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Wednesday, April 13, 2016

Statistics- How good are the US Women versus the World?

Weightlifting is full of data.  We can do many statistical analyses to interpret who our best lifters are and how they stack up versus the rest of the world with readily available continuous data.

In celebration of the Olympic year, this article examines the distribution of female weightlifter totals by weight class, and the percentile which the current top US woman in each weight class would score.  Using descriptive statistics, we can understand the level of competitiveness the US women and have insight on which females are best positioned to medal at the Olympics.

Method:
The dataset for each weight class was obtained from the IWF Olympic individual qualification rankings.  Specifically, the IWF dataset for individual qualification includes only the highest total registered for an athlete from every Olympic qualification event since 2014 through the present.  Further, there is one athlete total per weight class per country-- it is not the complete ranking list with every single athlete from every country that has competed internationally.   So, for example, Jenny Arthur is the highest totaling US 75kg in the last 2 years, so only her total out of all US 75's that competed internationally, is shown.  This is actually a better way to do the rankings since a country can only enter a maximum of two athletes per weight category, and, at the Olympics, no country can send a full team.  In effect, it is highly unlikely that a country with prospects of medaling in multiple classes will send 2 athletes in the same weight class. Outliers were not cleaned form the data as these stats are from actual people who lifted at actual weightlifting championships.  Plus, it would not be rational to remove the top lifter or even the worst lifter from the data; it makes physical sense that they should be outliers in many cases.

For comparison, the current USAW Olympic ranking list was used to compare US totals to the World ranking list.  To be consistent with the IWF ranking list, the top US total from each woman's weight class was compared to the IWF list, and the percentile rank was calculated. 

Results and Analysis

What the world looks like on the whole by weight class:

First, let us take a look at the distribution of totals by weight class across the world.

Here is a dotplot of each total in each weight class. The dotplots show the frequency at which each total occurs.  So a really high stack of dots means that multiple lifters hit a certain total; itt is the same idea as a histogram.  The dotplot is a little bit better visual to see frequencies, hence it is utilized.
 
The data tells us which weight classes have very large variation and hint at whether the data is normal (normality test must be done to confirm).

For example, the 48kg weight class seems to have the tightest distribution of the classes. This may be the effect of bodyweight --that there is no class lower than 48kgs for which to compete in, hence athletes can only move up and not down from this weight class.  Interstingly, the data is marginally normal; an Anderson-Darling normality test yields a .06 p-value.

In terms of medals, the data shows a clear favorite for the gold medal evidenced by the top total being in an echelon of its own.  Silver and bronze, however, are anybody's game as the athletes are so tightly clustered between 2nd through 8th place.

On the other hand, the 75+kg weight class has the most variability. Although at a first glance, the data looks non-normal, an Anderson-Darling normality test shows it is a normal dataset with a p-value of .307. 

More interesting are the top 2 totals in the 75+kg class- Tatiana Kashirina's 348kg total and Lulu Zhao's 334kg.  Kashirina's total is almost a full standard deviation from 3rd rank (Graboetskaya of Kazakhstan).  It can be implied that there are two lifters truly vying for Gold and silver at the Olympics, assuming both lifters are healthy, compete, and total at the Olympics.  Such can be said for the bronze medal between the 3rd, 4th, and 5th ranked athletes who are grouped around a 300kg total.  The remaining athletes are around 280kg or less. 

Here is where 75+kg, gets really interesting-- again, countries can only send a max of 4 female athletes to the Olympics. Its highly possible that not all the athletes in the 300kg total grouping will even show-up at the Olympics. It then makes the bronze medal anybody's game around the 280kg total mark.

The 75kg class is another fascinating weight class because it just doesn't have the same depth as the other middle weight classes (53,58, 63, 69,75) . Like 75+s, it has clusters of high totals, then a whole chunk of athletes over  a standard deviation away from the top. It is one of the easier weight classes.

69 women's appears to be the most competitive class for winning an Olympic Gold medal as there are 6 athlete totals in proximity to the first place total.

How the US women rank

This May, US women will be competing at the Olympic Trials in Salt Lake City, Utah for Olympic slots. The USA currently has 3 Olympic slots for women. 1 slot has already been designated to our top 75kg lifter, Jenny Arthur.  Mattie Rogers and Sarah Robles are ranked in the remaining 2 slots, per USAW's site.

The data can be examined rather easily for: (1)our best lifters in each weight class score versus the rest of the world, and (2) which athletes would be the top 3 in the USA based on their percentile rank in their weight class.

1. How US Female lifters score in their weight class on the IWF rankings

Per the below table, Mattie Rogers scores the highest across all weight classes with an 86th percentile rank.  Sarah Robles is in the 84th percentile, and Jenny Arthur is in the 82nd percentile.

The next closest lifter, Lucero, is in the 65th percentile. Interestingly, Morghan King scores equally well as a 53kg or a 48kg with  58th and 56th percentiles respectively.

2. Athletes best positioned to medal, or place the highest
The data shows us that Rogers, Robles, and Arthur are really in a grouping of their own at this point. The data supports the US ranking system which has all 3 currently projected to make the 2016 Olympic Team.

That being said-- this can all change should any of the other lifters on this list, or even any lifter competing at Nationals for that matter, have a huge Personal Record. The lower weight classes are more sensitive to change as, well, the totals are smaller. So, Morghan King might have the best chance of upsetting the 3rd ranked Olympic team spot should she have a big PR. For example, a 188kg total as a 48kg would put her in the 84th percentile.  However, by the USAW Olympic Games qualifying totals, King only needs 174kg to bump Rogers.

In this case, one could argue that the USAW ranking system has some deficiencies, which will always happen when rankings are based solely on percent of an average qualifying total. As mentioned in previous articles on this site, the population cannot be described by an average alone.


Weight Class N Maximum Mean StDev Minimum Q1 Median Q3 Top US female Percentile
48 52 205 164.13 23.07 91 153.5 163.5 180.75 170 KING 56th
53 58 233 178.43 25 104 157.75 181.5 194 184 KING* 58th
58 62 252 183.35 36.09 75 165 190.5 205 199 LUCERO 65th
63 61 261 195.66 35.95 75 180 197 214 206 MYERS 63rd
69 57 268 208.02 33.5 115 190.5 209 230 238 ROGERS 86th
75 53 292 215 35.93 120 193.5 217 238.5 244 ARTHUR 82nd
75+ 46 348 228.85 54.37 126 189.25 232 264.5 279 Robles 84th



The last table is the USAW current Olympic Ranking for female's. The USAW ranking method based on averages has the following athletes in spots 1 through 3:  Robles, Rogers, King.  Note Arthur is not even in the Top 3 per this method.    This differs from the percentile method where, again, the ranking would be Rogers, Robles, and Arthur per the same data.

PATH 1 PATH 2
 
RANK RANK NAME CREDITS <=2000 CAT BWT COMP TOTAL OG/100% %
1 1 Robles 2 1988 75+ 148.01 15WWC 279 290 96.21%
2 2 Rogers 2 1995 69 67.74 16NJCOQ 238 256.4 92.82%
3 3 King 4 1985 48 47.73 15WWC 170 186.6 91.10%
4 * ARTHUR 3 1993 75 74.65 15WWC 244 269.2 90.64%
5 4 Winters 1 1993 48 47.97 15WWC 165 186.6 88.42%
6 5 Chan 0 1987 53 52.84 15AO 187 212 88.21%
7
King 4 1985 53 50.44 16NJCOQ 184 212 86.79%

Conclusions

Based on the current US female totals, the data clearly shows that the US female athletes with the highest percentile score are Mattie Rogers, Sarah Robles, and Jenny Arthur in that order.  This implies that these would also be the USA's best chances of medaling, although a more complex model can be created to forecast medal potential.  Just going by raw ranking, all three lifter would place about 8th or 9th on the IWF ranking list. And, considering that countries cannot send full teams to the Olympics, these 3 women would be likely to score even higher at the Olympics assuming they do the same or greater total.
 
Secondly, the data supports the USAW decision to give Jenny Arthur an early qualification to the US Olympic Team.
 
Thirdly, the data tells us that the USAW may have a more accurate and fair model of ranking their athletes should they use percentiles of the IWF ranking list and not percent of an average.  The current ranking system gives a positive bias to the 48kg weight class and gives an negative bias to the 69kg weight class among others.  
 
Sarah Robles at the 2012 Olympics,
singlet by Risto Sports, official 2012 sponsor of podium attire
 

8 comments:

John Thrush said...

I like your work, Gwen. USAW needs to decide a methodology and stick with it got a set period of time (more than one tear , for sure. I would opt for a Wuad)so that we can gather data which will help us refine what we decide to use in the future. I have often recommended, to no avail, that our totals be based on where are our athletes rather than other international lifter ' s performances. Something like a qualifying total based on the Sinclair (yes, I know there are inherent issues with this formula). Say all Women's classes at Nationals should do a total equivalent to 260 (?) and Men 300. Then our International qualifying totals some percentile above that. Then the playing field even across all weight classes. But information like you have generated can be very enlightening and helpful. Kudos!!

Gwen Sisto said...

Thanks! Yes, I do like the idea of Sinclair-it would actually give us the same results as the percentile rank, except for the supers. Looks like Sinclair is correlated to ability to medal as the coefficient is based on weight class world records.

Rogers- 302kg Sinclair with a 238kg total @67kg bodyweight
Arthur- 294kg Sinclair with a 244kg total @74kg bodyweight
King- 285kg Sinclair with a 174kg total @48kg bodyweight
Robles- 279kg Sinclair with 279kg total @150kg bodyweight

Maybe at least some of the international teams can be based on a Sinclair- we could at least set a minimum Sinclair requirement along with the qualifying procedure. This would make it more fair for all weight classes below 75+kg, as the current system for qualifying for Nationals and for international teams is easy on Superheavyweights and to some extent 48's and 75's.

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fahiamalam said...


For the rest of this book I will refer to the art of weight lifting as strength training.
Strength training or weight lifting is the lifting of heavy weights and/or resistance in a prescribed manner as an exercise or in athletic competition.
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