentleman honors his debts, especially gambling debts. Second, although I haven't studied it I think the quarters may actually be negatively correlated. For example, if the first quarter has a low total it may be more likely that either team will have good field position at the beginning of the second quarter, and thus likely to make the second quarter high scoring, and vise versa. Oct. 18, 2005
Are you a Packers fan at heart? I am. It looks like you are betting with your heart and the packers are killing your great NFL picks. Great percentage even with the packers not coming through for you. Just thought you might like the observation. -- Stan from Coconut Creek

The reason has nothing to do with team loyalty. My program rated them the fifth best team at the close of the 2004 season, and I carry that power rating over into the 2005 season. However, maybe it is too slow too react to recent history. Something for me to think about. Oct. 3, 2005

With regards to your NFL picks, are they all weighted the same, that is to say, are any of the picks stronger than others according to your model? - Craig from Calabash, North Carolina

Some of them I like more than others. My model creates what it estimates to be a fair spread in every game and I list the ones that have a disparity of more than a chosen number of points. Personally, I bet more on the ones with the larger disparities. However, until I have proven my picks are any good I think it would be pretentious to post degrees of confidence. Sept. 18, 2005

I would love to see more detail on your "NFL picks" numerical model. Hey, if you start utilizing this to actually make bets, wouldn't this be defined as a "betting system"? -- Ed from Indianapolis

Some of them I like more than others. My model creates what it estimates to be a fair spread in every game and I list the ones that have a disparity of more than a chosen number of points. Personally, I bet more on the ones with the larger disparities. However, until I have proven my picks are any good I think it would be pretentious to post degrees of confidence. Sept. 18, 2005

Do you have any advice for picking the terminal digit in Super Bowl pools?

The office pools I have seen randomized the tables by assigning a random digit to each row and column. However, if you can choose the actual terminal digits, the following table shows the frequency of each terminal digit for the final score of either team, based on every NFL game from 1983 to 2003.

NFL Terminal Digits per Side

Digit

Frequency

Probability

0

1887

17.75%

1

1097

10.32%

2

348

3.27%

3

1382

13.00%

4

1608

15.13%

5

396

3.73%

6

848

7.98%

7

1945

18.30%

8

631

5.94%

9

488

4.59%

Total

10630

100%

So this table shows 7 is the best choice, followed by 0, 4, and 3. Feb. 21, 2005

I Hi Wiz, Let's suppose I conjure up a sports betting system which requires $1K bets to return $80K per year. In order to produce this return approximately 250-300 bets per year are needed. Would the sports books eventually bar me in a similar fashion to the way the casinos bar card counters? Can you become a successful sports bettor openly, or do you have to sneak around like a card counter? - Jim

First, I'm skeptical that anyone could make $80K with $1K bets and a bankroll of only $250K-$300K. And don't even get me started about the word "system". To answer your question, for the most part the best sports bettors may practice openly. Even if a sports book did forbid a professional's action or 86 them from the property, it would be easy to get someone else to do the betting. Then again, I once went to a Super Bowl proposition bet seminar by Fezzik, a professional gambler, and he gave his presentation in a Halloween mask. Dec. 20, 2004

I know there isn't an exact answer to this but what is a general ballpark for a good sample size in determining whether or not there is anything to a handicapping method? For example, if I have a test sample of 1303-1088 54.5%, is there reason to think that there may be something other than chance to the method?

You're right, there is no magic number of when you enter the "long run", as I've said repeatedly. However, the more impressive your results the fewer the hands you need to make a case that they are not just random. In your case, the probability of getting 54.5% or better out of 2,391 games is just about 1 in 200,000. So I would say that record is worthy enough to be taken very seriously. Here is how I arrived at that number:

Expected wins = 2,391/2 = 1,195.5
Actual wins above expectations = 107.5
Standard deviation = sqrt(2,391*(1/2)*(1/2)) = 24.45
Standard deviations away from expectations = (107.5 + 0.5)/24.45 = 4.4174
Probability of 4.4174 standard deviations or more = normsdist(-4.4174) = 0.000005 = 1 in 200,000 Oct. 25, 2004

My question was specific to the Monday night football game tonight (Dallas @ Washington). There is rain in Washington and has been for a few hours now. This rain will continue through the game and into the next day. I was wondering what effect rain had on an over/under NFL bet? Is there some trend or other advice you can give me?

I do not know the effect of rain on the total. However, I do know that sharp handicappers consider the weather very seriously and move the line to reflect the temperature, precipitation, wind speed, and things like that. Oct. 8, 2004

Sorry to bother you as your web page states, but have you used your mathimatical prowess to find anomilies in the odds on sports bets, or calculated a way to have a guarenteed return based on that info?

The last couple years I have been devoting a lot of time to sports betting, much more than any other form of gambling. Unless you can play two sport books against each other via different lines, an opportunity which is very rare, there are no guaranteed winning ways to make money sports betting. It is too early to reveal any secrets but I look for any perceived bet with a player advantage and then make my bet. You might like to see some information I presented recently in my sports betting appendix 2. Jan. 20, 2004

At Pinnacle Sports there is a "Multi-Way calculator on the right" that shows the house edge on money line bets. What is the formula they are using?

This is interesting. Normally the house edge is lower betting on the favorite, as I explain in my sports betting appendix 3. However, at Pinnacle, they evidently set the money lines so that each has the same house edge. Let d be the money line on the dog and f be the money line on the favorite. For example, if the money lines were +130 and -150 then d=130 and f=-150. The house edge on both bets at Pinnacle would be:

1-(1+(d/100))*(1-(100/f))/(2+(d/100)-(100/f))

The amount you must bet to get back one unit is 1/[(d/100))*(1-(100/f))/(2+(d/100)-(100/f))].

For example, with money lines of +130 and -150, the house edge on both bets would be 3.3613% and the expected return on a bet of 1.034783 units would be 1 unit.

At a land casino I would assume the fair set of money lines to be +140 and -140 in this example, resulting in a house edge of 2.78% on the favorite and 4.17% on the dog. All other things being equal, this would suggest that Pinnacle is a good place to bet on underdogs. Dec. 17, 2003

If I determine the fair line of a game to be -160/+160 and I find a rogue line of -145 what is my EV? Any formula you could provide in which I could derive my EV +/- after a fair line has been determined would be greatly appreciated.

Let p be the probability of the favorite winning. If -160 is a fair line then:

100*p - 160*(1-p) = 0
260p = 160
p = 160/260 = 8/13 = 61.54%.

So the expected return on a $145 bet at a -145 line would be (8/13)*100 + (5/13)*-145 = 75/13 = $5.77. So the player advantage would be $5.77/$145 = 3.98%.

Let's define t as the true money line with no house edge and a as the actual money line. Following are the formulas for the player's expected return:

A is negative, t is negative: (100*(t-a) / (a*(100-t))
A is positive, t is positive: (a-t)/(100+t)
A is positive, t is negative: (a*t + 10000)/((t-100)*100)

So in your case your expected return is 100*(-160 -(-145))/(-145*(100-(-160))) = 3.98%. Dec. 17, 2003

I'd like your opinion on an NFL pool. Tickets cost $25 each and consist of three random teams, in a given order. Each week the ticket holder with the highest three scoring teams, in the correct order, wins $1000. What is the actual value of each ticket?

There are 17 regular weeks in the NFL season and 32 teams. The probability of winning any given week is 1 in 32*31*30 = 29,760. The expected value of each ticket is $1,000*17/29,760 = 57.12 cents. So the expected return is 2.28%, or a house edge of 97.72%! Nov. 19, 2003

There is an online sport book that is offering a bet in which you are assigned a random horse (to win) and you receive a guaranteed payout of 15.3 for 1. There are 17 total horses listed. How would you calculate the house advantage on this bet? Does it matter what the odds are on the horses? If so, they are below. Thank you, and I apologize if this is a stupid question.

Assuming you had an equal chance at getting each horse, then the probability of winning would be 1 in 17, regardless of how the odds on each horse were distributed. The player's expected return can be expressed as (1/17)*15.3 + (16/17)*-1 = -0.0412. In other words, the house edge is 4.12%. However, there is another simple formula you can use. If a = actual odds paid and f = fair odds for bet, then the house edge is (f-a)/(f+1). In this case the fair odds are 16 to 1. So the house edge is (16-15.3)/(16+1) = 0.7/17 = 4.12%. June 14, 2003

I have seen various NFL handicappers boast about their percentages of winning picks. What is the probability a random picker would get 50%, 55%, and 60% over 1, 3, and 5 seasons? - Michael Bluejay from Texas

The following table shows the probability of attaining every percentage from 50% to 60%, in increments of 1%, by each number of seasons from 1 to 5. This is based on a 259 game season. I also assume that the overall percentage is rounded down. For example, if a handicapper picked 132 out of 259 games, for a percentage of 50.97%, he would only get credit for picking 50%, since he didn't quite attain 51%. It would not surprise me if these boasting handicappers are rounding in their own favor.

Probability of Handicapping Percentages in the NFL

Ratio

1 Seasons

2 Seasons

3 Seasons

4 Seasons

5 Seasons

0.5

0.5

0.517523

0.5

0.512393

0.5

0.51

0.354641

0.314437

0.282985

0.257059

0.234993

0.52

0.267178

0.178085

0.125486

0.101366

0.074229

0.53

0.160065

0.086589

0.049447

0.025155

0.015098

0.54

0.106982

0.035817

0.013066

0.004959

0.001926

0.55

0.053095

0.012519

0.002569

0.000687

0.000152

0.56

0.023385

0.00282

0.000373

0.000051

0.000007

0.57

0.012645

0.00067

0.000053

0.000003

0

0.58

0.00453

0.000133

0.000004

0

0

0.59

0.00213

0.000022

0

0

0

0.6

0.000617

0.000003

0

0

0

Jan. 11, 2003

Just read your latest 'Ask the wizard' section. You said that sport betting would be one of the ways to earn a living. Could you elaborate a little bit? Does it have similar edge over the bookmaker as blackjack with card counting does over the casino? Thanks. - Daniel from Hong Kong

Unfortunately, I can't elaborate much. Sports betting is not my strong point, although I plan to learn more about it when I have the time. I will say it is hard to compare the profitability of sports betting to card counting. Card counting is very technical and by the book. Making money sports betting requires more judgement and is more subject to opinion. There are various strategies one can employ to make money sports betting. For example, looking to arbitrage games by taking both sides at different casinos under different point spreads, looking to exploit unusual proposition bets, or going after correlated parlays. I would recommend "Sharp Sports Betting" by Stanford Wong for more information on winning at sports betting.

I was recently looking at a football pool that was taking place. This was one of those where there is a grid of 100 boxes and the numbers 0-9 run along the X and Y axises and correspond to the last number of the score. I am not a football fan and did not bet on this pool but I am a gambler and don't think it is such a great bet. I am taking for granted that you know the type of pool that I am referring to. Each box costs $5 and pay outs are each quarter. If your box wins you win $125 and it is possible to win all 4 quarters if the last numbers remain the same winning $500 for a payout of 100 to 1. The person soliciting the bet was trying to tell me that the odds of winning the $500 are 100 to 1. I dissagree. First the box that has 0 + 7 stands a much better chance of winning than the 2 + 9 box. However the odds of 0 + 7 remaining the last 2 numbers throughout the game must be high. If the boxes are chosen for you through a random process, can you tell me the approximate odds of winning the $500 prize? - Sam from Phillipsburg, USA

Assuming the cells in the grid are chosen at random, which by randomly picking the row and column headings they generally are, then the odds of winning any one quarter would be 1/100. If the row and column headings were scrambled for each quarter then the probability of winning all four quarters would be (1/100)^4, or 1 in 100,000,000. Feb. 10, 2001

Are there any states, other than Nevada, where it is legal to bet on professional sports such as baseball and football? - Roger from Bloomington, Indiana

I'm quite sure that Nevada is still the only state in which you can bet on all major sports. July 18, 2000

It seems to me that the winner pays the 10% commission, not the loser. What am I missing? - Bob Pierce from Lake Charles, Louisiana

It doesn't make any difference who pays. Lets suppose Atlanta is playing Miami and you want to bet on Atlanta and want to win $100. Either way you have to bet $110 to win $100. However, it is easier to explain the bet as if the loser pays. April 22, 2000

Current odds for a boxing match between Vargas and Quartey are -240 Vargas and +190 for Quartey. How does this work if I put $100 for Vargas or $100 for Quartey? - Steve from Albuquerque, New Mexico

A $240 bet on Vargas will win $100. A $100 bet on Quartey will win $190. Of course you can bet any amount but the winnings will still be in the same proportion. If you bet $100 on Vargas you will win $100*(100/240)=$41.67. Stay tuned for my new section on sports betting planned for this April. Mar. 18, 2000

See also questions I've answered about sports other than football.

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