Weightlifting has been contested as an international sport since the first modern Olympic Games in 1896. As of 2007, 167 countries are recognized by the International Weightlifting Federation. In the early part of the 20th century, the dominant nation in weightlifting was the United States. From the 1950s to the 1970s, the USSR was the most successful country. Between the 1970s and 1992, the USSR and Bulgaria shared the dominant position in weightlifting. After the dissolution of the Soviet Union in 1991, the number of elite competitors competing at international competitions increased, as many of the 15 former Soviet republics entered teams. Since 1996, China has also competed for top position, and recently, nations in the Middle East and South America have fielded competitive teams.
The most important annual competition in weightlifting is the World Weightlifting Championships (WWC), particularly as team ranking in these competitions has been used to determine the number of slots given to a country at the Olympics at the end of the quadrennial. The use of team rankings to allocate slots for the Olympics has been utilized since 1996. For the 1996, 2000, and 2004 Olympic Games, only the preceding year's team rankings at the WWC were considered. For the 2008 Olympics, the team rankings from 2006 and 2007 were considered. For the 2012 Olympics, the 2009, 2010, and 2011 WWC team rankings will be used to determine country quotas. The significance of team ranking and the large number of nations fielding competitive teams at the WWC highlights the importance of the team selection protocol.
Previous investigations have attempted to standardize performance across different weight classes in weightlifting using the two-thirds power rule (3), log transformations (4), and nonparametric curve fitting (2). However, these mathematical formulas only consider performance without regard to where (i.e., which competition) or when the performance occurred. More recently, an average method has been used, which involves averaging performance from either the annual international rankings or from recent WWCs. For all of these simple mathematical methods, a criterion total is generated for each weight class. An athlete's best performance is than expressed as a percentage of this criterion total, and athletes are ranked by their percentage score.
These methods appear to be well suited for standardizing performance, such as to determine the best weightlifter across the 8 men's or 7 women's weight classes, or to determine the highest caliber athletes to receive funding. They have also been used to rank and select athletes for international competitions. However, these statistical methods do not consider all factors that may be important for team selection. For competitions such as the WWC, where performance of the team may be more important than performance of individual athletes, these other factors should be considered for team selection. A major limitation of the previous mathematical methods is that they do not consider the number of potential athletes competing in a weight class. While an athlete may have a high ranking using one of these methods, they may not achieve a high placing at the WWC if a large number of competitors are in their weight class. Thus, if weightlifting coaches and officials determine that the primary goal of the WWC is to maximize the number of Olympic slots, the team selection process must consider these other factors. The purpose of this investigation was to analyze performance at the 2006 and 2007 WWC and propose a method for team selection.
Experimental Approach to the Problem
Performances from the 2006 and 2007 WWC were analyzed using descriptive statistics. Polynomial regressions were generated for each weight class to determine trends in performance. These statistics were utilized to generate a model for team selection.
Data were obtained from the official results of the 2006 and 2007 WWC, available at the International Weightlifting Federation website (www.iwf.net; accessed December 17, 2007). These data are published in the public domain, so the author did not seek written consent for their use from individual athletes. The 7 women's and 8 men's weight classes were analyzed independently. Performances from athletes who failed the in-competition doping tests were removed. As team points are given for 1st through 25th place, when more than 25 athletes participated in the weight class (1), only the top 25 competitors were considered.
The mean and median performance from the top 25 (or fewer) competitors was calculated. The placing for 100%, 90%, and 80% of the mean performance was determined. Additionally, for each weight class, the weightlifting total was determined for 1st, 5th, 10th, 15th, 20th, and 25th (or last if there were fewer than 25 competitors) place. The totals for 1st, 5th, 10th, 15th, 20th, and 25th place from the 2007 WWC were compared to the U.S. American Records. Polynomial regressions were generated for the top 25 (or fewer) competitors in each weight class. All statistical analyses were performed in Microsoft Excel 2003 software (Redmond, WA).
The numbers of competitors for each weight class are presented in Table 1. Mean and median performance and rankings for 100%, 90%, and 80% of these means are presented in Table 2 (2006 WWC) and Table 3 (2007 WWC). The mean performance increased for all weight classes from 2006 to 2007, with the exception of the men's 56-kg class. For the majority of weight classes, the number of competitors increased from 2006 to 2007. Polynomial regressions for the women's 63-kg and men's ≥105-kg classes are presented in Figures 1 and 2, respectively. Each weight class was best fitted using a third-order polynomial (Table 4). Totals for 1st, 5th, 10th, 15th, 20th, and 25th place in the 2006 WWC are presented in Table 5. Totals for 1st, 5th, 10th, 15th, 20th, and 25th place in the 2006 WWC are presented in Table 6.
The polynomial regressions indicate that performance from 1st to 25th place in each weight class decreased in a curvilinear fashion. The third-order polynomial fit suggests that performance decreased rapidly from the top competitors, reached a plateau in the middle of the class, and than decreased rapidly at the bottom of the class. The curvilinear trends in performance are corroborated by the large difference in ranking for 100% of the mean performance in the weight class compared to 90% and 80%. Furthermore, the drop in ranking from 100% to 90% of the mean performance was not uniform for all weight classes. These findings indicate that a team selection method based on a simple percentage system is not optimal. The mean and median performances were fairly similar, indicating that an individual whose total equals 100% of the mean performance would finish no lower than 13th place. However, depending on the weight class, an individual whose total is 90% of the mean performance would finish no higher than 22nd and as low as 42nd. While 2 athletes whose performance is 90% of the mean are of equal caliber, to maximize the number of team points earned, the individual who would place 22nd should be selected over the individual who would place 42nd.
The Senior American Records are comparable to performance required for 10th place or higher in the 2007 WWC. The Senior American Records in the women's ≥75-kg and men's ≥105-kg weight classes are closer to the total required for 5th place than 10th place. The team rankings for the 2008 Olympics were based on the points scored in 2006 added to the points scored in 2007 multiplied by 1.2. A full (N = 8) men's team who finished 10th in each weight class would have scored 120 points (8 × 15 points for tenth place). If 120 points were scored for each of 2006 and 2007, the country would score 264 points, finishing 7th overall and earning 5 men's Olympic slots. The maximum number of possible slots a nation can earn is 6. A full (N = 7) women's team who finished 10th in each weight class would score 105 points (7 × 15 points). If 105 points were scored in 2006 and 2007, the country would score 231 points, finishing 5th overall, and earning the maximum of 4 women's Olympic slots. Similarly, other countries can substitute their national records (in place of the American Records) to estimate the potential number of points their team could score.
As a simple percentage system is not optimal for team selection, a hybrid method involving ranking and percentage is proposed. The primary criterion for selecting an athlete to the WWC team is their potential ranking. Thus, 5 qualification tiers are proposed: 1st-5th place, 6th-10th place, 11th-15th place, 16th-20th place, and 21st-25th place. The totals for 1st, 5th, 10th, 15th, 20th and 25th place from the 2007 WWC (Table 6) are used to separate athletes into these tiers. An athlete who exceeds the 5th place total is ranked in the first tier, an athlete who exceeds the 10th place total is ranked in the second tier, and so on. If fewer than 8 athletes qualify in the first tier, all of these athletes are selected to the WWC team. The remaining slots are filled by athletes in the second tier. If any slots remain, they are filled by athletes in the same manner by athletes in the third, than fourth and finally fifth tiers.
If more than 8 men or 7 women qualify in the first tier, a secondary ranking will be generated. The performances for first tier athletes are expressed as a percentage of 1st place in the 2007 WWC, and the athletes with the highest percentage are selected. Thus, the athletes with the greatest potential to win the competition will be selected. The secondary ranking system can also be applied in the 2nd through 5th tiers, using the totals required for entry into the next highest tier. As an example scenario, 3 men qualify in the first tier, 3 in the second tier, and 5 in the third tier. The first 6 team members are selected from the first 2 tiers. To fill the remaining 2 positions, the performance for the 5 men in the third level are expressed as a percentage of 10th place in the 2007 WWC, and the 2 athletes with the highest percentage are chosen. In the event that there are not 8 men or 7 women in these 5 levels, additional athletes should be ranked as a percentage of 25th place in the 2007 WWC. Although it is not likely that these athletes will score team points at the WWC, failing to enter a competitor ensures that no points are scored.
This proposed team selection method is based on performances from the 2007 WWC. Performances from 2007 were generally higher than 2006, thus providing a more conservative and better indicator of potential ranking. For future WWC, totals should be based on the most recent preceding WWC. In the past (1996-2004), Olympic qualification was determined from the WWC immediately preceding the Olympic Games, thus performances in the first 2 WWC in the quadrennial were generally lower. However, as all 3 WWCs in the 2009-2012 quadrennial will count towards Olympic qualification, the most recent preceding WWC should be the best indicator of the potential competitors.
It should be noted that this team selection method is designed to maximize the number of points earned, rather than determine who is the best weightlifter. Other methodologies have been proposed to determine the best weightlifter, which are beyond the scope of this article (2-4). The different emphasis between the simple percentage method and the hybrid method will yield different results, which may benefit some athletes while being detrimental to others. When using the team selection method, a better weightlifter may be bypassed for a weightlifter that will score more points. Weightlifting coaches and officials must identify the priorities for competitions such as the WWC. If the priority is to reward the highest caliber athletes with the opportunity to compete at the WWC, a simple percentage system that determines the best weightlifter is appropriate. However, if the priority is to maximize team points, and therefore the number of slots for the Olympics, the hybrid method which considers both individual performance and the potential number of competitors should be superior.
Performance from the 2006 and 2007 WWC were analyzed to determine how to best select a team for future WWC in order to maximize team points and qualify slots for the Olympics. This selection method is based on the curvilinear trends observed for each weight class. As the ultimate goal of most weightlifters is to compete at the Olympics, it is recommended that this proposed method be used for WWC team selection, whereas the simple percentage system should be used for selecting the athletes competing at the Olympics. These statistical methods may also be effective for analyzing performances and selecting international teams in other sports with objective performance criteria.
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