Tuesday, 27 August 2013

Wisdom Of The Crowd Applied To Betting - What Happens When Crowds Act Like Herds?

If you have a difficult conundrum, it’s reasonable to assume that the more people you survey, the better your solution will be. This is known as the ‘wisdom of the crowd’, and is an effective way of making decisions under uncertainty, like estimating the probability of the outcome of sporting events.

The trouble is that sometimes the crowd acts like a foolish herd – so how do you know when the collective is getting things wrong?

How wisdom of the crowds works
The wisdom of the crowds works by averaging estimates from a wide variety of people. Participants will equally over- and under-estimate outcomes, leaving the average of their predictions as close to perfect.

Guessing the number of sweets in a large jar is a favourite game at fairs and fetes, and provides a simple illustration of the power of collective wisdom. The most effective way to predict the number of items is to wait until close to the contest deadline, and then simply average all the guesses.

By doing this you are benefiting from the estimates of all the pairs of eyes that have perused that jar. It may a be a little impractical and you will certainly draw a few strange looks as you perch your calculator on the trestle table, but it illustrates how to harness collective wisdom. And could win you a few sweets, too.

Predicting the unknown – the USS Scorpion
The wisdom of the crowds phenomenon was first observed in the early 20th century by the eminent anthropologist, Sir Francis Galton. When at a livestock fair he observed a competition to guess the weight of a butchered ox. No one-person got the correct weight but Galton calculated the median of guesses as being within 0.8% of the answer, stating that “the middlemost estimate expresses the vox populi, every other estimate being condemned as too low or too high by a majority of the voters.”

The vox populi or Wisdom of the Crowds transcends many aspects of decision-making, a wide and fascinating cross-section of which are examined by James Surowiecki in his 2004 book on the subject. Among its fascinating anecdotes is the story of search for the USS Scorpion submarine, which was lost in the North Atlantic in May 1968.

In its search efforts, the navy was only able to locate the wreck to within a 20-mile range. In a test of collective wisdom, naval officer – Dr. John Craven – gained individual insights from a wide and varied group of naval/salvage experts, and used their collective information to pinpoint a location that turned out to be just 220yds from the wreck of the Scorpion.

So how did these individuals’ unrelated opinions average-out to such accuracy?

Predicting the unknown – Sports betting
Just like locating a shipwreck, the results of sporting events cannot be known a priori, yet even under these conditions the crowd does generally provide an accurate assessment of the respective probabilities of the outcomes.

Odds gain accuracy from the wisdom of the crowds by shaping a bookmaker’s opening line and exposing it to public appraisal.

Very sharp bettors will have their own ideas about opening lines that, when they diverge with the bookmakers, will cause the sharp bettors to bet quickly and re-shape the markets. This happens a lot at Pinnacle Sports because we have the sharpest players – high precision individuals – attracted by the lowest margins.

As markets become more liquid – i.e. more people voice opinion by placing their bets – the market generally moves to its most efficient position, just as the more guesses of the number of sweets the more accurate the averaged guess.

However, in the Scorpion story, Craven restricted his ‘crowd’ to the best available experts, and garnered opinions independently, but in betting high precision individuals aren’t the only participants, and decisions aren’t made in a vacuum, so what happens when other less sophisticated bettors weigh in, and when there is a total absence of sharps?

Behavioural biases & information cascades
The bettors that contribute to the movement of a market are generally drawn from a wide spectrum of knowledge and experience, and there is often a specific distribution to the times that different groups place their bets.

One of the recurring themes in our articles is the importance of understanding behavioural biases, and how they can impede rational risk assessment. As already mentioned, sharp players tend to act soonest, while public money – effectively less informed betting – tends to happen closest to event start times, and frequently reflects very general rules of thumb, e.g. “which team am I more familiar with?”, “which team do I recall winning more often?”, “which team is everyone else betting on?”

These lazier judgments normally result in more money on the favourite, skewing the market away from its most efficient position. This is an illustration of how the wisdom of the crowd can be replaced by the foolishness of the herd.

Public money may distort rather than reverse a market, but this kind of collectively poor reasoning – known as an Information Cascade – can have far greater impact.

Wooden roads & Harry Redknapp
Examples of information cascades outside of betting include a run on the bank, or the rise and swift fall of wooden roads in the 19th century (if you are intrigued by this, read Surowiecki). In the betting world, the managerial markets often follow the information cascade model, with the events following Fabio Capello’s resignation as England manager on February 8th 2012 a salient example. Bettors were willing to wager huge amounts at very skinny odds that Harry Redknapp would replace Capello as the England manager.

In this situation, precision individuals were absent, as the market was driven to an inaccurate judgment, based on persuasive arguments for Redknapp’s appointment (there was momentum behind an English manager, Redknapp had enjoyed a successful spell with Spurs and the public was seemingly behind his appointment), while many bettors were willing to rely on the judgment of others (and the media). Not being privy to the information of others bettors assumed that the information amounted to more than just speculation or wishful thinking. It didn’t – Roy Hodgson was announced as the new England manager on 1st May 2012.

In an information cascade decisions are made sequentially, generating momentum, as the effect of incremental decisions being based on the existing opinion that helped build the feedback loop that drove the price down.

The information cascade phenomenon underlines the point from the Scorpion anecdote – the harder the question, and/or the weaker the knowledge pool the less reliable the collective wisdom. If bettors can avoid being swept away by the cascade, these situations can present significant opportunities.

Pump and dump – market manipulation
Motivation is a key factor in forming and movement of markets. Speculators are motivated by profit but the ways in which this can be achieved are divergent. In the financial world Pump & Dump commonly refers to the practice of hyping shares to inflate their price and enable short-term gains, while the inverse is also common with shortening of shares that are driven down by negative speculation. These tactics drive the market in an unnatural direction, and equally apply within betting. The speed with which information now disseminates (via social media) can make this even more pertinent, and is not a circumstance where the crowd can be trusted.

Niche markets
Notwithstanding some of biases we have outlined, the more liquid a market, the better the collective wisdom. This applies to major sports – big soccer leagues, US major league sports and tennis grand slams – which make it much harder for bettors to find value. Niche sports however, can provide opportunities because of the absence of information, and therefore wisdom.

There will be far fewer high precision individuals betting niche markets, and it will also test the knowledge of the bookmaker, which presents opportunities for those bettors prepared to do the research, and who are able to recognize when the crowd is lacking wisdom and react accordingly.

Monday, 19 August 2013

Gain A Football Betting Edge Using Home Team Advantage Statistics

There are numerous tools and techniques bettors can utilise when looking to gain a betting advantage over the markets. One of these is Home Field Advantage, which shows what advantage a home team has.

It’s widely understood that sports teams perform better at home than when they are away or at a neutral ground. For example, in the 2012/13 Premier League season 592 goals were scored by sides at home, while away teams found the back of the net just 471 times. That same distinction has emerged for every season since the football league’s inception in 1888.

Evidence of HFA in the Premier League
The table below shows a summary of every Premier League season, with home, away and draw percentages, as well as goals per game for home and away fixtures and the differential per game:

The numbers may not seem surprising at first glance, but it is the consistency across 21 Premier League seasons that stands out. Over that period, there was only a 9% variation between home win rates, a smaller variation for away wins (7%) and a rise in the range for draws (11%).

Therefore Premier League teams consistently win nearly half of all home games (46%), while there is a 27% chance of a draw, and 27% for an away win. In short, it shows that there is a lot of evidence for a home advantage in the Premier League.

HFA goal data for the Premier League
The table below showcases the HFA (in goals) of the 11 teams in the Premier League who have been present over the past five seasons. The figure represents the average goal difference for the teams when playing at home, and is predominantly positive:

A quick look at the above table shows some interesting points relating to teams’ home performances. For example, while the top performer at home over the last five years was Manchester United (winning by an average of 1.65 goals at home), the Red Devils had a comparatively poor season in 2012/13, winning by just 0.89 at home.

That was their worst record in the last five years by a notable margin – a strange results from a team that walked the league without much of a challenge. Could it be that Man Utd were excellent, but with some hiccups at home? Or perhaps they rested some of their best players for games at Old Trafford, knowing they were probably good enough to win with a less-than-full-strength team?

Liverpool have the fourth-highest HFA in the league, and therefore the much talked about “affect of the Kop” could be true

It’s also interesting to note Liverpool’s home performance. At 1.09 over five years, the Reds have the fourth-highest HFA in the league, and therefore it seems that the much talked about “affect of the Kop” could actually hold true. Their home form far outweighed their league position in those years.

The Merseysiders have had a poor last two seasons, however, at just 0.42 and 0.89 – is the Anfield effect fading? Or are Liverpool just getting worse, and even their 12th man can’t help them?

Stoke City are another side who are traditionally difficult to tackle at home, however their HFA is one of the worst in the league at 0.28. Are biases regarding their home form just a hangover from another time? Or could you consider a 0.28 home field advantage good for a team of Stoke’s ability in the tough Premier League? The above questions are important for you to answer if you want to correctly use HFA data to place bets.

Interestingly, every team that has been relegated from the Premier League in the past five seasons has had a negative HFA.

Goal-based HFA information has particular significance in Asian Handicap betting. If a team has a home handicap less than their Home Field Advantage, it might make a sensible bet – although this is just one of a number of factors to consider.

For a list of Premier League team’s HFA from last season, check out the table to the left.

Influences on HFA
There are many preconceptions on what influences HFA in soccer – crowd size, travel and weather are a few which have been proposed over the years.

Moskowitz and Wertheim who wrote Scorecasting compiled data to test a variety of these popular theories. What they found was that the most prominent influence was the referee. They found that home teams received small preferential treatment from the referee.

The authors make it clear that the bias is not done consciously, but rather being humans, the referees absorb the raw emotion of a home crowd, and sometimes make a decision subconsciously in favour of the close-by raucous crowd.

Harvard Research Assistant Ryan Boyko researched further proof for the influences on Home Field Advantage. Boyko studied 5,000 Premier League games from 1992 to 2006 to discern any officiating bias for home teams.

His conclusion was that for every 10,000 home team fans, home team advantage increased by 0.1 goals.
His study also showed that home teams are more likely to receive penalties, particularly from inexperienced referees. Therefore building referee profiles is also important when predicting a match’s outcome.

Monday, 12 August 2013

How To Calculate The Number Of Goals In A Soccer Match

Poisson Distribution, coupled with historical data, can provide a method for calculating the likely number of goals that will be scored in a soccer match. Read on for a simple method to calculate the likely outcome of a soccer match using Poisson Distribution.

Poisson Distribution Explained
Poisson Distribution is a mathematical concept for translating mean averages into a probability for variable outcomes. For example, Chelsea might average 1.7 goals per game. Entering this information into a Poisson formula would show that this average equates to Chelsea scoring 0 goals 18.3% of the time, 1 goal 31% of the time, 2 goals 26.4% of the time and 3 goals 15% of the time.

How to calculate outcomes with Poisson Distribution
To calculate the possible outcomes for a match using Poisson Distribution, we first need to calculate a value for each team’s “Attack” and “Defence Strength”. These numbers – calculated from last season’s performance data – allow us to model possible outcomes for each game of the season.

Selecting the data range is vital when using Poisson Distribution, too long and the data wont be relevant for the teams current strength, while too short may allow outliers to unfairly skew the data. For this analysis we are using the 38 games played by each team last season.

Calculate the average goals scored at home and away
To get the average number of goals scored last season, average the number of goals scored per team, per game, per season. In mathematical terms, that’s:
  • Season Goals Scored / Number of Teams / Number of Games
In 2012/13, that was 592/20/19 at home and 471/20/19 away, equalling an average of 1.558 goals per game at home and 1.239 away. The difference from this average is what constitutes a team’s “Attack Strength”.
  • Average number of goals scored at home: 1.558
  • Average number of goals scored away from home: 1.239
We’ll also need the average number of goals an average team concedes. This is simply the inverse of the above numbers (as the no. of goals a home team scores will equal the same number that an away team concedes.):
  • Average number of goals conceded at home: 1.239
  • Average number of goals conceded away from home: 1.558
We can now use the numbers above to calculate the Attack and Defence Strength of both Swansea City and Manchester United for their match on August 17th, 2013.

Predicting Swansea’s Goals
Calculate Swansea’s Attack Strength:
  • a. Take the number of goals scored at home last season by the home team (Swansea: 28) and divide by the number of home games (28/19): 1.473
  • b. Divide this value by the season’s average home goals scored per game (1.473/1.558), to get the “Attack Strength”: 0.946. This shows that Swansea scored 5.4% fewer goals at home than a hypothetical “average” Premier League side.
Calculate Man Utd’s Defence Strength:
  • a. Take the number of goals conceded away last season by the away team (Man Utd: 24) and divide by the number of away games (24/19): 1.263.
  • b. Divide this by the season’s average goals conceded by an away team per game (1.263/1.558) to get the “Defence Strength”: 0.81. Man Utd conceded 19% fewer goals than an “average” Premier League side on the road.
We can now use the following formula to calculate the likely number of goals the home team might score:
  • Swansea’s Goals = Swansea’s Attack x Man Utd’s Defence x Average No. Goals
In this case, that’s 0.946* 0.81 * 1.558, which equates to Swansea scoring 1.194 goals.

Predicting Man Utd’s Goals
Calculate Man Utd’s Attack Strength:
  • 1. Take the number of goals scored away last season by the away team (Man Utd: 41) and divide by the number of away games (41/19): 2.158
  • 2. Divide this value by the season’s average away goals scored per game (2.158/1.239), to get the “Attack Strength”: 1.742. This shows that the Red Devils scored 74.2% more away goals than a hypothetical “average” Premier League side.
Calculate Swansea’s Defence Strength:
  • 1. Take the number of goals conceded at home last season by the home team (Swansea: 26) and divide by the number of home games (26/19): 1.368.
  • 2. Divide this by the season’s average goals conceded by a home team per game (1.368/1.239) to get the “Defence Strength”: 1.104. Swansea conceded 10.4% more goals than an “average” Premier League side at home.
We can now use the following formula to calculate the likely number of goals the away team might score:
  • Man Utd’s Goals = Man Utd’s Attack x Swansea’s Defence x Average No. Goals
In this case, that’s 1.742 * 1.104 * 1.239, which equates to Man Utd scoring 2.383 goals.

Poisson Distribution Betting – Predicting Multiple Match Outcomes
Of course, no game ends 1.194 vs. 2.383 – this is simply the average. Poisson Distribution, a formula created by French mathematician Simeon Denis Poisson, allows us to use these figures to distribute 100% of probability across a range of goal outcomes for each side. The results are shown in the table below:

The formula itself looks like this: P(x; μ) = (e-μ) (μx) / x!, however, we can use online tools such as this Poisson Distribution Calculator to do most of the equation for us.

All we need to do is enter the different goals outcomes (0-5) in the Random Variable (x) category, and the likelihood of a team scoring (for instance, Man Utd at 2.383) in the average rate of success, and the calculator will output the probability of that score.

Poisson Distribution for Swansea vs Man Utd
Man Utd

This example shows that there is a 9.2% chance that Man Utd will not score, but a 22% chance they will get a single goal and a 26.2% chance they’ll score two.

Swansea, on the other hand, are at 30.3% not to score, 36.2% to score one and 21.6% to score two.
Hoping for a side to score five? The probability is 5.9% if United are the scorers, or 0.61% for Swansea to do it.
As both scores are independent (mathematically-speaking), you can see that the expected score is 2 – 1 to Man Utd. If you multiply the two probabilities together, you’ll get the probability of the 2-1 outcome – 0.095 or 9.5%.
Now you know how to calculate outcomes, you should compare your result to a bookmaker’s odds to help see how they differentiate.

For example, taking into account all possible draw combinations (0-0, 1-1, 2-2, 3-3, 4-4 and 5-5), this method gives a probability of 0.186 or 18.6%. Pinnacle Sports’ odds were 3.960 (a 25.3% implied probability).

Therefore if last season’s form was a perfect indicator of this season’s results, we should expect a 2-1 victory. Unfortunately it isn’t as simple as that, which is why pure Poisson analysis has limitations.

Poisson Distribution Betting – The Limits of Poisson Distribution
Poisson Distribution is a simple predictive model that doesn’t allow for a lot of factors. Situational factors – such as club circumstances, game status etc. – and subjective evaluation of the change of each team during the transfer window are completely ignored.

In this case, it means the huge x-factor of Manchester United’s first Premier League game without Sir Alex Ferguson is entirely ignored. The league is also arguably stronger this season, so United are less likely to score as many goals as they did last year.

Correlations are also ignored, such as the widely recognised pitch effect that shows that matches have some tendency to be either high or low scoring.

These are particularly important areas in lower league games, which can give punters an edge against bookmakers.

Thursday, 1 August 2013

Do NBA Teams Perform Poorly On Long Road Streaks?

NBA teams often face long stretches of road games, with 261 matches played per season as part of two or more back-to-back away games. Do NBA teams perform worse during these long road streaks? We investigated these sequences to see what this can tell us for NBA betting on the road.

Throughout the 2012 NBA season, away teams won 41.6% of games. However, when franchises were involved in road trips involving more than one game they won 42.3% of the time – an increase of 0.7%.

This goes against what most punters might assume – teams actually won more during sequences of away games than individual matches on the road.

Two is the Magic Number
Even more interestingly, teams that embark on a two game away streak have a better win percentage (44.4%) than the average of 42.3% – an increase of 2.1%. For some reason, teams won more away games if they played two in a row rather than single games or longer sequences.

A Drop off in Games 3 & 4
Despite better than average performances during a two game away run, franchises’ win percentages suffer dramatically during road streaks involving three or four games.

When franchises play three or four sequential road games, their win percentage drops to 37.2% and 37.1 % – down a huge 5.1% and 5.2% respectively.

There are a number of external factors that may affect a team during a run of three or four consecutive away games.

NBA teams on the road for longer than two games will often play back-to-back games over two days, which can result in players becoming fatigued due to a lack of recovery time, while teams also play around twice as many back-to-back games on the road as they do at home.

Confidence a Factor on Longer Away Runs
A common assumption is that the longer an NBA franchise is on the road the more likely they are to lose. However, by looking at the data from last season all sequences from five to nine games had a higher than average win percentage (42.3%).

Confidence could be a factor behind the unforeseen results, as each win during a road trip would galvanize a team, that otherwise may struggle with fatigue and a lack of motivation.

Also the longer the trip, the more rest days they will have, while being away from home for a longer period could create a ‘siege mentality’ amongst the squad, which is doubtful for trips spanning three games.

Over five seasons NBA scheduling ensures each team will have played 80 games against their division, 180 games against the rest of their conference and 150 games against the other conference.

For this reason punters betting on the NBA should evaluate five seasons of NBA action for a more accurate reflection of betting on NBA road teams.