Monday, July 30, 2012

US Target Shooter Medals in Fifth Straight Olympiad

US target shooter Kimberly Rhode won the gold medal in skeet shooting yesterday. She has now won a medal in five straight Olympiad:

1996: Gold -- Double trap
2000: Bronze -- Double trap
2004: Gold -- Double trap
2008: Silver -- Skeet
2012: Gold -- Skeet

Both skeet (description, video) and trap (description, video) shooting involve targets that are launched into the air. According to this AP article, Rhode has now become "the first American with individual medals in five straight Olympics." Further, she was a model of near perfection yesterday, "tying a world record and setting the Olympic mark with 99 points — meaning she missed once in 100 shots."

Saturday, July 28, 2012

Is There a Hot Hand in Olympic Archery?

Many Olympic sports got underway today in London and environs. One event that I watched today and that potentially is an excellent candidate for hot-hand analysis is archery. As I discuss in my book and in this video, sports that are most conducive to streakiness are those that consist of relatively simple motions that can be repeated with little delay between attempts.

The event I watched today, specifically, was the men's team archery final, between Italy and the United States. Each team has three shooters or archers. When it's a team's turn, each member will get one shot, so that several minutes will elapse between consecutive shots by any one person. This aspect is not optimal for detecting streakiness. Also, each member gets only eight attempts. Thus, even when aggregating over all six participants, the total number of shots is too small for traditional statistical analysis.

Still, for curiosity's sake, I thought I'd examine the arrow-shooting sequences. Archers receive 10 points for their team by hitting the bullseye, and 9, 8, 7, etc., for landing their arrow in each respective outward ring from the center. As I depict in the following chart, no archer earned below an 8 on any shots. Archery matches (in the team format, at least) are organized into four sets (known as "ends") of six shots each. Because each archer on a three-person team shoots twice in one end, I designate the shots as "1a" for first shot of the first end, "1b" for second shot of the first end, and so forth.

I decided to simplify my little analysis by dividing outcomes into two categories: 10's (bullseyes) and non-10's (i.e., 8 or 9). The "hot hand" concept, in the sense of "success begetting success," suggests that when an archer shoots a bullseye (10-pointer), he or she should have a higher probability than usual of hitting a bullseye on his or her next shot, as well. 

Highlighted in gold in the above chart are all attempts that immediately followed a 10. For example, USA Shooter A earned a 10 on his 3a shot, so his next cell (for 3b) is highlighted in gold. Shot 3b was also a 10, so 4a is gold. Unshaded white cells represent attempts immediately following a non-10. Each shooter's first attempt (green cells) is excluded from the analysis, because he had no prior attempts at that point.

As described above, the hot hand hypothesis predicts that 10's will be more common (percentagewise) in the gold cells than in the white cells. As shown at the bottom of the chart, this pattern is exactly what was found: Bullseyes occurred on 46% of the arrows fired after the same archer had hit a bullseye on his previous shot. In contrast, bullseyes occurred on only 28% of the arrows fired after the same archer had scored an 8 or 9 on his previous shot.

Given the small sample, the difference between 46% and 28% was not statistically significant, but it was in the direction predicted by hot-hand reasoning. Considering that the archers faced delays of several minutes between their own shots, this result isn't bad!

I will keep my eye out for additional archery events during these games (men's individual, women's team and individual) and I invite readers to do the same. Statistics for all sports are available at For the men's team archery final, all the shot-by-shot data were available online (albeit organized in a different format than I used), so I was able to verify the scores I wrote down while watching the event against what was listed on the website. However, as a precaution, I would urge readers interested in conducting their own analyses to write down as much data as they can while watching events on television.

Friday, July 27, 2012

Great Olympic Streaks: Basketball

Here is the 10th and final entry of my series on top Summer Olympic streaks and dynasties, leading into tonight's opening ceremonies of the London Games. To see the earlier entries, covering sports such as gymnastics, swimming, track and field, and volleyball, just keep scrolling down the page.

To my mind, no Olympic streak is more noteworthy -- either for its duration or its ending -- than that of the U.S. men's basketball program. As indicated below in a chart I created from Wikipedia data, the American men entered the 1972 gold-medal game against the Soviet Union with the U.S. having won all seven gold medals ever contested in Olympic history and with a 62-game winning streak (some sources list it as a 63-game streak, but they may be counting a first-round forfeit win over Spain in 1936). As the chart also shows, some of the greatest basketball players of all-time, such as Bill Russell, Oscar Robertson, Jerry West, and Bill Bradley played for the U.S. during basketball's early decades as an Olympic sport. (You may click on the chart to enlarge it.)

As many readers will recall, the '72 USA-USSR men's title game is best known for the Soviets, trailing by 1 point with 3 seconds left, receiving three chances to inbound the ball (an original and two do-overs) and finally winning, 51-50. An ESPN Sports Century documentary on the 1972 final is available from YouTube (Part 1, Part 2). If you're too young to remember what happened in that game, the YouTube videos are well worth your time.

Some observers have argued from a U.S. perspective that, even being in a position to lose in a fluke ending by not being well ahead of the Soviet Union reflected poorly on the coaching and preparation of the American team. I would say there's some truth to that.

Of course, in the larger scheme, with the murder of 11 Israeli athletes and coaches during the Munich Olympics (here and here), the results of a basketball game are trivial. I was just shy of 10 years old during the 1972 Olympics. I must say, though, that seeing the video on the '72 US-Soviet basketball game recently, 40 years after the fact, I still found it jarring. Whatever joy the Soviets got out of the game was probably short-lived also. Alexander Below, who scored the winning basket, died of cancer just 6 years later.

(For more pleasant reading on men's Olympic basketball [and other sports], including the Oscar Roberson and Jerry West led U.S. "dream team" of collegians, I would highly recommend the book Rome 1960 by David Maraniss, which came out a few years ago.)   

Whereas the U.S. men won all the early gold medals in basketball and later began to face stiffer opposition (requiring the infusion of NBA players), the U.S. women faced tough hoops competition from the beginning (1976) and then became more dominant over time. As shown on this Wikipedia page that covers both men's and women's Olympic hoops, the Soviet Union (and its 1992 post-break-up conglomeration of republics known as the "Unified Team") won 3 of the first 5 women's gold medals, with the U.S. winning the others (1984 and '88). However, the American women have won the last 4 gold medals (1996-2008), with the margin of victory always reaching double-digits in the 4 finals.

Before closing, I wanted to mention briefly several additional Summer Olympic streaks in sports I did not already write about:
  • Aladar Gerevich, an Hungarian fencer born in 1910, won gold in 6 straight Olympics ('32, '36, '48, '52, '56, '60; with the Games of '40 and '44  being cancelled due to World War II). Teammate Pal Kovacs won gold in 5 straight Olympics.
  • Cuban heavyweight boxers Teofilo Stevenson (1972, '76, and '80) and Felix Savon (1992, 1996, 2000) each won 3 straight Olympic golds. Hungary’s Laszlo Papp, who fought at various times as a middleweight and light middleweight, also won 3 straight golds (1948, '52, '56).
  • Vasily Alexeev, a Soviet weightlifter, won Olympic gold in '72 and '76, along with 8 straight World Championships from 1970-1977.
  • Hungary men’s water polo program won 5 out of 7 golds from 1932-1964 and has captured the last 3 (2000-2008).
  • Asian domination of badminton.
  • Paul Elvstrom, from Denmark, was a four-peat yachting champion from 1948-1960.
  • The German (previously West German) equestrian team dressage program won all 7 gold medals contested from 1984-2008.
On to tonight's opening ceremony!

Thursday, July 26, 2012

Great Olympic Streaks: Gymnastics

We're down to the final two entries of our daily series. Today, the sport is gymnastics. We're looking at athletes who have had "unparalleled" success, pardon the pun.

Athletes used to have greater longevity in the sport, which is now dominated by youth (with some exceptions). Some of the best-known gymnasts of the last generation, such as Mary Lou Retton, only competed in one Olympiad. Hence, records for gold medals in consecutive Olympics are held by athletes from earlier eras.

It is hard to match the former Soviet Union for gymnasts who excelled over long Olympic careers. These include the all-time record-holder for most Olympic medals in any sport, "Larisa Latynina, who competed in three Olympic Games (1956 to 1964) and won a staggering total of 18 medals, half of which were of the gold variety;" and Nikolai Andrianov, master of the floor exercise in his era, winning gold in 1972 and ’76, and silver in ’80.

Other gymnasts who performed at an elite level through two or more Olympiad include:
  • Japan’s Sawao Kato, winner of the men’s all-around gold medal in 1968 and ’72, and silver medalist in ‘76.
  • Romania’s Nadia Comaneci (3 golds in ’76, 2 in ‘80), best known as the “first female gymnast to be awarded a perfect score of 10 in an Olympic gymnastic event.” In addition, Comaneci is married to Bart Conner, a former U.S. gymnastics great.
  • Vera Caslavska (Czech Republic), “one of only two female gymnasts, along with Soviet Larisa Latynina, to win the all-around gold medal at two consecutive Olympics.”
In addition to the athletes' Wikipedia pages (linked to each person's name), a very helpful source is this all-time list.

In tomorrow's final entry of the series, we'll look at what I consider the most impressive Olympic streak, one that came to a most controversial end (hint, hint).

Wednesday, July 25, 2012

Great Olympic Streaks: Women's Swimming

Today's entry on great Summer Olympic streaks, the eighth of a 10-part series leading into Friday's opening ceremonies, focuses on women's swimming. One could argue that, whereas men's Olympic swimming historically has made headlines for athletes capturing large numbers of gold medals within a single Olympiad (e.g., Michael Phelps's 8 golds in 2008, Mark Spitz's 7 golds in 1972), the women's side may be characterized more by athletes' longevity.

That's not to say women's swimming is completely devoid of spectacular single-Games performances. In the 1988 Seoul Olympics, East Germany's Kristin Otto "won six gold medals, as well as setting world records in the 50 m freestyle, 100 m freestyle, 100 m backstroke and 100 m butterfly" (the other two golds came in the 4 x 100 freestyle and medley relays).

Several other women's swimmers exemplify longevity, however. Most visible to American fans would be Dara Torres, whose Wikipedia page describes her as “the first and only swimmer from the United States to compete in five Olympic Games (1984, 1988, 1992, 2000 and 2008) … [and who] won at least one medal in each of the five Olympics in which she [...] competed.” Torres tried to make the U.S. team yet again this year, at the age of 45, but failed to qualify at the Olympic Trials.

Australia’s Dawn Fraser claimed 3 straight golds in the 100-meter freestyle (1956, '60, and '64), making her “one of only two swimmers to win the same Olympic event three times.” The other is Hungary’s Krisztina Egerszegi, whose 3 straight golds occurred in the 200 backstroke (1988, '92, and '96).

Kirsty Coventry of Zimbabwe will be seeking to match Fraser's and Egerszegi's three-peat feat in London, going for her third straight gold in the 200 backstroke, having already won it in 2004 and '08.

Natalie Coughlin, the 100-backstroke gold medalist in ’04 and ’08, sought to try for three straight, but didn’t qualify in that event at this year’s U.S. Trials.

Tuesday, July 24, 2012

Great Olympic Streaks: Men's Swimming

Today and tomorrow, we will discuss great Summer Olympic streaks in men's and women's swimming, respectively. Two names obviously leap to the top of the list of great male Olympic swimmers, Michael Phelps and Mark Spitz.

What else can one say about Phelps, a swimmer who has won 14 Olympic gold medals (6 in 2004 and 8 in 2008)? These gold medals consist of 9 in individual events and 5 in relays. Phelps will be entered in 7 events in the upcoming Games (4 individual and 3 relays), raising the possibility that he could leave London with an unimaginable 21 career Olympic gold medals!

Phelps's dominance in his specialty events extends beyond the Olympic Games (OG), of course, also appearing in World Championship (WC) and Pan Pacific (PP) Championship meets (one of the three meets is held each year). The following chart shows his performances in his four main events, the 100- and 200-meter races of the butterfly stroke, and the 200- and 400-meter individual medleys (which consist of laps in each of the four strokes: freestyle, backstroke, butterfly, and breaststroke).

Phelps has won the 200 butterfly the last 8 times he's swum it in major international meets. Previously, he had won the 200 individual medley 7 straight times, before losing in the 2011 World Championships to Ryan Lochte.

Thirty-six years before Phelps won 8 gold medals in a single Olympics, Spitz won 7 in the 1972 Munich Games. Spitz had also captured a pair of relay golds in the 1968 Mexico City Games. In '72, Spitz's golds came from two freestyle races (100 and 200), two butterfly races (100 and 200), and three relays.

In addition to their own winning ways, Spitz and Phelps also contributed to a larger U.S. streak spanning nearly 50 years. The U.S. has won all 12 Olympic men's 4 x 100 medley relays ever contested (excluding 1980 when the Americans boycotted the Moscow Games). 

I have enjoyed the feats of Phelps and Spitz not only as a sports fan, but also as a statistical analyst. Shortly after the 2008 Beijing Olympics ended, I had my statistics class conduct comparisons of Phelps's and Spitz's swimming times, in a way that attempted to account for improvements in training, facilities, etc., between 1972 and 2008.

Aquatic sports also include diving. According to a Yahoo! News series on the Olympics, America's Greg Louganis in 1984 "swept the golds in the 3m springboard and the 10m platform in Los Angeles, becoming the first man to do so in 56 years. Four years later in Seoul, at the advanced diving age of 28 and competing against opponents half his age, he repeated this two-gold feat..."

Monday, July 23, 2012

Great Olympic Streaks: U.S. Dominant Stretches in Several T&F Events

For the sixth entry in our 10-part series on great Summer Olympic streaks and dynasties, we take one final look at track and field. In men's competition, the United States has dominated several events -- generally involving track races over short distances and field events of the jumping variety -- over different stretches of time in the 112-year history of the modern Olympics (i.e., dating from the 1896 revival of the Games). One such streak is relatively recent and still ongoing:
  • 7 straight golds in the 400 meters (1984-2008).
Three streaks occurred in roughly the middle portion of the 112-year history of the modern Games.
  • 9 straight golds in the 110-meter hurdles (1932-1972, no Games in 1940 and 1944).
  • 8 straight golds in the 4 x 100 relay (1920-1956).
  • 8 straight golds in the long jump (1924-1960).
Finally, two streaks began with the 1896 revival and lasted from 32 to 72 years.
  • 8 straight golds in the high jump (1896-1928; no Games in 1916).
  • 16 straight golds in pole vault (1896-1968; 1908 featured a tie of two Americans).
Interestingly, the long U.S. run of success in the pole vault was followed by 6 Olympiad (excluding the U.S. boycott year of 1980) without an American vaulter winning. Nick Hysong finally put the U.S. back atop the medal stand in the pole vault, winning in the 2000 Sydney Olympics.

It's interesting to speculate about why one country seems to "own" an event over an extended period. Why, for example, has a U.S. runner won the last 7 runnings of the 400-meter dash? It has not resulted from the dominance of only a few runners, as 6 different men have accounted for the 7 golds. Only Michael Johnson (1996 and 2000) won more than a single gold.

Perhaps the fact that the 400 is the longest race run entirely in lanes has something to do with the U.S. streak. In races where runners don't have to stay in lanes, there can be physical contact between competitors and tactical issues come into play (e.g., not getting "boxed in" by a phalanx of other runners). Both of these factors can disrupt the top runners and lead to upsets. Assuming the U.S. has had the best 400-meter runners, the strict adherence to assigned lanes has presumably strengthened the Americans' hands (or feet) by reducing the upset potential.

On the other hand, the great potential for hitting hurdles in the 110-meter hurdle race and for dropping the baton (or losing time due to an awkward pass) in the 4 x 100 relay would seem to increase the chances for upsets, compared to other events. Still, the U.S. had long streaks of dominance in these two races. In recent Olympiad, however, poor baton passing has cost the American men and women potential gold on multiple occasions (here and here, for example).

Another factor that can derail one nation's dominance in an event is, of course, the emergence of another nation as a powerhouse in that event. The U.S. dry spell in the pole vault from 1972-1996 can thus be accounted for, in part, by the then-Soviet Union fielding a great group of vaulters. Led by Sergey Bubka, the only person to ever surpass 20 feet, the Soviets swept the gold, silver, and bronze pole-vaulting medals in 1988. Then, even with Bubka faltering in the '92 Games, the Soviets still won gold and silver.

To find lists of all medalists in Olympic competition, see the site Database Olympics.

Sunday, July 22, 2012

Great Olympic Streaks: African Distance Runners

Today's posting, the second on track and field and the fifth overall of the series, examines the domination of distance races by runners from African countries. Because women's long-distance races are relatively new to the Olympics, this posting will focus primarily on men's events.

Back in February of this year, in anticipation of the London Games, New African magazine published a history of African (and African-American) performance in the Olympics. According to the article, "Africa first hit the world’s Olympic Games headlines with the marathon triumph of Abebe Bikila at Rome in 1960. He became an overnight hero everywhere the Games were followed because he ran the very long race bare-footed..." The article also noted that the Ethiopian Bikila "crossed the finish line in the record time of 2:15:16.2 to become the first sub-Saharan African to win an Olympic Games gold medal."

Bikila successfully defended his gold medal in the 1964 Tokyo Olympics, but had to drop out of the 1968 Olympic marathon in Mexico City midway through, due to a knee injury. Ethiopia held onto the marathon gold for the third straight time, however, as Mamo Wolde finished first.

From there, as they say, the rest is history. I have created the following chart (on which you can click to enlarge) to show which countries have won gold medals in the Olympic distance races (which I define as the 3,000-meter steeplechase [and previous flat 3,000 for women]; 5,000 meters; 10,000 meters; and marathon) from 1960-2008. As noted in the chart, there was an African nations' boycott of the 1976 Olympics. All-time results are available from a website called Database Olympics.

Clearly, the triumphs of Bikila and Wolde seemed to pave the way for future Ethiopian champion male runners, namely Miruts Yifter (1980 double gold medalist at 5,000 and 10,000 meters), Haile Gebrselassie (1996 and 2000 gold medalist in the 10,000), and Kenenisa Bekele (2004 and '08 10,000 gold medalist, and also '08 winner in the 5,000). There have also been a number of excellent Ethiopian female runners, including Derartu Tulu (10,000 gold medalist in 1992 and 2000) and Tirunesh Dibaba (2008 gold medalist at 5,000 and 10,000).

According to the aforementioned New African article, "The Kenyans hit the forefront in force at Mexico City in 1968." In terms of specific athletes, "Kipchoge Keino... represented the face of East African athletics... At Mexico City the Kenyan won the 1,500 metres with a resounding victory over world record-holder Jim Ryun and also took silver in the 5,000 metres. Four years later he won the 3,000 metres steeplechase and was second in the 1,500 metres."

The steeplechase, in which runners must clear hurdle-type barriers and a water-jump on each lap, has become something of an impenetrable Kenyan stronghold. From 1984-2008, Kenya has won every gold medal in this event and (as noted by asterisks in the above chart) swept gold, silver, and bronze in 1992 and 2004. Interestingly, seven different individuals have brought home the gold for Kenya during the streak, making it a national streak, as opposed to that of an individual athlete.

What are Kenya's chances for winning the men's steeplechase an eighth straight time? Pretty good. Looking at Track and Field News's form charts (predictions), in the most recently issued men's forecasts (July 7), Kenya is picked for gold, silver, and bronze in the steeplechase.

All in all, from 1968-2008 (excluding the boycott year of 1976), African nations have won 29 of 40 possible men’s gold medals in the four distance events. In more recent years, the African men's dominance has been even more pronounced, as from 1996-2008, African countries have taken 15 of 16 possible golds.

In women's competition, Ethiopia has won 6 gold medals in the 5,000 (2); 10,000 (3); and marathon (1).

Prior to Abebe Bikila putting African distance running on the map in 1960, of course, there were many illustrious distance runners from other parts of the world, who warrant mention.

Finland's Paavo Nurmi captured 9 gold medals from 1920-1928 (although these include individual and team cross-country, which is no longer contested at the Olympics). Emil Zatopek, a Czech runner, had a gold-medal trifecta in 1952, winning the 5,000; 10,000; and marathon. He also won a 10,000-meter gold in 1948. Finally, another Finnish runner, Lasse Viren, pulled off a gold-medal "double-double," winning the 5,000 and 10,000 in 1972 and doing the same in '76.

Saturday, July 21, 2012

Great Olympic Streaks: 4 Straight Golds in Track & Field

I will have postings on track and field for the next three days, beginning with today's on athletes who have been most successful in defending their titles in particular events. Two names rise to the top of this list due to their "four-peat" performances in their respective events, discus thrower Al Oerter and long jumper Carl Lewis (also a championship sprinter). Both represented the U.S. Athletes who came close to doing what Oerter and Lewis did (e.g., three golds and a silver) are also discussed.

The 6-4, 280-pound Oerter, born in 1936, was very young for someone who won four straight Olympic gold medals, ranging in age from roughly 20 to 32 as he won Olympic titles in 1956, '60, '64, and '68. As can be seen in the following graph I created from this database, Oerter improved his winning distance with each successive Olympic appearance (you may click on the graphics to enlarge them).

Oerter retired after the 1968 Games. Because of his relative youth, however, Oerter was still a viable competitor when he attempted a comeback in 1980. Because of the U.S. boycott of the Moscow Olympics that year (which was announced well before the Olympic Trials), there is no way to know how Oerter would have done, had he qualified for the American team. For what it's worth, Oerter finished fourth in the 1980 Trials (with the top three making the team), although he threw roughly 14 feet further (69.46 m, 227-10¾)  than he ever had when winning Olympic gold.

Lewis, born in 1961, won the long jump in 1984, '88, '92, and '96. As shown in the following plot of Olympic men's long-jump data, his best distances -- in the mid-28-foot range  -- came in winning his second and third long-jump golds.

In the 1991 World Championships, Mike Powell jumped a world-record 8.95 m (29–4½) to end Lewis's 65-meet long-jump winning streak. Lewis was roughly 3 inches short at 8.87 m (29–1¼). According to this ESPN Sports Century profile of Lewis, "At the 1992 Olympics in Barcelona, Lewis exacted revenge on Powell, who had the record that Lewis craved, when he edged him by 1¼ inches with a leap of 28-5½."

In 1996, the 35-year-old Lewis won his fourth straight long-jump gold, although his winning mark (8.50 m, 27-10¾) was off a bit from his previous Olympic bests. Second-place finisher James Beckford (Jamaica) was roughly 8 inches behind (8.29 m, 27-2½). Powell finished fifth.

Three athletes won three straight Olympic golds in their respective events. Men's javelin thrower Jan Zelezny of the Czech Republic took a silver medal in 1988, then won gold in 1992, '96, and 2000. An attempt to tie Oerter and Lewis resulted in a 9th-place finish for Zelezny in 2004.

Viktor Saneyev of the then-Soviet Republic of Georgia captured gold in the triple jump in 1968, '72, and '76. With Saneyev jumping at home in the 1980 Moscow Olympics, fellow Soviet Jaak Uudm√§e (17.35 m, 56-11¼) edged Saneyev (17.24, 56-6¾) for the gold by a 4.5-inch margin. This report from Sports-Reference, like other accounts over the years, suggests that some questionable foul calls (e.g., for touching their foot beyond the take-off board) on non-Soviet competitors may have helped Uudmae and Saneyev.

If one counts events that are no longer held, in this case the standing (no run-up) versions of the jumps, then Ray Ewry of the U.S. warrants mention among three-peat winners. He won gold medals in 1900, '04, and '08 in the standing high and long jumps (plus 1900 and '04 titles in the standing triple jump).

But for the 1980 boycott, American 400-meter hurdler Edwin Moses almost certainly would have won three straight golds, as he easily won the event in 1976 (in world-record time) and 1984. His quest for three (non-consecutive golds) came up short in 1988, as he won a bronze medal. During the bulk of his career, Moses compiled a 122-race winning streak.

Among women, Jackie Joyner-Kersee is widely considered one of the greatest, if not the greatest, track and field athletes of her time. She won a silver medal in the 1984 heptathlon (a cumulative competition involving seven events), then golds in the '88 and '92 heptathlons. She set a world record at the 1988 Games for most points in the heptathlon, which still stands.

Friday, July 20, 2012

Great Olympic Streaks: Wrestling

Olympic-style wrestling combines brutal physical confrontation with aspects of finesse that award competitors points for executing moves such as takedowns, escapes, and reversals. Unless one wrestler pins his opponent's shoulders to the mat, thus earning an immediate victory, the outcome of a match is determined by who has the greater point total.

With this information in mind, one can fully appreciate the magnitude of American lightweight-division freestyle wrestler Dan Gable “winning gold at the 1972 Olympic Games in Munich, Germany while not giving up a single point” in six matches. I have not been able to find records on the frequency of wrestlers going unscored upon in an entire Olympic competition, but suffice it to say, it's pretty rare!

Aleksandr Karelin, practitioner of Greco-Roman wrestling, which "forbids holds below the waist," won three straight Olympic gold medals spanning 1988-1996. As noted on Karelin's Wikipedia page, the super-heavyweight went "13 years [1987-2000] undefeated in international competition and six years without giving up a point." Karelin's name presumably was well known to American viewers of the 2000 Olympics, as it was Rulon Gardner of the U.S. who prevented the Russian from taking a fourth consecutive gold. This TIME Magazine article recounts the 2000 final between Gardner and Karelin.

Women's wrestling has been part of the Olympics since 2004. Japan's Saori Yoshida (freestyle) won gold medals in 2004 and 2008, while holding winning streaks as long as 119 matches during her international career. Yoshida will be trying for a third straight gold in London.

Bleacher Report has compiled a slideshow of great Olympic wrestling moments, which can be accessed here.

Thursday, July 19, 2012

Great Olympic Streaks: Rowing/Kayaking

Rowing and kayaking are similar, though far from identical sports, in which participants in boats use some type of implement (e.g., oar, paddle) to propel themselves or their teams along a body of water. This YouTube video discusses the differences between the two disciplines.

Each of these sports has a dominant figure who compiled a gold-medal-winning streak lasting a full generation.
Kayaker Birgit Fischer, first representing East Germany and then, from 1992 onward, a unified Germany, won gold medals in 6 straight Olympiad: 1980, [1984 boycotted], 1988, 1992, 1996, 2000, 2004. She wanted to come back and participate in the London Games, but her physician put an end to that, based on some undisclosed medical-examination results.

This year's host country is home to one of the all-time greats in rowing. According to the Wikipedia, Sir Steven Redgrave “won gold medals at five consecutive Olympic Games from 1984 to 2000.”

Wednesday, July 18, 2012

Great Olympic Streaks: Volleyball

Starting today and running each day until next Friday's (July 27) opening ceremony of the Summer Olympics in London, I will be reviewing great winning streaks and dynasties in Summer Olympic history.

I would like to start today with volleyball, both of the beach and indoor varieties. Two of America's best known and most successful Olympic athletes in recent times are the beach volleyball duo of Misty May-Treanor and Kerri Walsh.

According to a USA Volleyball profile: “…the pair won the 2008 Olympic beach volleyball tournament to become the first team to win two beach volleyball Olympic gold medals. The pair finished the tournament with a 7-0 record and did not drop a set... The team finished the [2008] Olympic Games with a 108-match winning streak… [It also] went 14-0 to win the [2004] Olympic Games in Athens.”

May and Walsh will be going for a third consecutive gold medal on the sand in London. The two players have faced some challenges over the past four years, including a torn Achilles tendon by May in late 2008 while practicing for the television series Dancing with the Stars.

In women's indoor volleyball, the US will be seeking to end an 0-for-11 slump of never winning the gold medal. The most noteworthy string of success in recent decades belongs to the Cuban women, who won the indoor volleyball gold in 1992, 1996, and 2000.

One name is most synonymous with success in modern Olympic men's volleyball history: Karch Kiraly. The former UCLA setter helped lead the USA to gold in the 1984 and '88 indoor competitions. Kiraly then returned to Olympic play in 1996, in the then-new sport of beach volleyball, and took home a third gold.

Tuesday, July 17, 2012

Cubs' Ryan Dempster's Streak of Scoreless Innings Pitched

It's been a rough season for the Chicago Cubs, but the team has played better of late. One major reason is the pitching of Ryan Dempster, who has not allowed a run in his last 33 innings pitched. According to this article, "The 33 scoreless innings is the club’s longest such streak since Ken Holtzman in 1969 and is the longest in the major leagues this season."

Based on Dempster's 2012 game-by-game log, I created the following chart of how many runs he has allowed in each inning he has thrown this season (you can click on the chart to enlarge it).

By looking at the games on the left-hand side, we can obtain Dempster's pre-streak proportion of innings started in which he retired the side without allowing a run. As detailed in the summary statement on the chart, that proportion is .803. We then apply this baseline percentage to the streak by raising it to the 33rd power (to represent the 33 straight innings). That calculation yields .0007, or roughly 1-in-1,428, for the probability of Dempster's 33 scoreless-inning streak, given his prior pitching proficiency this season.

Because Dempster has pitched so well all season, allowing relatively few runs during April and May, the probability of his throwing 33 consecutive shutout innings, while not large, is not astronomically small, either. Note that, in his first nine starts of the season, in only two games did he give up a run in more than one inning.

In fact, the statistics charted above don't do justice to how well Dempster has pitched, in my view. In his season debut vs. the Washington Nationals, for example, he was officially credited with allowing 1 run, in the 8th inning. As can be seen in the play-by-play sheet, Dempster pitched to three Washington batters in the top of the 8th (Chad Tracy, Ian Desmond, and Danny Espinosa), who respectively struck out, singled, and struck out. However, because reliever Kerry Wood allowed the runner to score, that run was attributed to Dempster.

Dempster's next start is scheduled to be this Friday night at St. Louis, although he is the subject of rampant trade rumors as the Cubs seek to rebuild with younger players.

Sunday, July 15, 2012

Stricker's Streak of Winning John Deere Classics Ends

Steve Stricker has fallen short in his attempt to make it four straight wins in the John Deere Classic golf tournament.

According to this Associated Press article, "Stricker [was] attempting to join Tom Morris Jr., Walter Hagen, Gene Sarazen and Tiger Woods as a winner four straight times in the same tournament. Woods has accomplished the feat twice."

Woods won the Bay Hill Invitational (now known as the Arnold Palmer Invitational) in Orlando, Florida each year from 2000-2003, and the Buick Invitational (now known as the Farmers Insurance Open) in San Diego, California, each year from 2005-2008.

Sarazen won the Miami Open four times between 1926-1930 (there officially was no 1927 version; the tournament was moved from December to January so what would have been the December 1927 playing of it was moved to January 1928).

Hagen won the PGA Championship four times from 1924-1927.

Morris was an old-time golfer, who won the British Open four times between 1868-1872 (the tournament was not held in 1871).

Let's come back to Stricker and estimate the probability of his winning three straight John Deere Classics. There were roughly 150 golfers in this year's event, so a very simple statistical model might assign Stricker a probability of 1/150 of winning the John Deere in a given year. However, my brother Steve, a very knowledgeable golf observer and also a Stricker fan, acknowledges that the John Deere tends not to have as deep a field of top professionals as other tourneys, apparently because many elite golfers prefer instead to use this time of year to prepare for the upcoming British Open. The weaker the John Deere field, the greater Stricker's likelihood of winning.

In fact, I checked this year's list of the Top 25 PGA money winners, and only five of them played in this year's John Deere Classic: Zach Johnson (who ended up winning the event), Carl Pettersson, Kyle Stanley, Mark Wilson, and Stricker.

Of course, someone outside the Top 25 tour money winners can win a tournament. If we assume there are 10 golfers each year in the John Deere field who are capable of winning it, Stricker among them, his single-year win probability would be 1/10. Raising this value to the third power to estimate Stricker's probability of three straight John Deere wins would yield 1-in-1,000.

If we assume there are 20 golfers in the John Deere field capable of winning, Stricker's probability of winning three straight is  (1/20) to the third power, yielding .000125 or 1-in-8,000. Finally, if we assume 50 entrants conceivably could win the John Deere Classic, Stricker's probability of three straight wins is .000008 or 1-in-125,000.

Regardless of which assumption one makes, Stricker's three straight John Deere victories before this year are noteworthy. Before one considers the probabilities above as being astronomical, however, one should realize that there are many fine golfers and many tournaments out there, creating a large number of opportunities for someone to win three straight.

There have been 21 instances of a player winning the same tournament exactly three straight times. If one adds the five occurrences (listed above) of a player winning the same event four consecutive times, then we have 26 instances in which a player has won the same tournament three or more times in a row.

Wednesday, July 11, 2012

Senator Collins Nears 5,000th Roll-Call Vote Without an Absence

It's not in the realm of sports, but it's definitely a long streak! U.S. Senator Susan Collins (R-Maine) is on the verge of casting her 5,000th consecutive vote on Capitol Hill without ever missing a vote due to absence. Heading into this week's legislative sessions, her streak stood at 4,997. This article (located via Political Wire) describes some close calls Collins has had since her election to the Senate in 1996. The article also presents some other statistics on consecutive votes cast:
  • "Among sitting senators, only Republican Chuck Grassley of Iowa [first elected in 1980] has a longer voting streak, having cast 6,444 consecutive votes dating back to 1993, when he missed votes to join President Bill Clinton in touring flood damage in Iowa."
  • "Grassley and Collins pale in comparison with the Senate's record holder, Wisconsin Democrat William Proxmire, who had 10,252 consecutive votes from April 20, 1966, to Oct. 18, 1988."
Not everyone is a fan of consecutive-votes streaks in government, however. Former Senator Eugene McCarthy (D-Minnesota) has said that voting on the Senate floor "is in many ways the least important thing that senators do." He went on to add that, "Shortly after I left the Senate, a roll-call vote was taken on what to do with the remains of Smokey the Bear."

Monday, July 02, 2012

D-Backs' Hill Hits for the Cycle -- Twice Within 10 Games!

Three nights ago, Friday, June 29, Aaron Hill of the Arizona Diamondbacks hit for the cycle, the second time he had done so in 10 games. The previous occasion was on June 18 (click here for the D-Backs' game-by-game log).

According to a Wikipedia page on the subject, "Cycles are uncommon in Major League Baseball (MLB), and have occurred 294 times... The cycle is roughly as common as a no-hitter (272 occurrences in MLB history); it has been called 'one of the rarest' and 'most difficult feats' in baseball."

With the rarity of hitting for the cycle, one might think it extremely rare for any player to have done it twice (or more) in a career, never mind twice in one season or twice in the same month. Remarkably enough, multiple-cycle seasons for the same player have occurred three times previously, although you have to go back 81 years for the last instance before 2012 (Babe Herman in 1931). Even more remarkably, the first two players to hit for the cycle twice in the same season (Tip O'Neill in 1887 and John Reilly in 1883) apparently accomplished the feat in quicker succession than did Hill (O'Neill and Reilly are each listed as having hit for the cycle 7 days apart; unless either of them faced a heavy supply of doubleheaders, it is almost certain each player's two cycles occurred within fewer than 10 games).

So how likely (or should I say, unlikely) was Hill's recent pair of cycles within 10 games? An excellent starting point is Jeff Sackmann's 2010 article, "The Odds of a Cycle." The foundation of Sackmann's tutorial is the relatively simple "multiplication rule" for joint probability (e.g., obtaining the probability of double-sixes on dice by multiplying together the probability of a six on each die, 1/6 x 1/6 = 1/36).

Also helpful was a brief analysis specifically focused on Hill's recent pair of cycles, by Justin Hunter, which provided some of the necessary statistical inputs for Hill. I used Hill's empirical frequencies of recording different types of hits, provided by Hunter, rather than what Sackmann used (something known as CHONE projections). A key insight of Hunter's was to identity Hill's low rate of producing triples historically (which was actually around 0.4% instead of the 0.3% figure Hunter gave).

Sackmann starts out with the simple case of a "natural cycle," that is, hitting a single, double, triple, and home run in that specific order, in four total plate appearances (PA). Filling in Hill's probabilities of the different types of hit, shown in the following table, we then multiply the numbers in the first four columns by each other, yielding the answer in the fifth column.

p (single) p (double) p (triple) p (homer)
p (Nat Cycle | 4 PA)
.162 .053 .004 .027

As Sackmann further notes, having the benefit of 5 or 6 plate appearances in a game instead of 4 improves a player's odds of hitting for a natural (or any) cycle.

With 5 plate appearances, there are 5 ways a natural cycle can happen, as listed below (1, 2, 3, and H represent, respectively, a single, double, triple, and home run; x = non-fitting outcome, such as an out, whose probability we apparently don't care about):


For 5 PA games, we thus multiply our original probability (.000000927) by 5, yielding .00000464.

With 6 PA, there are 15 ways a natural cycle can happen  (those with semi-advanced mathematical training may be familiar with the n-choose-k principle, in this case, 6 choose 4). These are the 15 ways:


For 6 PA, we would multiply our original probability (.000000927) by 15, yielding .0000139.

To get one overall probability of a natural cycle for Hill, we next average the probabilities given 4, 5, and 6 plate appearances, weighted by the frequency of occurrence of the different numbers of PA. Sackmann provided relative frequencies of how often players (in general) get different numbers of PA in a game -- not figures specific to any particular player, but overall averages. Because it would be too time-consuming to look at box scores for Hill's nearly 1,000 games played, we'll use the overall relative frequencies, too.

PA Proportion of Time (for avg. player) p (Nat Cyc) with those # PA Column 2 x Column 3
3 .101 --- ---
4 .591 .000000927 .000000548
5 .274 .00000464 .00000127
6 .034 .0000139 .000000473

Summing the yellow numbers (and dividing by 1.00 for the aggregated PA proportions) yields .00000229, the weighted average for the probability of Aaron Hill attaining a natural cycle (based on his batting statistics, weighted by PA patterns for an average player).

In reality, however, we're interested not just in natural cycles, but all possible kinds of cycles. As Sackmann says, “There are 24 permutations of the sequence 'single, double, triple, home run.' Thus, a garden-variety cycle is 24 times more likely than a natural cycle.” For scenarios beginning with a single, there are 6 possible sequences (only one of which, shown in red, is a natural cycle):


There are also 6 sequences beginning with a double, 6 beginning with a triple, and 6 beginning with a homer, thus yielding the 24 permutations. Multiplying our previous probability by 24 yields the following probability of Hill hitting for the cycle in a game (regardless of how the single, double, triple, and homer are sequenced).

24 x .00000229 = .000055 (roughly once every 18,182 games)

Before we get to the final steps, let's reflect on what we've discovered thus far. We have a player, Aaron Hill, who would be expected to hit for the cycle once every 18,182 games. Yet, he has done it twice in only 10 games!

We now bring in an online binomial probability calculator, which can help us answer questions of the form: How likely is it that, with an underlying probability of .000055 of an event (the cycle) occurring, 2 or more occurrences will be observed in 10 trials. This probability is .000000136, or approximately once in every 7 million (7,352,941) 10-game sets.

Ten-game sets are pretty numerous, however. Each time a player appears in his first career game, he is establishing a 10-game set (i.e., Games 1-10), then the next day, he establishes another (Games 2-11), etc. Sackmann notes that, “When 30 teams play a 162-game season, that's 43,740 player-games …”

In earlier times, there were fewer teams than 30 and fewer games on a team's schedule than 162. For simplicity, however, let's use Sackmann's figure of 43,740 player-games per year, each of which inaugurates a new 10-game stretch, with rare exception (e.g., when a player has 9 or fewer games left in his career).

Dividing 7,352,941 (the expected number of 10-game stretches for Hill or a player of similar abilities to hit for the cycle 2 or more times) by 43,740 (a rough estimate of the number of player-specific 10-game stretches launched in a single season) yields 168.1. We would thus expect a double-cycle by the same player within 10 games about once every 168 years.

Major League Baseball (and its organizational forerunners) have been around for 143 years, so it is not all that surprising to see two cycles by the same player occur within 10 days, at least once. In fact, it apparently has happened 3 times, but only once after 1887.

If you've stuck with me this far, you're probably really interested in the subject matter! I would recommend the following article to gain additional perspective:

Stefanski, Leonard A. (2008). The North Carolina lottery coincidence. The American Statistician. 62, 130-134.

Stefanski reflects upon the different interests of statisticians and laypersons (including the media) in understanding rare occurrences involving lotteries, sports, and perhaps other phenomena. Whereas laypersons seem to be interested in what Stefanski calls a "narrow" perspective (e.g., Aaron Hill's achievement), statisticians embrace a "wide" perspective, seeking to contextualize an occurrence in the larger set of opportunities for an event to occur. Writes Stefanski:

Statisticians should point out when seemingly rare events are not really that rare. But in doing so we should not lose sight of the fact that for some human interest stories, a probability calculation from the “narrow perspective” is appropriate. My hunch is that we sometimes do lose sight of the human-interest angle because we are geared toward the “wide” perspective (p. 131).

If you notice any faulty assumptions or calculations, please let me know in the Comments section or by e-mailing me via my faculty homepage (see links section to the right).