In sports betting a prop bet is loosely defined as a bet made on anything other than which team will win the game and how many points will be scored. Generally speaking a prop is a wager on the exact outcome of a certain proposition. This could be anything from which team will score first, how many field goals will be kicked, the total rushing yards of a certain player (or team, or position), who will win the Super Bowl MVP trophy, or any other set of circumstances a bookmaker has though up. This is an extremely vast topic that I’m going to run through the best I can in this article; after reading, you should have enough info to increase your sports betting profits for many seasons to come.
Understanding Derivatives
In betting terms, a derivative is any wagering opportunity that that is derived from another. For example in baseball, a totals proposition on runs+hits+errors is a betting opportunity derived from the games over/under betting line. Where things gets interesting… certain bets are derivatives of one of more other derivatives, for example in NBA basketball a first quarter point spread is a betting line derived from the half time line, which is derived from the full game line. Guess what a prop team on first team to score 10 points is? The answer: that’s a derivative, of a derivative, of a derivative. If you understand the correlation between various betting lines you can make a lot of money sports betting. I’ll get back to that a moment, but first let me dissect a popular prop bet.
Which Team Will Score First
This prop bet is offered at dozens of betting sites for all NFL games, the terms are simple: whichever team scores first the backers of that team win and the backers of the other team lose. What I happen to know already is the betting line for this prop is derived from the game’s first half betting line. In order to get an idea of fair odds I need to predict the game first half score. To do this let’s go line shopping using an actual example from last season’s NFC Championship. A few hours before this game started I shopped several betting sites and these were the lines available for the first half.
 Bookmaker: Packers 3 +100  Bears +3 120 / o21 120 / u21 +100
 Bodog.com: Packers 3 +100 / Bears +3 120  o21.5 105 / u21.5 115
 Sportsbook: Packers 3 +100 / Bears +3 120  o21.5 110 / u21.5 110
 5Dimes: Packers 3 103 / Jets +3 117  o21.5 110 / u21.5 110
The first thing I notice is the point spread is shaded here. The line is 3 Packers and +3 Bears however the line is reflecting the bears have a little better than 50% chance of covering +3. I’m going to go ahead and remove vig to look at this line in terms of percentages. To do this I’ll use our moneyline converter.
 Packers +100 requires a 50% break even rate.
 Bears 120 requires a 54.55% break even rate.
These total 104.55%. To remove vig we divide each figure by 104.55%.
 Packers 50/104.55= 47.82% no vig win probability.
 Bears 54.55/104.55= 52.18% no vig win probability.
You see the probabilities now total 100% probability. We’ve removed vig and I now know the market is telling me the Packers have a 47.82% chance of covering 3.
I happen to know offhand, small favorites win by exactly 3 about 10% of the time. When dealing with one side of a push we always use half the probability because the push probability is distributed equally to both sides of a betting line. So a team moving from 3 to 2.5 changes their probability by about 5%.
Using some simple logic and ball parking this, I see 47.82% is a little more than half way between the difference of 2.5 and 3.0. This means the market has told me roughly the predicted first half score is Packers winning by about 2.8 points.
Going back to the total, Bookmaker is just offering an alternate base for their line in order to attract bets, where Bodog, a recreational site, is shading the lines slightly due to fan bias. It looks like the no vig total here is about 21.5 with it being 50% on the over and 50% on the under. So what I need to do… predict a score that has Packers winning by 2.8 and the total being 21.5.
My predicted score is:
 Packers 12.15
 Bears 9.35
You’ll notice the margin of victory is 2.8 points and the total is 21.5. Considering we’ve covered in another article “NFL football betting is very close to an efficient market” our market based prediction here is mathematically sound.
From here you need the magic formula, which is the equation on how to calculate the chances the team favored scores first. That equation is: 100 * (Favorite Score / Underdog Score).
To plug it in with our predicted score I get 100*(12.15/9.35) which solves to 129.94. We’ll round it and say the favorite is 130, and likewise we now know the underdog is +130. So with no juice involved, this is how the prop bet would be priced.
Which Team Will Score First
 Packers 130
 Bears +130
Knowing this info, I went shopping to see what the betting sites were offering and found the following available:
 Bookmaker: Packers 140 / Bears +110
 Bodog.com: Packers 140 / Bears +110
 5Dimes: Packers 140 / Bears +120
 Pinnacle: Packers 140 / Bears +120
 BetOnline: Packers 135 / Bears +105
As a professional sports bettor I’m going to pass as I’m only looking to make +EV bets. However, to a recreational gambler who likes to use simple strategy to bet against a much slimmer bookmaker advantage, that 135 at BetOnline might be quite tempting. Let me now get back to my earlier statement that “If you understand the correlation between various betting lines (derivatives) you can make a lot of money sports betting.”
There are dozens of ways to bet essentially the same thing. A sharp sports bettor examines the market and then decides which bets offer the most value. What I mean by this… let’s say he’s heavily interested in getting action down on New England Patriots at any price better than 6.5 112. Even if he finds this price, he’s still going to examine all the possible derivatives. Perhaps he really loves the Patriots at 6.5 112 and wants to bet so much his wagering limits are exceeded. Betting derivatives such as the Patriots scoring first, is a great way to get action in above the maximum wagering limit the bookmaker allows. The bottom line… If you want to win the most money in sports betting, study and learn derivatives.
Novelty Propositions
Many prop bets are far less correlated to a major market than the example I just used. Such props include will a quarter back throw an interception, how many turnovers where there be in the game, total number of punts by both teams, the list truly goes on and on. In fact it is not uncommon for a betting site to have over 500 propositions on the Super Bowl. These loosely correlated props are considered novelty propositions. With these the limits are generally quite conservative ($50 to $300 max bet) and as a result… bookmakers are not always worried about getting the line correct, and professional bettors don’t take much interest. These novelty wagers are one of the few areas in sports betting where the market is not always efficient and are a great way for the smaller player to build his bankroll.
The best way to get started beating these props is to just shop dozens of sites looking for arbs. At least a few times per week a serious line shopper will encounter a situation such as Betting Site 1 offering Ben Roethlisberger total passing yards under 270 +100 while another betting site is offering his total passing yards at over 265 +105. This means an arb with middle; if you balance the action you can be guaranteed profit while also having a chance to win both bets.
To take it beyond line shopping you need to start understanding how lines are set. The reality here is prop betting is a small market and no one s going to give you exacts of how they’re beating a certain prop, which would be foolish as you’re their opponent. I’ll however give some ways to get a ballpark price on various props.
Will the First Score of the Game be a Touchdown?
To properly price this prop we need to know the total number of touchdowns, field goals and safeties that have been scored on the season. Considering at the time I’m writing this article it is the offseason I’ll use stats from the completed 2010/11 regular season. After checking NFL.com I found there were 2077 scores on the season. These broke down as follows:
 1270 Touchdowns (61.14%)
 794 Field Goals (38.23%)
 13 Safeties (0.63%)
Many bettors would be tempted to say 1270 of 2077 scores were touchdowns so the league average states 61.14% of all scores are touchdowns. While true, the question here relates to the first score of the game. If we use full game stats we’d have to assume there’s an equal chance each scoring play results in a touchdown, which is false. The final score of each half is a field goal about 50% of the time. This isn’t due only to time running out in the first half, but also due to teams running the clock and playing in hopes of kicking a game winning field goal.
In order to solve this problem lets break this down to points scored per scoring drive.

 61.14% of the time the drive scores 7 points = 4.28 points
 38.23% of the time the drive scores 3 points = 1.15 points
 0.63% of the time the drive scores 2 points = 0.01 points
 We’ve now determined each scoring play results in 5.44 points.
Let’s do some more math:


 1270 Touchdowns x 7 points = 8890 points
 794 Field Goals x 3 points = 2382 points
 13 Safeties x 2 points = 26 points

There are 256 games in an NFL season, and adding the total number of points we get 11,298. One other note worth mentioning is missed extra points and successful twopoint conversion have historically offset, while I didn’t rerun the math for the purpose of writing this article, I did once calculated that every touchdown resulted in 7.0014 points, or some fractional number like that. This indicates 7 is a safe figure to use here for touchdowns. So back on topic 11,298 points over 256 games = 44.13 points per game.
44.13 points per game divided by 5.44 points per scoring drive tells us we’re expecting 8.11 scores. Considering we know 38.23% of them will be field goals this means we’re expecting 3.10 field goals per game.
Let’s now do some algebra to remove the final scores of each half.
3.10 Field Goals (per 8.11 scores) = 7.11 scores not at end of half * (x) + (1 end of half score) (0.5)
x = (3.10 – 0.5) / 7.11 = 36.57%
36.57% is the odds the final score is a field goal. This leaves us a 63.43% chance of a touchdown or safety.
There were 1283 scores on the season that were not field goals, 13 were safeties, 13/1283= 1.01%. So let’s take that 1.01% from the 63.43% to determine the odds of the first score being a touchdown are 62.42% which leaves the odds the first score is a field goal or safety at (36.57% + 1.01%) 37.58%. These total 100% so we’re spot on.
We can then use our odds converter to determine that in American odds format:


 37.58% = +166
 63.43% = 166

So if we were using league averages the fair odds with no vigs for this first score prop would be:
Will the first score of the game be a touchdown:


 No +166
 Yes 166

Now this only tells us the league average, and the good news is you don’t need to run the above calculation on season data each time. However, to beat props you will need to run team matches and consider other factors.
So let’s say the game was between Saints and Packers and their stats happened to be:


 Saints Points Scored: 44 touchdowns / 25 field goals / 1 safety
 Packers Points Scored: 46 touchdowns / 22 field goals / 0 Safeties
 Saints Points Allowed: 32 touchdowns /28 field goals / 0 safeties
 Packers Points Allowed: 24 touchdowns /24 field goals / 0 safeties

Considering it makes no difference who scores, only whether that score will be a TD or not, we add all these figures together and see there were 246 scores which broke down as:


 Touchdowns: 146 (59.35%)
 Field Goals: 99 (40.24%)
 Safeties: 1 (0.41%)

We could then run through the same math again:


 59.35% of the time the drive scores 7 points = 4.16 points
 40.24% of the time the drive scores 3 points = 1.21 points
 0.41% of the time the drive scores 2 points = 0.01 points

Our total points per scoring drive are 5.38
If the posted over/under betting total was 47, we now take 47/5.38=8.74 total scoring drives. We expect 40.24% to be field goals, so we’re expecting 3.52 field goals for this game.
To calculate the chances the first score will be a field goal we again solve for x again using:
3.52 Field Goals (per 8.74 scores) = 7.74 scores not at end of half * (x) + (1 end of half score) (0.5)
x = (3.52 – 0.5) / 7.74 = 39.02% chance of the first score being a field goal.
These two teams had 147 non field goal scores of which one was a safety. 1/147=0. 68% so add this to the 39.02% and we see the chances the first score of the game will be a field goal or a safety are 39.7%. By process of elimination, the probability the first score is a touchdown is 60.3%.
Using only the two teams, we get:
Will the first score of the game be a touchdown?


 No +152
 Yes 152

If we were dealing with a sample size of thousands of games it would be fine to leave it at that. What we do know is the league average without juice is +166 and using only these teams we got +152 on the no. If we find anything outside of that range we most likely have a +EV bet. If we needed to price this in a hurry we could average 152 and 166 and say the fair line is probably about 159 Yes / +159 No.
To get more accurate we could find as many similar games as possible and see how often the first score was a touchdown, or we could get really advanced and run game simulations over thousands of trials. The truth is… props like this are novelty wagers. The bookmaker sets them in a hurry and due to the low limits there are lots of recreational players moving the lines. Chances are if you use just basic mathematical and statistic analysis you can beat props. If 80% of the bets you make are +EV, and 20% are –EV and when they’re –EV it is still close, you’re going to come out way ahead in the long term. Time wasted trying to get exacts is time spent that could have otherwise been spent searching and analyzing more props.
Prop Betting Tips
Prop Betting Tip 1
When you find props where arbs are available be sure both betting sites are reputable. It is never fun to have a rouge sportsbook claim their line was significantly off and grade the bet noaction after you win, especially so when you might be betting larger than your normal limit because this was an arbitrage wager.
Prop Betting Tip 2
When betting props it is extremely important to make sure the rules are stipulated. Let’s look at a prop bet that is worded as follows:
During the Olympics how many times will a figure skater fall?
If this is the only question and there are no other rules stated, this is a prop bet that should be avoided. First off how many times will “a” figure skater fall? I assume the prop bet is most likely on the total number of falls of “all” figure skaters and not “a” figure skater; however could it be the total number of falls for the person that fell most often. That would be silly, so maybe not an issue. The next question comes is what constitutes a fall? How do we know the difference between a fall and a stumble? These types of prop bets tend to get sports bettors in trouble. You don’t want to bet on anything that can be left up to interpretation.
Prop Betting Tip 3
Avoid sucker bets. Back in the day bookies used to make a killing offering the NFL prop will either team score three unanswered times (extra points / 2point conversion not counted as scores). Many players would bet on no at 110, even though far more times than not one team does score three consecutive times.
Prop Betting Tip 4
Avoid clearly –EV bets. For example, betting on the coin toss (unless both sides are +100) is a bad idea. Don’t buy into the myth that a standard US coins when flipped land a certain side more often than the other because weight on one side of the coin is greater; this is pure myth and physics has proven it so.
Prop Betting Tip 5
Line Shop, Line Shop, Line Shop. The more betting sites you use the better chance you have to beat a prop bet.
Getting Better at Prop Betting
I realize a lot of what I covered in this article might seem complex to most bettors. It’s really not the difficult; this is seventh grade math we just need to get into the practice of using again. Also, do realize: no one is going to teach you everything they know about sports betting. If you want to learn you’ll need to hang out on forums and weed through lots of bad advice in hopes of finding rare gems.
In addition to forums books will help. If you’re completely new to advantage betting: Weighing the Odds in Sports Betting by King Yao is a great book to read. For those ready to get more advanced, Conquering Risk: Attacking Vegas and Wall Street by Elihu D. Feustel will help get you on the right track. The goal is to learn a little at a time. While learning sounds complex, already right here from reading this article you’re familiar with how to beat certain props.
You might feel I covered only two props: “which team will score first” and “will the first score of the game be a touchdown”… while true, just in what I covered, there were other props you’re now well equipped to beat. If you understand these props you can probably use the market to cap first team to score 10 points in NBA basketball. Also how many field goals will there be in a game… most all you need to know to beat that prop was covered already (the rest is covered in both books I recommended where you can learn about Poisson distributions) . As you learn a few props, you’ll begin to find cracking other props becomes progressively easier.
Finally that last prop I priced of Saints / Packers will the first goal of the game be a touchdown. I didn’t tell you at the time, but all the stats I used in that example were legit. The date I am publishing this article is June 12, 2011. Guess what? On September 8, 2011, the Saints are in fact playing the Packers and the betting total is over/under 47. Keep an eye out for any line better than No +159 / Yes 159 when the first score of the game touchdown prop opens up for betting in early September.
As always we at Online Gambling wish you the best of luck this betting season. We also appreciate any support you can give our site including linking to us on a forum, blog, or Facebook, or joining one of our recommended sports books.