_Here is a glossary of what we have found from the articles on this website.

Our work on various simulators has provided too many articles and facts for this page, instead there are dedicated pages giving overviews in the Simulators part of the website.

Article	Discoveries
Penalty Shootouts: Lottery or Not... ery	A penalty taker should shoot to his natural side (the left-hand side of the goal for a right-footer, and vice versa) with 57.6% of his penalties. A goalkeeper should dive to the taker's natural side 62.7% of the time. 79.3% of penalties should be scored; in the Premier League from 2001 onwards, 80.02% have been scored. Chelsea FC don't understand game theory.
​England Player Specialities	At the moment, England are considerably worse at producing goalkeepers than outfield players. Of the outfield positions, England are best for central midfielders, followed by full backs, centre backs, wingers and finally strikers.
Qualification for International Tournaments (UEFA)	​It is not very complicated to create a new qualification method for World Cups under UEFA, which suits all parties. The new 24-team European Championships is a pitiful idea.
​Goalkeeper Footedness	Outfield players are over twice as likely to be left footed than goalkeepers. This seems explained by bias in team selections. The percentage of left-footed outfielders is stable across all major European leagues. Goalkeeper footedness is more variable. Spain has the highest amount of left-footed goalkeepers, followed by Germany, France, Italy then England.
​Premiership Wages	The wages of top-flight footballlers seems justified by the increase in revenue their teams have seen, at least during the years of the Premiership. Astronomical increases in wages can be easily explored and explained once logarithmic scales are used. The biggest impact on English top-flight wages was the success English clubs had in Europe in the mid 70's to early 80's. The factors which were held to have a huge impact on wages, such as the Bosman Ruling, the advent of the Premiership and Chelsea's spending, had relatively little effect.
​Cricket Batting Averages, by Opposition	A new system can be developed for determining averages, taking the quality of the opposition into account. Under our new system, the top two batsmen of the last 22 years are BC Lara and SR Tendulkar, neither of whom were previously in the top 2 for averages. The average of every other top batsman during this period dropped under the new method.
​Cricket Batting Averages, by Age	​Cricket players hit their batting peak aged between 31 and 32. The ages of Test players follows a normal distribution. Australia field the oldest players, on average, from 1990-onwards. New Zealand field the youngest. England stick with average players for too long.
The New Boss Effect	Changing your socks can help you flip heads more often. Americans are convinced that athletes can be jinxed by being on the front of a magazine. This is the same as teams sacking managers after a few bad results.
​Premiership Statistics (Part 1 - scoring goals or keeping clean sheets?)	It takes months, not weeks, to break down a massive database of football statistics. Sorry about that. Teams who want to avoid relegation from the Premiership are best off trying to keep clean sheets. Teams who want to challenge for the title are best off trying to score goals.
​Premiership Statistics (Part 2 - indicators of position)	Penalties for and against are both fairly poor predictors of league position, as is shot accuracy. The number of shots on target per game is the strongest indicator of position, of the statistics we tested
Euro 2012 Permutations	​Whilst it is arguable whether the head-to-head system is better than using goal difference, it certainly is more interesting for making articles on here.
Olympic vs. Paralympic Success	We can use Olympic success to normalise Paralympic success. Over the long term, the richer countries seem to be increasing their share of Games medals. We've finally managed to produce a table with Great Britain at the top.
Do the Aussies Stand a Chance?	The best indicator before an Ashes of which team is going to win is the batting average of the sides. Due to their inferior batting, Australia only have a 7% chance of lifting the urn this summer. The batting of Michael Clarke is worth a whole Test to the Australians.
Deciding Frames	The best snooker players at coming through deciding frames at Ebdon, Selby and Davis. The worst are Bingham, Williams and Stevens. Older players are generally more likely to win deciders.
​Olympic vs. Paralympic Success - Winter Edition	By repeating analysis done on Summer Games, we can see which of the big players in Winter sport support their Paralympic athletes the best. Japan are the best nation at over-achieving in Winter Paralympics, whilst China are by far the worst. Ukraine has an astonishing record in Paralympic games, which comes from funding provided after the Chernobyl disaster. Almost one in five medals won in all summer and winter Olympic Games from 1998-2012 have been won by either USA or Russia Over time the number of medals won by the elite Winter sport nations is decreasing as more countries get facilities enabling them to compete to a high level despite their natural resources.
Does Commonwealth success predict Olympic success?	​ A nation will earn 148.2% their usual medal tally if they host a Games. There seems to be no correlation between teams' performances in a Commonwealth Games and their performances in the following Olympics. Great Britain almost seems to have a negative relationship.
​Associate Performance at the Cricket World Cup	Since 2003, Associate Nations have scored runs at a faster rate in each subsequent World Cup. Since 2007, the gap between Member and Associate nations has declined. Due to the lower data samples, the Associate performances in the Twenty20 World Cup are far more variable.
The Value of Odds	​We can measure to what extent bookies weight their odds so that they make a profit. The best-value competitions are those with the least competitors involved. The Grand National is surprisingly well-priced for its size.
​The Nervous Nineties	​The run-scoring patterns in Test cricket have largely remained the same since 2000. The worst years for run-scoring occurred in 2000 and 2007, whilst 2015 is also on track to be similar. Contrary to popular belief, batsmen are actually less likely to get out in the 90s than any run-scoring 'decade' below 120.
Short-term versus long-term odds	By comparing bookmakers' short-term odds (i.e. odds for individual matches) versus long-term odds (i.e. odds for whole tournaments), we can see where value lies. In the 2016 Six Nations, value was to be found in betting on Scotland for individual matches, whilst long-term bets on France were best value. ​Generally, the bookies were in consensus over each team's chance.
Transfer policy #1: what does money buy you?	There is a clear relationship between spending more on a player and him having better performances. However, for low-to-medium priced players, there is a lot of variability. By spending over £30m on a player a club should ensure they avoid a dud signing. The best signings over the last four seasons are Payet, Kanté and Sánchez. The worst signings in this time are Batshuayi, Bastón and Juanmi.
Transfer policy #2: where to buy from?	Premier League clubs have recently struggled to find good value in minor European leagues.  The nation which Premier League clubs have found best to sign players from is Scotland. Of the major leagues, France has provided a significant number of good-value signings.
Transfer policy #3: how well do players adapt?	For all leagues with available data, the average performance level drops for new signings at Premier League clubs. Unsurprisingly, those players signed from Premier League rivals stay closest to their original level. Players signed from the Championship are more likely to stay at their previous level compared to players from Serie A and the Bundesliga. Players signed from the Netherland's Eredivisie perform the worst compared to their previous level.
Transfer policy #4: which clubs have done the best?	Surprisingly, QPR have the best record of signing players which perform well given their fee. However, this is mainly due to a low sample size. Of the clubs with a sufficient number of transfers, Arsenal have the best record of transfers.
Tactical voting in European Elections (Scotland)	It is possible to vote tactically in proportional elections Change UK currently appear to be denying fellow anti-Brexit parties MEPs without looking like having their own elected
Crucible Players	The data shows that Ronnie O'Sullivan is, unsurprisingly, the best snooker player currently playing Judd Trump's career record sees him best of the rest Matthew Stevens seems to be the player with the best Crucible record given his career performance