Tuesday, 24 September 2013

How To Win At Betting Using Expected Value

Expected Value is a great a way to measure whether a bet is potentially profitable. In fact, one mathematician even used EV to guarantee multiple lottery jackpot wins. Despite its usefulness, however, many bettors are unfamiliar with the technique. Learn about it here.

Expected Value – or EV – is a method used to measure the relative values in a two-sided decision, like ‘will a coin land on heads or tails?’ It does this by using a simple decision matrix that weighs up the upside and downside of the two options.

It’s best used by bettors to determine the amount you can expect to win or lose on a given bet – with a positive EV indicating a profitable proposition. The UK National Lottery, for example, has a negative EV of -0.50p – you theoretically lose 50p for every £1 invested – which means that it is a bad bet for making money.

How to Calculate Expected Value
The formula for calculating Expected Value is relatively easy. Multiply your probability of winning by the amount you could win per bet, and subtract the probability of losing multiplied by the amount you stand to lose per bet:

(Amount Won per Bet x Probability of Winning) – (Amount Lost per Bet x Probability of Losing)

The easiest betting example is a fair coin toss, in which there are two choices. Imagine you wager £10 on the two outcomes, which both pay out at the same rate (probability of 0.5 or 2.0 in Decimal odds). This produces a decision matrix that has an EV of 0 for either outcome. This is because the probability of the two outcomes is the same, so if you tossed a coin forever you would theoretically just end up all square.

If, however, we change the return on Heads to pay £11 – so a probability if 0.48 or odds of 2.10 – this changes the matrix, and produces a positive EV of 50p for backing Heads. This means that if you were to make the same bet on Heads over and over again, you can expect to profit an average of 50p for each bet of £10, because the odds received are better than the implied odds of the event.

Expected Value of Coin Toss
Choice:
Calculation (Heads – Tails):
EV
Heads
(£10 x 0.5) – (£10 x 0.5)
0
Tails
(£10 x 0.5) – (£10 x 0.5)
0

EV of Coin Toss (£11 return on Heads)
Choice:
Calculation (Heads – Tails):
EV
Heads
(£11 x 0.5) – (£10 x 0.5)
£0.50
Tails
(£10 x 0.5) – (£10 x 0.5)
0

You should bite the hand off anyone offering you that opportunity, because in the long run you will not lose. And it is important to stress it is in the long run, because EV is theoretical.

Winning the lottery with EV
EV originated way back in the 17th Century after a discussion between a trio of eminent mathematicians about payouts for dice games. One of them, Blaise Pascal – later to become famous for his work on binomial expansions (Pascal’s Triangle) – was the first to use the idea of Expected Value, as he struggled with much a weightier quandary – the existence of God.

Many years later, a Romanian mathematician, Stefan Mandel, understood only too well how the EV for lotteries worked, and used his knowledge to take advantage of circumstances when lotteries can actually be a good bet. The UK National Lottery has a negative EV of 50p for every £1 staked.

To win the National Lottery, you need to match six numbers drawn from 1 to 49, of which there are 14 million possible combinations, meaning the chance of winning is 14million to one. Therefore in order for this to be a profitable bet, the return – the jackpot – would have to be greater than the odds, but lotteries tend to function as a risk-free method for governments to generate treasury funds, so the odds normally outweigh the return as stated above.

A ranking of common gambling activities from bingo to blackjack (in terms of EV) would have large lotteries at the bottom. The UK National Lottery as an example has a negative EV of 50p for every £1 staked (so -0.50p). This is why it is derided as an indirect form of taxation. Of course, lottery players, even when presented with the EV calculation – or an equivalent argument – are happy to put their money down seeing the 50p as the cost of buying the excitement of being in with the chance (no matter how small) of winning a life changing amount of money.

There is however, an exception to the standard EV for lotteries, however. When a winning ticket isn’t sold for a given draw, the jackpot rolls over and is combined with the jackpot from the next draw. When a jackpot rolls over enough times, it can rise to a point where the EV becomes positive. Mandel understood this and set about finding a way to exploit it.

The theory was simple. Wait for a big enough rollover, and then cover all the possible permutations. The practical implications enormous – he needed to buy tickets to cover all the permutations – that is long time at the local convenience store. Despite the extent of the challenge he succeeded in that monumental task (on a number of occasions). His outlay was less than the jackpot, which having bought tickets for every possible combination of numbers, he scooped (notably benefiting from a lack of shared winners).

The principle of exploiting specific situations of positive EV is at work when card counters try to get the better of casinos at the blackjack table, focusing on fleeting situations when the make up of the deck gives the player a potential edge over the house.

Buying up 14 million lottery tickets, or learning to count cards are both beyond the means of the average bettor, but there are two situations when positive EV is a realistic objective. Arbitrage & Niche Market Handicapping.

Arbitrage & Positive EV
Arbitrage is the explicit exploitation of odds from separate bookmakers which when brought together to form an artificial market provide a positive EV.

Arbitrage is an increasingly popular form of betting, having been the successful and legitimate basis of financial trading for many decades. Arbitrage is not a flakey system – the mathematical logic is irrefutable. The issue lies with the reluctance of many bookmakers to accommodate arbitrage players, which is where Pinnacle Sports stands out, operating an arbitrage welcome policy.

Implied EV
Whereas arbitrage trading exploits explicit situations of positive EV – the opportunities are concrete if fleeting – there are also situations where the positive value can be implied, emanating from a variation in opinion. Serious bettors build their own handicapping systems, and therefore generate their own opinion of a given market. When the odds that their system generates differ widely with what a bookmaker is offering, they perceive positive EV – based on their assessment.

This is likely in niche markets, when the playing field between bookmakers and independent bettors is more even. This can produce a decision matrix in which you are receiving odds that are better than those implied by the bet, and therefore in the long run the wager would give you a profit.

A brilliant mathematician wrestling with the biggest question of all may have created EV, but it is actually better suited for more humble means. It is an excellent tool for bettors to establish how profitable a bet might be. If you haven’t been using it, there is no need to resort to a decision matrix to reason why.




Thursday, 12 September 2013

How Do NFL Preseason Favourites Fare? Are The Odds Stacked Against The Preseason Favourites?

There’s an interesting phenomena in NFL betting. Teams picked as favourites for individual matches are more reliable than those marked as preseason favourites who often disappoint. In fact, over the last ten seasons, only one preseason favourite has gone on to win the Super Bowl.

The only team to survive the “Curse of the Super Bowl Preseason Outrights” in the last decade was the Indianapolis Colts in 2006, who had odds of 7.000, and beat the Chicago Bears 29 – 17 in Florida.

See the table below for a rundown of pre-season favourites and the eventual winners over the last 10 years:

Pre-Season Winners Over The Last 10 Years
Year
Pre-Season Favourite
Eventual Champion
2001
St. Louis Rams
New England Patriots
2002
St. Louis Rams
Tampa Bay Buccaneers
2003
Tampa Bay Buccaneers
New England Patriots
2004
Philadelphia Eagles
New England Patriots
2005
Indianapolis Colts/ Philiadelphia Eagles/ New England Patriots
Pittsburgh Steelers
2006
Indianapolis Colts
Indianapolis Colts
2007
New England Patriots
New York Giants
2008
New England Patriots
Pittsburgh Steelers
2009
New England Patriots
New Orleans Saints
2010
Indianapolis Colts
Green Bay Packers
2011
New England Patriots
New York Giants
2012
Green Bay Packers
Baltimore Ravens

This year’s favourite is the 5.760* San Francisco 49ers, who couldn’t manage one of the greatest comebacks in Super Bowl history last season and finished just one touchdown away from lifting the Lombardi Trophy.

However, in the last sevens years, no one of odds that short has succeeded in the NFL. The table below shows you the odds for the eventual winners for the last seven years:

Pre-Season Super Bowl Odds For Eventual Champions
Super Bowl
Year
Team
Preseason Odds
XLVII
2012
Ravens
14-1
XLVI
2011
Giants
20-1
XLV
2010
Packers
16-1
XLIV
2009
Saints
20-1
XLIII
2008
Steelers
20-1
XLII
2007
Giants
30-1

This year, the following teams have odds of 20.00* or less:

Favourite-To-Under 20.000 Range
Team Name
Odds
San Francisco 49ers
5.760
Denver Broncos
6.890
Seattle Seahawks
7.390
New England Patriots
9.020
Atlanta Falcons
15.200
Green Bay Packers
15.860
Houston Texans
16.840
New Orleans
18.890

So what’s behind this inability to correctly predict a correct favourite? There are numerous possibilities, so we’ll just list a few potential ideas below:
  • The draft system/no relegation in NFL makes talent more fairly distributed, so it’s more difficult to accurately predict how well teams will play each season
  • Even a small miscalculation in skill, when extrapolated over the many games played in a season, means that a season-long prediction is difficult
  • The market could be shifting as bettors allow bias for their teams outweigh rational thought, backing their favourites to win rather than an objectively better team
  • Pressure of being favourites
  • Playoff system should bias the best teams
  • Absence/ reasons for long winning streaks
It’s also important to remember exactly what the 49ers odds imply. Odds of 5.760* imply that the probability of San Francisco actually winning the Super Bowl is 17.4%. To put that in context, the New Orleans Saints’ (at 19.000*) have an implied probability of 5.29%, so just 12.1% lower than the 49ers, despite the odds difference being quite noticeable.

This pattern suggests that preseason is the perfect time to back longer teams and fade favourites, with bets on the longer teams potentially gaining more value as the season progresses when a clearer picture emerges.

Whatever happens, however, it goes without saying that there is a lot of value to be had if you can accurately predict the winner in the preseason. Even the smallest win in the last seven years would have netted you £130 on a £10 bet.



Wednesday, 4 September 2013

How To Bet On The NFL

NFL is becoming more and more popular outside of the US, and with more regular season games planned on UK soil over the next few years, betting on the NFL is set to become more prominent.

Despite the NFL only arriving on these shores once a year, American football fans can still watch the NFL all year round, so with more and more fans watching, this is the perfect time to learn how to bet on the NFL.

Betting On The NFL
There are three basic NFL bets. Most bookmakers offer a two-way win market on the outcome of the game – the equivalent of a soccer 1×2 but without the draw, in North America called the Money Line, Handicap and Total Points markets.

The win market 1×2 is popular, because it is straight forward. You simply bet on either side winning the game.
The only thing to check is what the policy is towards the unlikely event of a draw. At Pinnacle Sports any two-way win bets are refunded when a game is tied in regular time. Though the game will actually go into over-time to be decided, as standard bets apply to regular time unless otherwise stated.

The Handicap market is the most popular way to bet on the NFL in North America, and is the standard reference point for referring to relative chances in a game. As is the case in all sport, opposing NFL teams vary in strength. To effectively, counter the perceived bias in abilities, bookmakers offer a ‘handicap’ to level the playing field.

The Handicap market is the most popular way to bet on the NFL in North America
By using a fictional example, we can explain how betting on a handicap works. Both teams are offered associated odds on either a plus or minus points score, so for example the Indianapolis Colts are offered at -6 1.909 against the New York Giants +6 2.020.

A bet on Indianapolis would have won if the Colts won by six or more points, and similarly a bet on Chicago would have paid if the Giants had won the game, or lost by less than six points.

Saying the result was (29-17) to the Colts, those punters who bet on the Colts to win -6 1.909 would have won as the point difference was 12. Six more than the point’s handicap offered.

Totals betting on the NFL focuses on how many combined points will be scored by both teams during the game. Bookmakers will generally offer an option to bet on whether or not the total points will be either over or under their mark. This is why this is often referred to as the Over/Under. (Click here to learn more about each bet type).

In both the Handicap and Totals markets, when a team exceeds the required points for a successful bet it is called ‘covering the bet’.

NFL Betting – Developing Strategies
Once you have mastered the basics of NFL betting, you may want to explore some more advanced strategies. For example, punters looking to bet on the NFL handicaps must take into consideration a number of other factors than just the chances of team X beating team Y, but by how many points X is better than Y?

Professional NFL bettors spend time building power ranking systems to evaluate teams’ relative strengths and calculate who will have the advantage in any given game. This is then measured against the handicaps and odds offered by bookmakers – looking for discrepancies that represent value.

However, for those bettors new to NFL betting, there are some accessible handicapping systems that can produce accurate results in the short term.

Yardage Differential
At the most basic level the NFL is about the battle between offensive and defensive units. So one simple way to evaluate the strength of an NFL team is to look at the average offensive yards gained per play and the average defensive yards allowed per play.

As you would expect, teams that gain more yards than they allow, tend to win. While this isn’t exclusively accurate, this measure is at least as good a predictor of future performance. (Learn more about yards per play rankings here)

Home Field Advantage
NFL operates in a unique ‘closed’ league system, where relegation and promotion do not occur. From a statistical point of view, the data from successive seasons for such factors as Home Field Advantage (HFA) is robust.

To work out HFA for each franchise competing in the NFL you should subtract the total points scored by visiting teams from the home teams, and divide by the total number of games played.

You will notice after working out the HFA for the past 20 years, each Franchise HFA is close to a 3-point mark, which has become standard for handicapping purposes. (Learn more about calculating HFA here)

Key NFL Numbers
When betting on the NFL handicap there are a few key numbers to be aware of. These numbers are the margins most landed on relative to the NFL final score.

By understanding what the key numbers are, you can avoid betting on a bad handicap and can even work out which team the bookmaker wants you to bet on.

For instance 3 is the most common margin of victory in the NFL as most games are decided late on by a field goal, while 7 is the second most common winning margin, as this is how many points a team is awarded for a touchdown plus an extra point for a successful conversion.


You are now in a position to handicap the NFL, and use your figures to compare against the handicap available at the bookmakers.