Definitions

hook ball

Ten-pin bowling

Ten-pin bowling is a competitive sport in which a player (the “bowler”) rolls a bowling ball down a wooden or synthetic (polyurethane) lane with the objective of scoring points by knocking down as many pins as possible.

The wide, lane is bordered along its length by "gutters”—semicircular channels designed to collect errant balls which also pose an obstacle to advanced bowlers, because a straight ball cannot be rolled on a regulation lane at the angle required to consistently carry (knock down) all ten pins for a strike. Most skillful bowlers will roll a more difficult-to-control hook ball to overcome this. There is a foul line at the end of the lane nearest to the bowler: if any part of a bowler’s body touches the lane side of this line after the ball is delivered (rolled), it is called a foul and no pins knocked over by that delivery are scored. (The bowler is allowed a shot at a new rack of ten pins if he fouled on the first roll of a frame.) Behind the foul line is an “approach” approximately long used to gain speed and leverage on the ball before delivering it. from the foul line, where the lane terminates, it is joined to a roughly , wide surface of durable and impact-resistant material called the “pin deck” where each rack of pins is set.

The bowler is allowed ten frames in which to knock down pins, with each frame being composed of up to two rolls. The tenth frame may be composed of up to three rolls: the bonus roll(s) following a strike or spare in the tenth (sometimes referred to as the eleventh and twelfth frames) are fill ball used only to calculate the score of the mark rolled in the tenth. Bowling has a unique scoring system (see below) that is notoriously confusing to newcomers who attempt to score a game with multiple marks (strikes and spares). Bowling scores tend to be unintuitive: if a bowler was to knock down 9 pins with his first shot but miss his spare every frame, he would have a score of 90; if the same bowler were to make all of his spares and knock down 9 with the bonus ball, he would have a score of 190. If he were to carry all ten pins with each shot and strike with each of his bonus balls in the tenth frame, he would have shot a perfect game of 300.

Since being brought to the United States from Europe, ten-pin bowling (thought to be descended from the game of skittles) has risen in popularity as its technology has improved. The sport is most popular in the United Kingdom and the United States. Both nations maintain national regulatory organizations that govern the sport’s rules and conduct and many of those countries’ best players participate in tournaments on both the national and international stage. Because of the rise in popularity, many companies are now making bowling balls and apparel for professionals as well as for recreational bowlers. Bowling has also become more prevalent in the media in recent years, with the continued popularity of bowling publications and the appearance of films centred around the culture of the sport. However, the sport continues to face challenges in garnering mainstream coverage of the athletic aspects of the game.

History

Bowling is a game in which players attempt to score points by rolling a bowling ball along a flat surface called the lane in order to knock down objects called pins. There are many forms of bowling, with the earliest dating back to ancient Egypt; it is now known that the Egyptians had invented bowling. Origins can also be traced to ancient Finland and Yemen, and much later in 300 A.D. in Germany.

Origins

In 1930, British anthropologist Sir Flinders Petrie along with a team of archaeologists, discovered various primitive bowling balls, bowling pins and other materials in the grave of an Egyptian boy dating to 5200 BC. Their discovery represents the earliest known historical trace of bowling. However, some dismiss these findings , arguing that bowling originated in Germany in AD 300. The first written reference to bowling dates to 1366, when King Edward III of England banned his troops from playing the game so that they would not be distracted from their archery practice. It is believed that King Henry VIII bowled using cannon balls. In Germany the game of Kegal (Kegelspiel) expanded. The Kegal game grew in Germany and around other parts of Europe with Keglars rolling balls at nine pins, or skittles.

Ninepin bowling was introduced to America from Europe during the colonial era, similar to the game of skittles. It became very popular and was called “Bowl on the Green.” The Dutch, English, and Germans all brought their own versions of the game to the new world, where it enjoyed continued popularity, although not without some controversy. In 1841 a law in Connecticut banned ninepin bowling lanes due to associated gambling and crime, and people were said to circumvent the letter of the prohibition by adding an extra pin, resulting in the game of ten-pin bowling.

A painting that which dates from around 1810, and has been on display at the International Bowling Hall of Fame and Museum in St. Louis, Missouri, however, shows British bowlers playing the sport outdoors, with a triangular formation of ten pins, chronologically before it appeared in the United States-a photograph of this painting appeared the pages of the US-based "Bowler's Journal" magazine in 1988.

Modern American ten-pin bowling is most closely related to the German nine pin game Kegelspiel. Germans were instrumental in fostering the game’s popularity as they formed their own bowling clubs both before and after the American Civil War. The first indoor bowling alley was Knickerbockers of New York City, built in 1840. The Brunswick Corporation’s addition of bowling equipment to their product line also served to increase the sport’s popularity. In 1914 Brunswick replaced their line of wooden bowling balls, mostly made with lignum vitae, with hard rubber Mineralite bowling ball. The change was met with great approval.

Organization and increased popularity

Bowling has long been seen as a sport of the working classes. Accordingly, most bowling alleys at the turn of the century were small, private establishments, mainly frequented by men. This began to change as the sport became increasingly regulated and generally gained in prestige. Although it has not shed its working class image entirely, today bowling is no longer only a unisex sport, and is enjoyed by people the world over. In 1895 the American Bowling Congress was started in New York City. This was soon joined by similar organizations geared toward female bowlers. These groups began creating the standard rules for bowling that have survived to the modern day. At the same time, the sport’s image among the upper classes was enhanced by the opening of more luxurious and elegant alleys like The White Elephant in New York City, opened by restaurateur Joe Thum, whom many consider to be the father of bowling, along with Dick Weber. Thum created the first bowling organization in the United States on September 9, 1895, when he pulled together representatives of various regional bowling clubs into an overarching organization, the American Bowling Congress (ABC). This spurred greater interest in the game, with the number of officially sanctioned alleys rising from 450 in 1920 to 2,000 in 1929.

1940 to 1960

The period from 1940 to 1960 is known as the golden age of bowling due to the sport’s great popularity and advances in its play. Indeed, by 1945, bowling was a billion-dollar industry in the United States. Promotion by the U.S. Armed Forces and its image as a sport for the common man made bowling an enticing choice of activity for Americans. For this reason, racial integration was perhaps inevitable. The American Bowling Congress had been a whites-only organization throughout its existence, but lobbying by numerous labor organizations and individuals after the war quickly led to a reversal of this policy.

This era also saw a great increase in bowling technology. Pins had previously been set by human pinsetters or “pin boys”, but with the invention of the semi-automatic pinsetter in 1936, the process became much easier. In 1946 AMF Bowling launched the first commercial fully automatic pinsetter to replace the earlier Brunswick semi-automatic and fully manual bowling establishments. Brunswick itself introduced its own automatic pinsetter design to bowling centers in 1955. The television age of the 1950s also helped to increase the popularity of ten-pin bowling, as images of the sport began to enter the homes of millions across the United States. Eddie Elias founded the Professional Bowlers Association in 1958, and its Pro Bowlers Tour became a permanent part of ABC’s sports lineup.

1960 to the present

Ten-pin bowling was introduced in the United Kingdom in 1960. This was driven by the opening of the Stamford Hill and Golders Green bowling alleys in London. Ten-pin bowling took the UK by storm, with alleys opening up one after the other. At its peak there were over 160 bowling alleys in the UK, but a lack of re-investment and waning interest left the fad in a sorry state. This led to a general deterioration of bowling alleys, with a commensurate decline in their image. In the 1970s a major chain operator pulled out of bowling and converted many of the more luxurious alleys into Bingo halls. The industry nearly collapsed, with two thirds of the existing alleys closing over the next few years.

Until the mid 1980s there was little, if any, new investment in the sport with the decline in interest being attributed to the complex scoring system, especially as it was a manual process then. However, this all changed with the introduction of computers and automated electronic scoring systems. This meant that the general public only had to enter their names into the computers and everything else was done automatically. This changed the face of bowling and was largely responsible for the newfound interest in the sport.

AMF carried this revitalization of the sport by embarking on a major refurbishment programme. This re-investment led to the construction of many bright, modern and attractive sites and began the second golden age of bowling. During the late 1980s and early 1990s the number of ten-pin bowling alleys across the country rose to over two hundred. This was higher than it had ever been in the sixties, then the peak of the sport’s popularity.

Today, over 100 million bowlers play in over 90 different countries. More men and women worldwide bowl than play any other sport, with the possible exception of football (soccer in the USA and Canada). Bowling has far more registered dues-paying participants than any other sport. The bowling industry spends significantly more money each year than any other sport on airlines, restaurants, hotels and rental cars. There is an active movement to make bowling an Olympic sport, especially by the Fédération Internationale des Quilleurs, the world governing organization for nine and ten-pin bowling. The most elite players regularly play in televised tournaments, and new bowlers continue to delight in learning the game. In addition, modern bowling alleys have changed greatly. As people have become exposed to a wider range of entertainment options, the trend has shifted to building large entertainment centers that allow people to enjoy many different activities. These developments often include multi-screen cinemas, restaurants and night clubs. This has had a great impact on the image of the sport among families.

Play

A game of ten-pin bowling is divided into ten rounds (called “frames”). In a frame, each player is given two opportunities to knock down the skittle targets (called “pins”). He or she rolls the first ball at the pins. If the first ball knocks down all ten pins, it is called a “strike” and the frame is completed. When pins are left standing after the first ball, those that are knocked down are counted and then removed. Then the player rolls a second ball and if all the remaining pins are knocked down, it is called a “spare.” There are bonuses for removing all the pins. If there is more than one player scheduled on a lane, play passes to the next player until all players have completed the frame. Then play continues with the next frame. The final or tenth frame of a game may involve three balls. See Scoring below.

The ten pins are usually automatically set by machine into four rows which form an equilateral triangle where there are four pins on a side (Pythagorean Tetractys). There are four pins in the back row, then three, then two, and finally one in the front at the center of the lane. The pins are numbered one through ten, starting with one in front, and ending with ten in the back to the right. This serves to ease communication; one could say that the 4 and 7 pins were left standing. Neighboring pins are set up apart, measured from center to center. Due to the spacing of the pins and the size of the ball (about in diameter), it is impossible for the ball to contact every pin. Therefore, a tactical shot is required, which would result in a chain reaction of pin hitting pin. In an ideal shot, for a right-hander, the ball will contact only the 1, 3, 5 and 9 pins. (For a left-hander, the 1, 2, 5 and 8 pins).

In order to count, a pin must be knocked over entirely. Even if a pin wobbles, unless it is knocked over completely, it is not scored. If the pin is wobbling as the automatic pin machine picks it up (or the machine itself knocks over the pin while it is wobbling), it is still considered standing and is not scored. Also, if a pin is moved, it does not change its designation. For example, if the 10 pin was still standing and the 7 pin slid into the 8 pin position, converting this spare would still be considered and given a 7-10 split award (if performed in sanctioned play).

There are generally two primary styles of rolling the ball down the lane. Most newer players play by rolling the ball straight, hopefully into the 1-3 pocket for right-handed bowlers or the 1-2 pocket for left-handed bowlers. More experienced bowlers usually roll a hook, which means that they make the ball start out straight and then curve towards the pocket. To produce a hook the player needs to let go of the ball with his or her thumb first, then the middle and ring finger release almost simultaneously. This gives the bowling ball its spin needed for the hook. If the player is right-handed, an ideal position of the thumb after letting go of the ball is “10 o’clock”, meaning that the thumb has gone from 12 to 10, as looking at a clock. The corresponding position for left-handed players is 2 o’clock. Of course there are innumerable variations in style and technique and the position of the thumb can vary from person to person. Lab research has shown that the ideal shot will enter the pocket at an angle of 6 degrees with respect to the lane boards, which means that a straight ball should be thrown from the side of the lane, near the gutter.

The conventional bowling styles use either a four or five step approach beginning 8 to 16 feet (2.4 to 4.8 metres) behind the foul line. Some extremely young or physically challenged players may use both hands to swing the ball forward from in between their legs. This kind of style has the bowler start close to the foul line, and is called “Granny style.” Another method for novice bowlers is the “bounce pass” technique which is performed by thrusting the ball from your chest with two hands towards the pins. This technique is easily picked up by weaker players but is seldom used because it is frowned upon by the bowling community due to the potential to damage the lanes and/or ball.

There are systematic ways of using the lane arrow marks and approach dots to make it easier to hit the pocket to get strikes, and for making spares. Focusing on these targeting guides helps eliminate fear of the gutters.

Rules and regulations

The regulations listed here are generally based around regulations set by the United States Bowling Congress and the British Tenpin Bowling Association. These rules are followed by all sanctioned leagues and events, such as tournaments.

This information is clarified by the World Tenpin Bowling Association in its “Statutes & Playing Rules”

Playing area

The sport of ten-pin bowling is performed on a straight, narrow surface known as a lane. This bowling lane is from the foul line to the head pin (1-pin). About from the foul line are a set of guide arrows. The lane is wide and normally consists of 39 wooden boards or a synthetic material. The bowling lane has two sets of approach dots; from the foul line back to the first set of approach dots is about and to the second set of approach dots is about (an additional ). Although this figure varies, the lane is protected by about 18 ml of oil. The PBA events use about 30 ml of oil, and the PWBA events use 25 ml. The oil starts from about 4 inches from the foul line and is applied for about down the lane from that point.

Pins

USBC rules specify that a pin must be tall and about wide at its widest point, where a rolling ball would make contact. There are additional measurements which delineate the shape. The weight of a single pin must be at least 3 pounds, 6 ounces (1.47 kg) and no more than 3 pounds, 10 ounces (1.64 kg). Within a set of ten pins, the individual weights may vary by no more than 4 ounces (113.4 g), if made from wood or plastic coated, or just 2 ounces (56.7 g) if synthetic. The top of the pin shall have a uniform arc with a radius of 1.273 inches, ± 1/32 inch (31.5 – 33 mm).

The USBC also has regulations governing the weight distribution of the pin from top-to-bottom. Pins are allowed one or two “voids” (holes) in the belly area (which can be viewed if the pin is cut in half from top-to-bottom). The voids are needed to balance the narrower top half of the pin with the wider bottom half. Without them, the pins would be too bottom-heavy to fall properly when struck.

The pins must show the name and mark of the maker, either “USBC Approved” or “BTBA Approved” and appear uniform.

The head pin or 1 pin stands on board 20 of the lane.

Bowling ball

The circumference of the ball must not be more than , and the ball cannot weigh more than 16 pounds (7.26 kg). The ball must have a smooth surface over its entire circumference except for holes or indentations used for gripping the ball, holes or indentations made to bring the ball back into compliance with weight-distribution regulations, identification letters and numbers, and general wear from normal use.

For much of the history of bowling, bowling balls were made using a three piece construction method. Starting in the mid 1990s, however, most manufacturers switched to a two-piece method. In response to these innovative ball designs, the American Bowling Congress placed further restrictions on the technical characteristics of the ball such as the radius of gyration and hooking potential.

Rules of play

A game of bowling consists of ten frames. In each frame, the bowler will have two chances to knock down as many pins as possible with their bowling ball. In games with more than one bowler, as is common, every bowler will take their frame in a predetermined order before the next frame begins. If a bowler is able to knock down all ten pins with their first ball, he or she is awarded a strike. If the bowler is able to knock down all 10 pins with the two balls of a frame, it is known as a spare. Bonus points are awarded for both of these, depending on what is scored in the next 2 balls (for a strike) or 1 ball (for a spare). If the bowler knocks down all 10 pins in the tenth frame, the bowler is allowed to throw 3 balls for that frame. This allows for a potential of 12 strikes in a single game, and a maximum score of 300 points, a perfect game.

Scoring

In general, one point is scored for each pin that is knocked over. So if a player bowls over three pins with the first shot, then six with the second, the player would receive a total of nine points for that frame. If a player knocks down 9 pins with the first shot, but misses with the second, the player would also score nine. When a player fails to knock down all ten pins after their second ball it is known as an open frame.

In the event that all ten pins are knocked over by a player in a single frame, bonuses are awarded.

  • strike: When all ten pins are knocked down with the first ball (called a strike and typically rendered as an “X” on a scoresheet), a player is awarded ten points, plus a bonus of whatever is scored with the next two balls. In this way, the points scored for the two balls after the strike are counted twice.

Frame 1, ball 1: 10 pins (strike)
Frame 2, ball 1: 3 pins
Frame 2, ball 2: 6 pins
The total score from these throws is:
*Frame one: 10 + (3 + 6) = 19
*Frame two: 3 + 6 = 9
TOTAL = 28

Two consecutive strikes are referred to as a “double.” (image unavailable)

A double's pinfall is:

Frame 1, ball 1: 10 pins (Strike)
Frame 2, ball 1: 10 pins (Strike)
Frame 3, ball 1: 9 pins
Frame 3, ball 2: 0 pins (recorded as a dash '-' on the scoresheet)
The total score from these throws is:
Frame one: 10 + (10 + 9) = 29
Frame two: 10 + (9 + 0) = 19
Frame three: 9 + 0 = 9
TOTAL = 57

Three strikes bowled consecutively are known as a “turkey” or “triple.” (image unavailable)

A triple's pinfall is:

Frame 1, ball 1: 10 pins (Strike)
Frame 2, ball 1: 10 pins (Strike)
Frame 3, ball 1: 10 pins (Strike)
Frame 4, ball 1: 0 pins (Gutterball)
Frame 4, ball 2: 9 pins
The total score from these throws is:
Frame one: 10 + (10 + 10) = 30
Frame two: 10 + (10 + 0) = 20
Frame three: 10 + (0 + 9) = 19
Frame four: 0 + 9 = 9
TOTAL = 78

Any longer string of strikes is referred to by a number attached to the word “bagger,” as in “four-bagger” or “five-bagger” for four or five consecutive strikes. Recently, the event of bowling four consecutive strikes has also been called a “sombrero” or “ham bone.” This terminology is used most often when a bowler is “off the strikes.” (i.e. has previously bowled a string of several strikes but failed to strike on his most recent ball.) When a player is “on the strikes,” a string is often referenced by affixing “in a row” to the number of strikes bowled consecutively. Six strikes in a row are sometimes referred to as a “six pack.”6 strikes and 9 strikes in a row can also be referred to “Wild Turkeys” and “Golden Turkeys” respectively. Any string of strikes starting in the first frame or ending “off the sheet” (where all of a bowler’s shots from a certain frame to the end of the game strike) are often referred to as the “front” or “back” strikes, respectively (e.g. the “front nine” for strikes in frames 1-9, or the “back six” for strikes in frames 7, 8, and 9 with a turkey in the tenth). A “Perfect Game” or 12 strikes in a row is also colloquially referred to as the “Thanksgiving Turkey.”

A player who scores multiple strikes in succession would score like so:
Frame 1, ball 1: 10 pins (strike)
Frame 2, ball 1: 10 pins (strike)
Frame 3, ball 1: 4 pins
Frame 3, ball 2: 2 pins
The score from these throws are:
*Frame one: 10 + (10 + 4) = 24
*Frame two: 10 + (4 + 2) = 16
*Frame three: 4 + 2 = 6
TOTAL = 46

The most points that can be scored in a single frame is 30 points (10 for the original strike, plus strikes in the two subsequent frames).

A player who bowls a strike in the tenth (final) frame is awarded two extra balls so as to allow the awarding of bonus points. If both these balls also result in strikes, a total of 30 points (10 + 10 + 10) is awarded for the frame. These bonus points do not count on their own, however. They only count as the bonus for the strike.

  • spare: A “spare” is awarded when no pins are left standing after the second ball of a frame; i.e., a player uses both balls of a frame to clear all ten pins. A player achieving a spare is awarded ten points, plus a bonus of whatever is scored with the next ball (only the first ball is counted). It is typically rendered as a slash on scoresheets in place of the second pin count for a frame.

Example:
Frame 1, ball 1: 7 pins
Frame 1, ball 2: 3 pins (spare)
Frame 2, ball 1: 4 pins
Frame 2, ball 2: 2 pins
The total score from these throws is:
*Frame one: 7 + 3 + 4 (bonus) = 14
*Frame two: 4 + 2 = 6
TOTAL = 20

A player who bowls a spare in the tenth (final) frame is awarded one extra ball to allow for the bonus points.

Correctly calculating bonus points can be difficult, especially when combinations of strikes and spares come in successive frames. In modern times, however, this has been overcome with automated scoring systems, linked to the machines that set and clear the pins between frames. A computer automatically counts pins that remain standing, and fills in a virtual score sheet (usually displayed on monitors above each lane). However, even the automated system is not fool-proof, as the computer can miscount the number of pins that remain standing.

The maximum score in a game of ten-pin is 300. On Feb. 2, 1997, University of Nebraska sophomore Jeremy Sonnenfeld became the first person ever to roll three perfect games of 300 in a three-game series (as approved by the American Bowling Congress). This has only been achieved a handful of times since.

In Britain, the youngest bowler ever to achieve a perfect single game score of 300 (12 consecutive strikes), in a sanctioned competition was old Elliot John Crosby, at AMF Purley in South London, England in the Surrey County trials on January 7 2006. Crosby beat the previous British 300 shooter record holder Rhys Parfitt by more than a year. Parfitt was 13 years, 4 months when he achieved a 300 point game at the London international tenpin bowling tournament in 1994. In the United States, the youngest ever bowler to achieve this in a sanctioned competition is two-handed bowler Chaz Dennis of Columbus, Ohio. He achieved this competing in the Hillcrest Preps-Juniors league at Hillcrest Lanes in Columbus, Ohio on December 16, 2006 at old. Dennis was 20 days younger than the previous record-holder, Michael Tang of San Francisco, California, who set his record when he was old competing in the Daly City All Stars Scratch Trios League at the Sea Bowl in Pacifica, California.

Brooklyn Side

The Brooklyn Side is the spot opposite of a bowler’s pocket, the place where he or she’d be most likely to achieve a strike. A left-handed bowler’s pocket is in between the 1 and 2 pin, making a left-handed bowler’s Brooklyn side the right-handed bowler’s pocket, between the 1 and 3 pin. Vice versa for that of a right-handed bowler.

World tournaments

Major world tournaments

The “Weber Cup” is the ten-pin bowling equivalent of golf’s Ryder Cup. It is the world famous major world tournament of Team Europe vs. Team USA bowling championships that happens annually. Other major world-famous bowling tournaments include the World Tenpin Masters and the Qubica/AMF World Cup.

All of the three world major bowling tours above are televised on Sky Sports by Matchroom Sport who have established a tried and tested formula to highlight televised bowling at its best. All three events are also presented by broadcaster and journalists, Nick Halling and Cass Edwards.

There is also the influential European Tenpin Bowling Federation, which has the prestigious European Bowling Tour, and under that the PTBC Storm English Open.

Among the leading world tournaments is the Professional Bowlers Association (PBA) Tour. The PBA Tour takes place in North America, except for one stop in Japan (Dydo Japan Cup) that is considered a PBA event. This tour has 20 or more events per year (running from October to April), and includes four major championship events: the PBA U.S. Open, USBC Masters (known as the ABC Masters prior to 2005), the H&R Block Tournament of Champions and the Denny's World Championship. Although PBA headquarters are based in the USA, the PBA has members from all over the world whom also compete in all of its events. The PBA tour is televised in America and certain parts of the world by ESPN and ABC.

Along with increased coverage in recent years, these tours have become more profitable for bowlers. Earl Anthony, who bowled left-handed, became the first bowler to earn more than $100,000 (U.S.) in a single season when he finished the 1975 PBA Tour schedule with $107,585. He broke the $1 million mark in career earnings in 1982. The PBA now has some single tournaments that pay $100,000 to the winner. Norm Duke is the youngest person to win a PBA Tour tournament. He won the 1983 Cleveland Open at age 18 years, 345 days. The youngest person to bowl a PBA event is 15-year-old Jack Perry of Ontario, Canada, who rolled in the 2004 PBA World Championship. The oldest player to win a regular PBA Tour title is John Handegard, who won the 1995 Northwest Classic at age 57 years, 139 days. Walter Ray Williams Jr. is the all-time leader in PBA titles with 44.

The USBC (United States Bowling Congress) has two major championship events: the USBC Open Championships and the Women’s Championships and the USBC Masters (known as the ABC Masters prior to 2005).

There is also the Commonwealth Tenpin Bowling Championships.

World Ranking Masters

Ten-pin bowling has an international ranking system, as with professional tennis. This ten-pin equivalent is known as the World Ranking Masters and is made of three vast tours: the European, Americas and Asian bowling tours.

Minor world tournaments

Other minor tournaments, although major in their respective countries, include Britain’s prestigious BTBA Nationals (BTBA National Championships), the Brunswick Ballmaster Open, Brunswick Euro Challenge in Greece, ETBF European Youth Championships and the European Gold Cup. The world’s premier amateur event is the FIQ World Championships (Fédération Internationale des Quilleurs) which is held once every two years.

League play

Traditionally, a major form of organized bowling has been through league competition. Leagues are typically groups of teams that compete with one another over the course of a 28 to 36 week season, generally starting in September and ending in the spring. Summer leagues are often offered with a much shorter schedule of 10 to 15 weeks, usually starting in May. Additionally, "short" (~12 week) season leagues are now offered in many bowling centers to entice bowlers who may not want to commit to a "long" season league. These "short" leagues generally start around September/October and January/February.

In most leagues, teams of individuals bowl three games (called a “series”) each. A typical league will schedule two teams to compete against one another each week. Usually the winner of each game is decided by adding up the scores of all teammates. Leagues typically decide standings by awarding a certain number of points for each team game win. Additionally, points are usually awarded for total pincount for each team over the course of all three games (commonly referred to as “total wood”). Throughout the course of a season, each team will usually face all of the other teams in competition.

Leagues can have various formats. While most leagues are mixed leagues, containing both men and women, men’s and women’s leagues are still common, along with junior leagues for young bowlers. There are also different types of competition. Scratch leagues are those in which the actual pin count determines the winner. Most leagues are not scratch, but handicap leagues. In handicap leagues, the scores are a combination of the actual pins knocked down, plus addition of a handicap value, to give teams with lower averages a chance to compete against teams that have higher averaged bowlers. The handicap system provides a means to compare scores across the whole league. The best leagues set up their rules, so that every team has benefit of handicap for every game bowled, every league session, for their whole schedule. Every league determines its own basis for the handicap. It can select a team average basis or an individual average basis. The basis is set at a percentage, nominally in the 80-100% range, of a value higher than the highest average in the league, including an allowance for average improvement over the league’s schedule. (Note: Some leagues use an inferior handicap system, that only allows comparison of scores between two teams that are scheduled to compete against each other, on one particular date. Instead of using the same basis value for every team, that system uses the average difference between just those two teams. The resultant handicap is given to the lower average team, while the higher average team opponent receives no handicap. The inferior system only covers points won for game or series. As there is no common basis, it does not allow comparison of scores across the whole league and therefore is counter-productive for all teams in the league.) The ability to compete for “league high score honors” would normally help to keep all teams involved in all of the competition aspects, points won and league high scores. A properly organized league can provide many opportunities for recognition of both personal and team accomplishments.

Currently, over three million people compete in bowling leagues. At its peak in the late 1970s, over nine million men and women competed in leagues throughout the United States.

Fun Play

While League bowling and tournaments are very important in the bowling world, there is also another side to the game which must not be forgotten. Fun games give players a break from normal bowling, and can often be played competitively. Some give bowlers a chance to practise picking up odd pins—some of which they might not come across very often in a normal game. Others give youngsters a chance when bowling against more experienced bowlers.

No-Tap Game

In this game the bowler does not need to knock down all ten pins to score a strike. A no-tap value is assigned to each bowler, which states the number of pins each must knock down to score a strike, and can be from 3 to 9. As each bowler can have his or her own no-tap value, novices and experienced bowlers can compete together.

Monte Carlo Game

This is a game of chance which used colored pins in the pin deck. When the colored pins are set in a designated position and the bowler records a strike, spare or split, he or she is awarded a prize from the bowling center.

Colored Red Pin Game

This is similar to Monte Carlo although it is played with only 1 colored pin in the pin deck, and the bowler only receives a prize if they score a strike when the colored pin is the head pin (1).

Odd/Even Game

In this game there is only 1 ball thrown per frame. If the pinfall is an even number, the frame is scored as a strike. If the pinfall is an odd number, the frame is scored as a spare where the first score of the frame is the pinfall number.

Best Frame Game

This is a team game with 2-5 bowlers per team. All bowlers bowl as usual, and the best score out of all bowlers in the team is used to score the “team game.”

Low Ball Game

In Low Ball the lowest possible score wins. The bowler MUST knock down at least one pin for every ball thrown. Gutter balls and misses are counted as 10 points. The lowest possible score is 20. This game is very competitive and great for practicing picking up the sometimes elusive 7 or 10 pins.

Poker

This incorporates the card game where the best hand wins. The game is played in the traditional way, but for every strike or spare a card is dealt. The game is also play in another way in which you are dealt a card for a strike or split. At the end of the game, the best five-card stud poker hand wins the game. Each lane uses a single 52 card deck, and no more than 5 cards are dealt to each player.

Governing bodies

In ten-pin bowling there are two major world organisations which govern the sport and have predominant influence over its rules. These two central bodies are based in the United Kingdom and the United States, but their influence and ascendent ruling are highly respected globally and are projected world-wide. Additionally, there is the World Tenpin Bowling Association (WTBA) who govern the sport of tenpin bowling throughout the world of which is divided in three zones; the American Zone, Asian Zone and European Zone.

United Kingdom

In the United Kingdom, ten-pin bowling is sanctioned and governed by the BTBA (British Tenpin Bowling Association). The BTBA is devoted to the interest of the game itself and like the US equivalent it ensures the integrity and protection of the future of the sport, providing programs and services and enhancing the bowling experience, including a coaching education and qualification system. The NAYBC (National Association of Youth Bowling Clubs) is responsible to the BTBA for organising ten-pin bowling for the under 18 year olds. There is also the Tenpin Bowling Proprietors Association (TBPA), the trade association for ten-pin bowling of Britain. For BTBA qualified Instructors and Coaches the British Tenpin Bowling Coaching Association has been set up to help with the exchange of information and ideas between members. In addition, affiliated to the BTBA is the Young Adults Club (YAC). University & College tenpin bowling was administered jointly by the UCTBA (Universities & Colleges Tenpin Bowling Association) and the Tenpin Bowling Sport Management Group of BUCS (British Universities & Colleges Sport) until the Summer of 2007. Since then, the two organisations have combined under the BUSA name.

  • UKtenpin.com The home of UK bowling - UKtenpin.com is the original home of UK bowling on the web. Featuring all of the news and stories from leagues and tournaments, intractive community of members plus online pro shop.
  • Talk Tenpin - UK based tenpin ezine, featuring all the very latest news, entry forms and results from around the world, and interviews with top UK and World bowling stars.

United States

In the United States of America, the governing body of ten-pin bowling is the USBC (United States Bowling Congress). The USBC became the “administering organization” on January 1, 2005, after following separate groups merged: the American Bowling Congress (ABC), which was the earliest founded (in 1895) of the USBC’s constituent organizations, and the first codifier of ten pin bowling rules and equipment specifications; the Women’s International Bowling Congress (WIBC), founded in 1927 as the women’s equivalent of the then “male-only” ABC; the Young America Bowling Alliance (YABA), formerly known as the American Junior Bowling Congress (AJBC); and College and USA Bowling. The USBC's main function is to ensure the integrity and protect the future of the sport, while providing programs and services to enhance the bowling experience. The International Bowling Hall of Fame in St. Louis, Missouri includes separate wings for honorees of the American Bowling Congress (ABC), Professional Bowlers’ Association (PBA), and Women’s International Bowling Congress (WIBC). The museum does not include the new Ladies Pro Bowlers Tour Hall of Fame, which is located in Las Vegas, Nevada.

Drug testing authorities

In the United Kingdom, UK Sport, the official sports body that governs drugs testing on ten-pin bowlers and other athletes in the UK on a regular basis and is conducted by a Doping Control Officer (DCO), is Britain’s “National Anti-Doping Organisation” (NADO). It is a subsection of the internationally recognised and authoritative World Anti-Doping Agency (WADA). WADA is recognised by the Olympic Games and Commonwealth Games of which ten-pin bowling plays a part.

Controversy

In December at the Premier Tenpin Bowling Club Tour (PTBC), hosted by Airport Bowl, the year 2005 saw the first ever known ten-pin bowlers worldwide, two of Britain’s BTBA Nationals Team England, banned for the reason of testing positive for the chemical produced from the consumption of cocaine. UK Sport was responsible for the testing and reported their findings to the BTBA governing body. The individuals were subsequently banned for two years, which is standard WADA recommendation. They are due to be re-instated into the official bowling tournament community in early 2008 but this will be subject to WADA and BTBA review. This story was first reported on in Go Tenpin magazine.

Technology changes and controversy

For the machine that sets bowling pins, see pinsetter.
''For the ball that is used to knock down the pins, see bowling ball.

Pin characteristics, the bowling ball, and the lane surface are regulated by the USBC, BTBA and others. Technological changes throughout the history of the sport have often required new regulations. This continues today, often with great debate. The controversies usually involve “scoreability” related to greater strike carry on less-than-perfect shots. The increasing frequency and degree of higher scoring irks many bowling purists, who say that it is damaging the integrity of the sport.

History of technological changes

In the 1950s and 1960s, nearly all bowling balls had a hard rubber surface. As the coatings applied to wood lanes changed from softer lacquer to a harder urethane in the early 1970s, the first plastic balls became widely available. Subsequent changes -- particularly urethane and later “reactive” resin or composite (“particle”) bowling balls -- have been altering the physics of how the ball rolls and strikes the pins. Coupled with synthetic lane surfaces and advanced oiling machines presenting the opportunity to lay out lane oil patterns that make targeting easier, there have been numerous concerns. Honor scores (for 300 games, 800 series, etc.) have increased by several thousand percent on a per-member basis in the time period from 1980 to the present. To many, this has cheapened the intrinsic value of honor scores and created other workarounds.

Up until the early 1970s, the ABC/WIBC honor awards were genuine treasures because they were so rarely won. In response to the view that advanced equipment is spoiling the integrity of the sport, the USBC introduced in 2000 the “Sport Bowling” program which offers a different optional league certification and the USBC provides a separate set of honor awards. In Sport Bowling, lane conditions are more highly regulated and controlled than in traditional leagues, and the oiling patterns used are generally more even with regards to volume and ratios of oil across the surface of the lane. Sport Bowling conditions are similar to those used at some major championships of professional bowling, particularly the U.S. Open. In more recent years, “PBA Experience” leagues have been introduced that allow bowlers to compete on the five main lane conditions currently used on the PBA Tour.

Not everyone has embraced the Sport Bowling concept. PBA Hall of Famer Johnny Petraglia argues that Sport Bowling combats changes in bowling balls simply by making it tougher to roll a shot into the “pocket” (the 1-3 pins for a right-hander, 1-2 pins for a left-hander). According to Petraglia, Sport Bowling is merely an attempt to “create the scores that were shot 30 years ago. The problem is, 30 years ago the game wasn’t tougher. You could hit the pocket as easily as you do now, but you couldn’t knock over the same [number] of pins with a rubber bowling ball. Sport bowling is, for the first time, intentionally trying to make the lanes tough.” Petraglia’s suggestion to combat high-tech bowling balls is to use heavier pins that are single-voided on the bottom (versus double-voided), making them less top-heavy.

Bowling alley proprietors and lane maintenance personnel have also argued that changes in ball technology have made it more difficult to lay out fair and credible conditions for participants. This is because advanced players using high-tech balls need more oil to score high, and might complain about the radical behavior of their balls on “dry” lanes. At the same time, less aggressive players with older equipment might complain when they can’t get their balls to hook on ever-increasing amounts of oil. Such complaints about lane conditions have actually been part of the game throughout bowling history, and will likely continue.

USBC technology study

Among advanced players, there is little argument about whether technological changes have enabled higher scoring. The general consensus has been that they have. Yet there are those who have seen their scores decline, often due to not changing their technique or bowling balls appropriately. Some argue that such high technology unfairly affects competition, making high scores too dependent on how much money one spends on equipment. The USBC, for various reasons, has struggled to regulate these changes well enough to protect the integrity of their honor score award program.

At the end of 2007, the USBC completed a two-year study on bowling ball motion and how advanced, high-tech equipment may influence lane conditions and scoring. Establishing a Bowling Ball Specifications Task Force -- comprising research engineers and volunteers from ball manufacturing companies -- the USBC sought to better understand the motion of bowling balls using scientific research and data analysis. Test equipment included, but was not limited to, a robotic ball-thrower, a Computer Aided Tracking System (“Super C.A.T.S.”), 59 reactive resin and particle bowling balls from various manufacturers, and eight lanes in a climate-controlled facility.

The driving force behind the study was summed up by USBC Technical Director Neil Stremmel: “USBC is concerned that technology has overtaken player skill [as the primary factor] in determining success in the sport of bowling.”

The USBC completed data analysis and released a lengthy report on its website (www.bowl.com) to the public in the spring of 2008. To date, no specific bowling ball specification changes have been announced as a result of the study.

Brands

Today there are an exceptional number of major sports-related and non sports-related companies that focus specifically on designing, producing and or supporting the production of many items specifically designed for ten-pin bowling equipment. Such items include balls, bags, cleaning products, wrist supports, shirts, shoes, trousers, shorts and gloves, etc. Some of the major world famous equipment producers and supporters include AMF, Brunswick, Dacos, Ebonite, and Storm.

Other manufacturers and suppliers include Lane#1, Track, Roto-Grip, Hammer, Circle Athletic, Columbia 300, Dyno-Thane, Fun Balls, Legends, MoRich, Robby, and Via Bowling. Specially designed shoe design and manufacture is also a significant enterprise that many companies have gotten involved in next to ball production. Some of the major shoe designers are Circle, Dexter, Etonic, and Linds.

Individual stores that sell the merchandise made by these companies specifically for ten-pin bowlers are called Pro Bowl stores or Pro Shops.

In the USA, Bowling equipment sales totaled 215 million US dollars in 1997 which is around the same figure as in 1996 when the Sporting Goods Manufacturers Association (SGMA) released their reports. In Britain “Mintel International Group Ltd” produced a “Market Research Report” in July 2004 which gave the UK’s Tenpin bowling sales and market by sector from 1999-2003 and also the type of customer.

Bowling terms and jargon

  • Frame: A single turn for a bowler, constituting one or two rolls, depending on pinfall.
  • Line: The path that a bowling ball takes down the lane. Also can be used to describe one game of bowling.
  • Strike: All ten pins down on the first roll of a frame.
  • Double: Two strikes in a row during a single bowling game.
  • Turkey: Three strikes in a row during a single bowling game.
  • Hambone: Four Strikes in a row during a single bowling game.
  • (Number) Bagger: Always preceded by a number from three to eleven, denoting a string of consecutive strikes. ("Six-bagger")
  • Strike out: To roll three strikes in the 10th frame of a game (the maximum possible). Also used to denote a longer string of strikes to end a game. ("He struck out after that open in the 5th frame.") Also referred to as "going sheet."
  • (Go) off the sheet: To end a game with many consecutive strikes. ("He can go off the sheet for a 259 game." See "Strike out", directly above; comes from long ago when bowling was scored on paper.)
  • Spare: All ten pins down on two ball rolls of a frame.
  • Conversion: Another word for a spare, often preceded by the number(s) of the pins left before shooting the spare. (Example: “3-6-10 conversion.”)
  • Mark: A spare or a strike.
  • Open Frame: Any frame in which a strike or spare was not made.
  • Split: A spare leave where the head pin is knocked down and at least two non-adjacent pins are standing. (Example: the 8 and 10 pins left by themselves would be considered non-adjacent. The 6 and 10 pins are adjacent, and thus not considered a split.) Common jargon for certain splits include: “baby split” (most commonly 2-7 or 3-10), “big four” (4-6-7-10), “Greek church” (4-6-7-8-10 or 4-6-7-9-10) and “fit-in split” (most commonly 4-5 or 5-6).
  • Washout: A spare left where at least two non-adjacent pins are still standing, but the head pin is also standing.
  • Chop: An open frame where the front pin of a combination consisting of two or more adjacent pins is struck in the middle and neither the ball nor front pin takes out any other pins of the spare. (Example: The ball striking the middle of the 2-pin in a 2-4-7 combination, and leaving the 4-7 pins, is considered a chop.)
  • Hook: Rolling the ball with enough side-spin to make the ball curve as it rolls toward the pins.
  • Cranker: A bowler known for rolling the ball with extreme revolutions, making it hook more.
  • Stroker: A bowler known for smooth timing and delivery with relatively low amount of hook on the ball.
  • Power stroker: A bowler who combines the high hooking power of a cranker with the smooth delivery and timing of a stroker. Power Stroking is a form of “tweening,” meaning the form lies somewhere in between cranking and stroking.
  • Pocket: The ideal place for the ball to hit the pins in order to maximize strike potential. The pocket for a right-hander is between the 1 and 3 pins (1 and 2 pins for a left-hander).
  • Brooklyn: A throw that results from the ball hitting the wrong “pocket” based on the bowler’s handedness. For example, a right-handed bowler rolls the ball but it hits the 1 and 2 pins first. This may also be referred to as “Jersey.”
  • Carry: A condition where a good shot (or even a less-than-perfect shot) rolled into the pocket results in a strike.
  • Tap: A condition where a good shot that appears to hit the pocket properly results in less than ten pins being knocked down. The most common “tap” situations for a right-hander include leaving the 8 or 10 pin by itself (7 or 9 pin for a left-hander).
  • Oil: The conditioner used in the front two-thirds of the lane, which allows the ball with side-spin to roll the necessary distance down the lane before it starts to generate friction and hook.
  • Back end: The last 15-20 feet of the lane, where the ball is supposed to develop the most friction (due to lack of oil) and hook into the pocket.
  • Carry-down: A condition where oil from the front of the lane is transferred farther down the lane than desired, usually due to excessive ball traffic in the same area of the lane. This condition can cause the ball to “slide” in the area of the lane the bowler would desire it to hook.
  • Track: The pattern of oil left on a bowling ball after a shot. This indicates what parts of the ball have contacted the lane on its path.
  • Track flare: The migration of the ball track from the bowler’s initial axis (the axis upon release) to the final axis (the axis at the moment of impact with the pins). Track flare is used to expose fresh, dry ball surface to the lane surface. While on oil, this means little to the performance of the ball, but when the ball crosses from the oil to the dry, the dry ball surface bonds with the dry lane surface to increase friction which causes earlier hook and greater overall reaction.
  • Light shot: A shot that rolls into the pocket, but is closer to the 3-pin (or 2-pin for a left-hander) than the head pin.
  • Heavy or High shot: A shot that hits more of the head pin than desired, often resulting in a split.
  • Foul: A shot where the bowler's foot crosses the “foul line” at the end of the approach (and start of the lane), which often results in a light and/or buzzer being triggered. A foul also occurs when any part of the bowler's body touches the lane beyond the foul line, whether or not the foul light or buzzer is triggered. A foul counts zero for the ball roll in which it occurs, regardless of how many pins are knocked down. In “lowest-score-wins” fun-games, a foul results in a strike. Crossing the foul line only results in a foul if the bowler releases the ball.
  • Series: A set of full bowling games, typically three games in league play.
  • Sleeper: The name for a pin standing directly behind another pin, making it hard to see, eg. 8 behind 2, 5 behind 1 or 9 behind 3. Also known as a “phantom pin”, “double wood” or “mother-in-law.”
  • Big Four: A very hard split to convert, this leaves pins 4-6-7-10. If a BTBA member converts it in a BTBA Sanctioned League he or she can be awarded a badge. USBC members are awarded a patch for converting this split in league play.
  • Lily: Another tricky split, this time leaving pins 5-7-10.
  • Bedposts: The 7-10 split, considered one of the most difficult to convert. Also known as the fence posts or goal posts.
  • Messenger: A pin that goes across the width of the pin deck and knocks down another pin or pins, resulting in a strike. Also known as a birddog, scout, shrapnel, or rogue pin.
  • Greek church: The 4-6-7-8-10 or 4-6-7-9-10 split. Also known as a cathedral.
  • Back-Up Ball: A Right Handed Bowler that Hooks the ball Left to Right instead of Right to Left.
  • (Grandma's) Teeth: The 4-7-9-10 split for a Right Handed Bowler and the 6-7-8-10 split for a Left Handed Bowler.

Ten-pin bowling in media

Ten-pin bowling in print

Ten-pin bowling is once again becoming a majorly-contending athletic sport that is becoming more and more visible. It now far outweighs its 1970s high-point and subsequent 1980-1990s downfall. The sport has become much more popular, with television regularly broadcasting its major tournaments and written publications such as magazines becoming increasingly popular around the globe.

The British Tenpin Bowling Association (BTBA) produces the magazine Go Tenpin. However, it is not specific to the United Kingdom and is highly respected around the globe in ten-pin bowling circles. The United States Bowling Congress (USBC) publishes a magazine for its entire membership called U.S. Bowler.

Other widely acclaimed ten-pin magazines and news services are the international and world-renowned Bowling Digital News, the international Bowlers Journal Online and the International Bowling Industry. Specific American magazines of note are the Bowling This Month magazine and the Bowling Digest.

Additionally, other than books written by bowling instructors on the coaching and training of the sport, books on the humorous and historical side of ten-pin bowling have become extremely popular. Some of these include A Funnier Approach, The Funniest Approach, Bowled Over, The New Bowling Trivia Book, Two For Stew and The Tour Would Be Great.

Ten-pin bowling has been referenced in many fictional works. One of the most notable recent examples is Harry Potter and the Philosopher's Stone by J.K. Rowling. Although it and its sequels establish that the magical characters featured know nothing about the non-magical (i.e. “real”) world, Philosopher’s Stone reveals that one major character, Professor Albus Dumbledore is a fan of ten-pin bowling.[

Ten-pin bowling on film

Ten-pin bowling is once again becoming a major athletic sport, and interest has once again risen to levels last seen in the 1970s. Independent companies continue to sponsor the sport, and televised broadcasts of the sport by such companies as Matchroom Sport are increasing bowling’s visibility on the international stage.

Sporting documentaries such as the widely acclaimed “A League of Ordinary Gentlemen”, comedic movie sketches such as “Life in the Bowling Lane!”, and major Hollywood productions like “Dreamer”, “The Big Lebowski”, and “Kingpin” have all become popular in recent years.

Major ten-pin Bowling coaching/training DVDs have also been released world-wide under great demand. Some notable examples are those produced by world-renowned bowling coaches Fred Borden and Ken Yokobosky known as “Bowling Fun And Fundamentals For Boys And Girls”, “Essential Keys To Better Bowling”, “Advanced Bowling Techniques, Tips And Tactics” and “Walter Ray Williams Jr's Secrets to Better Bowling.”

Ten-pin bowling video games

Since the electronic gaming industry began, ten-pin bowling has been seen in many formats on many big name gaming machines. However, it has yet to be represented by what is considered the eminent creator of sports video games, EA Sports. However, JAMDAT Mobile (now known as EA Mobile), made the Jamdat Bowling series. Some of the many bowling games include PlayStation’s “Bowling Xciting”, “Black Market Bowling”, “Strike Force Bowling”, “Brunswick Circuit Pro Bowling”, “King of Bowling” and “Big Strike Bowling.” Some of those on the PC are “Fast Lanes Bowling”, “Flintstones: Bedrock Bowling”, “Arcade Bowling”, “Bowling Mania”, “10 Pin Bowling Fever” and "GutterBall 3D" amongst many others on other gaming units.

More recently, Bowling appeared as one of the games featured in Wii Sports for Nintendo’s Wii. To throw the ball, the player swings the Wii Remote in a motion similar to throwing a real bowling ball. “High Velocity Bowling,” released for Playstation 3 in December 2007, likewise mimics the arm movement using the motion sensors of the “SixAxis” controller.

Ten-pin bowling is also featured as one of the various minigames in Grand Theft Auto IV that the character can play.

Mainstream media portrayal

The Professional Bowlers Tour on ABC was the second-longest live sports series on network television, behind only college football. ABC broadcasted PBA tournament finals from 1962 until 1997. Events can now be seen on ESPN.

However, while the prevalence of bowling media has greatly increased in recent years, many mainstream media outlets continue to lack adequate coverage of the sport. Reasons for this discrepancy may include bowling’s blue collar demographic, its lack of corporate sponsorship, and the lack of any one bowling star to follow.

It has also been suggested that the perpetuation of negative stereotypes about bowling pushes away the elite members of the journalism community. This includes the bowling atmosphere, as well as the personality and physical condition of the average bowler. These ideas may stem from the notion of bowling as only being a recreational activity. Professional bowlers have disputed this idea by offering demonstrations of the complex technique required to bowl successfully. However, the debate over whether bowling should be considered a “sport” or a “game” continues.

Mathematics of ten pin bowling

Statistical analysis of scoring

In “Quantitative Aspects of Five-Pin Bowling”, Wejun Chen and Tim Swartz [The American Statistician, Vol. 48, No. 2 (May, 1994), pp. 92-98] analyzed 2,100 five-pin bowling scores and show that the logarithms of bowling scores are approximately normally distributed. The game of five-pin bowling uses a very different scoring system however and this result will not translate to ten-pin bowling at the elite level.

A comprehensive distribution table for scores with regards to ten pin bowling may be found at http://www.balmoralsoftware.com/bowling/bowling.htm.. It clearly displays that there are just under 6 billion billion possible methods to obtain a score, ranging from 1 method of getting zero (20 gutterballs in a row) to 1 method of getting 300 (12 strikes in a row). The data also makes point of the 11-ball game (9 strikes followed by an open frame) which always results in a score higher than 240.

Pin patterns

Residual pins can be modeled as multivariate binary random variables whose correlation is quite complicated. A model for the first bowl implies a discrete probability distribution on all 1024 possible outcomes, but specifying each of these individually is problematic.

See also

References

Further reading

External links

UK

USA

Leading Ten-pin Bowling Magazines, Forums & News sites

Other

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