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