Gender Inequality and Women's Gymnastics – Redux

Click the image to enlarge it.

My first post about gender inequality went awry, but no matter! In writing the original post, I thought of an even more interesting question about gender inequality and women's gymnastics.

When it comes to women's gymnastics, does gender inequality pose a barrier to entry? Is there some kind of threshold for inequality – a point where it becomes increasingly more difficult for women to participate in major competitions?

 Let's discuss the graph above. 

What is the GII?

The United Nations has developed a gender inequality index (GII), which takes into consideration things like adolescent birth rates, labor market participation by gender, and proportion of parliament seats occupied by women. 

If you want to read more about this index, I suggest that you hop over to the UN's website.

To create this chart, I took every country from the UN's database, eliminating the countries that didn't have an index score for 2013. (Sorry, Hong Kong. Sorry, Liechtenstein. Sorry, Brunei Darussalam. Sorry, Andorra.)

Then, I looked to see if the countries on the U.N. list had women compete at the 2014 World Championships.

Understanding the Graph

When you look at the chart, you'll see countries that had women participants in the World Championships at the very top. (They're coded 1.) The countries that didn't have any women participants appear at the bottom. (They're coded 0.)

The countries with more gender inequality are farther to the right. That's where you see countries like Afghanistan (0.705),  Chad (0.707), Niger (0.709), and Yemen (0.733).

Countries with more gender equality appear farther to the right. That's where you see countries like Slovenia (0.021), Switzerland (0.030), Germany (0.046), Sweden (0.054), and Austria (0.056).

Fun fact: Of the top 5 countries, with the least amount of gender inequality, only Slovenia didn't send a women's gymnastics representative to Nanning. (If I somehow missed the Slovenian gymnast, please let me know. The SVN abbreviation isn't showing up in the searchable PDFs.)

Because I'm sure that you're dying to know, here are the index scores for the Big 4:

China: 0.202

U.S.: 0.262

Russia: 0.314

Romania: 0.320

General Observations about the Graph

When you look along the bottom of the graph, you'll see that the red dots gradually get more frequent.

When you hit the 0.4 mark, BAM! The individual dots get almost impossible to decipher. Disney's 101 Dalmatians couldn't compete with this graph between the 0.4 and 0.6 mark. That means that a lot of countries with a gender inequality index of 0.4 to 0.6 didn't send women to Nanning.

What's interesting is that there are a few countries in the 0.4 to 0.6 range that did participate in the 2014 Worlds. These include:

Brazil (0.441)

Colombia (0.460)

South Africa (0.461)

Venezuela (0.464)

Panama (0.506)

Qatar (0.524)

India (0.563)

Egypt (0.580)

Gymternet Discussion Question 1:

Why do you think that these countries have sent women gymnasts to the World Championships?

For your reference, other countries with similar GII index scores include:

Ecuador (0.429)

Jamaica (0.457)

Morocco (0.460)

Indonesia (0.500)

Iran (0.510)

Guatemala (0.523)

Why does this silly chart matter?

1. History

Hold onto your seats. I'm about to make a sweeping generalization.

In a society with more gender inequality, women tend to get fewer opportunities outside the home. As countries develop and attitudes toward women change, the opportunities for women increase (and the societal attitudes towards women being physical become more liberal).

This problem isn't unique to gymnastics, but as a man who lives in the United States and who travels to Europe, I often forget this. And I'm guessing that some of my readers do the same.

2. The FIG

It's no secret that the FIG is trying to increase the diversity in the sport. If I were Bruno Grandi, I'd look at this chart and ask myself:

How can we encourage more participation from women around the world? Is there something that we can do, or do we have to wait for history to run its course?

I'd also look at some of the countries in the 0.15 and 0.4 range to see where the "lowest hanging fruit" is. That is, which of those countries are most likely to participate – if the FIG just gave them a little nudge.

Croatia (0.172), for example, didn't send any women gymnasts to Nanning, yet their country sends male gymnasts. The same could be said of Thailand (0.364).

Gymternet Discussion Question 2:

What can the FIG do to encourage the participation of more women from around the world? I'd love to hear your thoughts.

3. The Gymternet

I understand that gender inequality is a really complex issue. It's not an easy problem to solve, and I don't mean to suggest that gender inequality is the only thing preventing women from participating at major competitions like the World Championships.

With that caveat out of the way, I do think that the gymternet needs to spend more time thinking about the place of gymnastics in the world. We're extremely focused on the minutiae, on D and E scores, on who got chosen for a team, etc. And, yes, there's a time and place for that.

But we (myself included) often forget to think about gymnastics in a larger context. This post ultimately seeks to open up that conversation.

So, gymternet! Discuss Away!

Final Notes for the Stats Nerds:

This is a blog – not an academic article. So, I'm not going to create a table with all the details of β, SE β, etc.

Here are a few points from R:

Pr(>|z|) for the Participation variable: 0.00724

Null deviance: 25.689  on 151  degrees of freedom

Residual deviance: 17.867  on 150  degrees of freedom

1-pchisq(25.689-17.867, 151-150) = 0.005161405

So, I'd say that this line of research is something that is worth exploring more. If doing this type of research were my full-time job, I'd…

• Look at data from more competitions – If I could, I'd go back in time to see the evolution of this phenomenon
• Run the same kind of analysis, but look at whether the countries participated in the team competition
• See if there are similar trends on the men's side
• Explore more variables that could affect women's gymnastics

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Which event is the strongest predictor of all-around rankings?

Gymternet, my apologies. I'm on a myth busting tirade.

In my previous post, we looked at whether D-scores were strong predictors of final all-around rankings.

Now, I want to set that post aside, and I want to look at which event is the strongest predictor of final all-around rankings.

On the men's side, conventional wisdom would say that pommel horse is the "make it or break it" event.

And on the women's side, NBC would have us believe that balance beam is the "make it or break it" event.

Well, let's take a look and see how things played out at the 2014 World Championships… 

TL;DR:

• When it comes to final rankings in the all-around competition in Nanning, all individual event scores are statistically significant.
• So, the question really is, Which event is a stronger predictor of your all-around rank?
• For the men, high bar is the strongest predictor of your final all-around rank.
• For the women, uneven bars is the strongest predictor of your final all-around rank.
• You can see this in the charts of relative importances below.
• Note: We're looking at the final scores for each event.

For the stats nerds…

	B	SE	t	Beta	p
B0	243.0460
FX	-1.9482	0.5463	-3.566	-0.1885550	0.00238
PH	-2.4427	0.3393	-7.200	-0.2624963	1.49e-06
SR	-2.1156	0.7591	-2.787	-0.1505461	0.01265
VT	-3.8930	0.6731	-5.784	-0.2642798	2.20e-05
PB	-2.3847	0.3934	-6.061	-0.2713863	1.27e-05
HB	-3.0664	0.4630	-6.622	-0.3108039	4.32e-06

	B	SE	t	Beta	p
B0	177.4893
VT	-2.4841	0.7887	-3.150	-0.1935402	0.00528
UB	-3.4230	0.3775	-9.068	-0.4794243	2.48e-08
BB	-2.9556	0.4198	-7.040	-0.3589602	1.06e-06
FX	-3.0725	0.4615	-6.658	-0.3764892	2.29e-06

Eureka! This explains so much!

No wonder Oleg Verniaiev struggles in the all-around so much.

High bar is undoubtedly his weakest event, and when it comes to the final all-around rankings, high bar is pretty darn important.

Bretschneider? Epke? How much do I have to pay you to teach Oleg a Kovacs?

We need to improve Oleg's high bar! STAT!

#PrayForOleg

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E-Scores vs. D-Scores: Which is the strongest predictor of all-around rank?

It's time to look at another controversial subject among gymnastics fans.

It goes something like this:

"The gymnast who performs the most difficulty will win the all-around competition."

In other words, gymnastics fans tend to believe that D-scores are stronger predictors of a gymnast's final AA rank than E-scores.

I was curious about this, so I did some sexy data analysis. I ran some multivariate regressions, and here's what I found…

TL;DR:

• When it comes to final rankings in the all-around competition, both D and E scores are statistically significant.
• So, the question really is, Which is a stronger predictor of your all-around rank?
• The answer to that question depends on your sex.
• For the men, the D score is a stronger predictor of your final all-around rank.
• For the women, the E score is a stronger predictor of your final all-around rank.
• You can see this in the charts of relative importances below.

For those who aren't used to looking at charts of relative importances…

Look at the charts as you would look at a bar graph. See which bar is higher than the other – the D bar or the E bar.

All data comes from the 2014 Worlds AA finals.

MAG

For the men, the size of the D matters.

For the super stats nerds out here, here's everything you need to know:

	B	SE	t	Beta	p
B0	242.6414
D	-2.5106	0.1395	-17.99	-0.6744886	3.08e-14
E	-2.7293	0.1819	-15.01	-0.5625657	1.07e-12

WAG

For the women, the size of the D matters. But what you do with it matters even more.

For the super stats nerds out here, here's everything you need to know:

	B	SE	t	Beta	p
B0	180.6621
D	-3.0248	0.2415	-12.52	-0.5798	3.30e-11
E	-3.0400	0.2120	-14.34	-0.6640	2.54e-12

Discuss!

Gymternet, I need your thoughts.

Why do you think that E-scores are a stronger predictor for the women, while D-scores are a stronger predictor for the men?

In the meantime, men, good luck trying to get a bigger D. It ain't easy.

You might like…

• Which event is the strongest indicator of all-around rankings?
• Do Height and Weight Matter in Women's Gymnastics?

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More Difficulty = Better Execution Score? - The 2014 AA Edition

Let's face it, gym fans. We're human. We like to find examples and then make sweeping generalizations.

The relationship between difficulty scores and execution scores is no exception. Many gymnastics fans feel that judges are more lenient on difficult routines and reward the big Ds with high execution scores.

I was curious about this theory of ours. So, after the 2013 Worlds, I looked at the data from the qualifying rounds to see whether there was a correlation between difficulty and execution, and generally speaking, there wasn't a strong correlation.

This year, I decided to look at a smaller sample of scores. I focused on what happens when the best-of-the-best compete against each other during the all-around finals. So, I ran the data from the all-around final in Nanning.

And for those who like tl;dr statements, here you go: once again, the results were similar. Typically, there isn't a strong relationship between D-scores and E-scores. In other words, more difficulty does not equal higher execution scores – with a few exceptions.

Let's take a look.

Methodology

For the stats nerds, here's what you need to know:

• All scores from the all-around competition have been considered in the initial analyses. You'll see why at the bottom of this post.
• As you look at these scores, remember that you're looking at the upper echelon of gymnasts. So, there should be less variation in the scores, which will place the value of 'r' closer to 0.

For the non-stats nerds, here's what you are looking for:

• On individual events, we're looking for a value of 'r' that is greater than or equal to 0.404.
• What does it mean if the value of 'r' is equal to or greater than 0.404? This means that the relationship between the D and E scores are statistically significant.
• More specifically, 95 out of 100 times, the D score was correlated with the E score during the all-around finals in Nanning.
• Those are pretty good odds.

Okay, enough math babble. Let's take a look at some Ds, shall we? Woof.

WAG

On vault, r = -0.258. For the stats nerds, r(22) = -0.258, p > 0.05.

On uneven bars, r = 0.057. r(22) = -0.057, p > 0.05.

On beam, r is equal to 0.589. r(22) = 0.589, p < 0.05.

On floor, r is equal to 0.443. r(22) = 0.443, p < 0.05.

When you look at all the scores from the 2014 all-around finals, r is equal to 0.105.

MAG

On men's floor, r is equal to 0.333. r(22) = 0.333, p > 0.05.

On men's pommel horse, r is equal to 0.188. r(22) = 0.188, p > 0.05.

On rings, r is equal to 0.028. r(22) = 0.028, p > 0.05.

On vault, r is equal to -0.240. r(22) = -0.240, p > 0.05.

On parallel bars, r is equal to 0.268. r(22) = 0.268, p > 0.05.

On high bar, r is equal to 0.020. r(22) = 0.020, p > 0.05.

Conclusions

1. Vault

During the all-around finals in Nanning, the vault scores tend to trend downwards. In other words, the more difficult vault, the lower the execution score.

This tends to contradict popular wisdom among gymnastics fans, which says that an Amanar will get a better E-score than a full-twisting Yurchenko. However, on both the men's and women's side, the correlation between D- and E-scores isn't all that strong. So, I wouldn't be too quick to jump to conclusions.

2. MAG

The numbers for the men are kind of boring. We didn't really prove any judging controversy. The value of 'r' didn't hit the 0.404 mark on any event. So, the strength of the correlation on the men's side is fairly weak.

On first glance, it's tempting to chalk this up as a win for the men. The MAG judges are far superior to WAG judges. The E-score judges don't let big Ds sway their opinions.

But before we jump to conclusions, we should note that there are other factors that we should consider. For example, on the men's side, there tends to be more parity in the all-around final. So, there's less variation in scores. Less variation in scores tends to lower value of 'r', and when you look at the amount of variation in the men's scores, it's pretty consistent across all events – except for the execution score on rings.

Event	Standard Deviation - D Score	Standard Deviation - E Score
Floor	0.408	0.430
Pommels	0.500	0.486
Rings	0.445	0.223
Vault	0.332	0.436
P-Bars	0.435	0.564
High Bar	0.563	0.432

So, maybe the judges are better? Maybe not? I'll leave that up to you to decide.

3. WAG

For the women, we exceeded the magical number of 0.404 on two occasions: beam and floor. So, it seems like there tends to be a stronger connection between your D score and your E score on those events.

So, it's tempting to immediately point fingers at the floor and beam judges. Those lousy judges don't know how to judge!

But we shouldn't be so hasty. The judges don't exist in a vacuum. There could be other factors at play, like parity. Generally speaking, it is believed that there are fewer top contenders for the all-around title on the women's side, and when you look at the charts above, you can see the lack of parity, especially on beam and floor.

Lisa Hill competed a beam routine with a 4.0 difficulty score, which received a lower execution score of 7.366. Laura Waem competed a floor routine with a 4.4 difficulty score, which received a 6.233 in execution. When you look at the charts, both of those scores are obvious outliers.

So, what happens when you move those scores from the data sets? Let's take a look.

When you remove Laura Waem's floor score, the value of 'r' drops to 0.147, and the correlation is weakened a lot.

r is equal to 0.147.

So, it appears that Laura's score was really affecting our analysis. Maybe the floor judges aren't so bad after all.

However, when you remove Lisa Hill's beam score, the value of 'r' is still pretty high. It's at 0.551…

… which raises some suspicions. And now compare the beam example to what happens when we remove Shang Chunsong's bar routine with a 5.600 E-score from the data set. As we saw with floor, we still don't hit the 0.404 mark.

So…

Dear Nellie Kim,

What's up with beam?

If I were you, I'd be watching my beam judges during the all-around final very carefully.

xoxo,

Uncle Tim

P.S. I'm curious: Does anyone know if the FIG has a team of data scientists looking at these numbers? I want to know what their conclusions are.

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Sexy Data Dump

During the World Championships, I made many, many charts for GymCastic, and they need to live somewhere. So, why not my blog?

Click on the images to make them larger.

1. A breakdown of the execution scores during the men's all-around.

2. A breakdown of the difficulty scores during the men's all-around.

People need to stop talking about how difficulty always trumps execution.

3. How did our top men do last year during the all-around finals?

Holy upgrades, Max Whitlock! And holy improvement, Oleg!

In the words of Oleg, "Next year I should focus more on the all-around because it is high time, high time indeed."

If we start praying now, gymternet, the gym gods are bound to give in and find a place for Oleg on the podium in 2015!

4. A comparison of 2013's floor scores vs. 2014's floor scores

Sometimes, I wonder, "Would that score been medal-worthy last year?" I decided to make some charts to find out.

Has Shirai grown? Or why is he having troubles keeping his tumbling passes within the lines?

5. …and the same for pommel horse…

If your leg cuts don't look like Berki's, you're doing it wrong.

6. …and the same for rings…

This was one of the closest finals! But I do wish that the judges had drawn clearer distinctions between routines. In a field of 8, should there really be 2 ties?

7. …and the same for vault…

Ri Se Gwang, I'll donate my foot bones to you!

8. …and the same for parallel bars…

All my prayers finally paid off! Oleg produced the most beautiful routine of the entire World Championships! (Sorry, Kohei-Lovers! But Oleg was sublime!)

If you don't like this routine, you have no soul.

9. …and the same for high bar…

Epke, your execution is improving!

Even though girls have cooties…

I did make some WAG sexy data!

1. How did our top women do last year during the all-around finals?

Vanessa Ferrari with the upgrades. Simone Biles with the consistency. Kyla Ross and Aliya Mustafina with the injuries and the downgrades. :(

2. A comparison of 2013's vault scores vs. 2014's vault scores

Praise the gym gods! There were no injuries during women's vault this year!

And this chart makes you wonder, Does McKayla Maroney really need to upgrade her second vault in order to stay competitive?

3. …and one of the women's bars…

The women are upping the ante on bars! A high 14 is no longer going to put you in medal contention!

4. …and one of the women's beam…

If Kharenkova can get it together next year (and stay away from the Russian Vortex of Injuries), women's beam should be one of the more exciting finals next year. *Fingers crossed*

5. …and one of the women's floor…

An 8.933 in execution on floor in the current state of gymnastics? SPLIT LEAPS TIMES INFINITY!

Oh, and if you get extremely nationalistic about gymnastics meets…

Here's the MAG medal count…

And here's the WAG medal count…

Yet again, there's more diversity on the men's side.

Other tidbits…

• The FIG has released the official results book
• Bruno Grandi is talking about changing the scoring system… AGAIN!

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2014 Men's World Team Finals: When Difficulty Edges Out Execution

At the 2004 Olympics, Marian Dragulescu performed his eponymous vault. He completed it nearly flawlessly and earned a 9.900, a ginormous score at the time. For his second vault, Dragulescu did a Kaz 1.5. But he went over the lines, put both hands to the mat, and stepped off the vault mats.

Magically, Dragulescu still scored a 9.325 on his second vault. Many thought that Dragulescu should have scored a maximum of 9.100 on the Kasamatsu. The Canadian gymnastics federation lodged a protest on behalf of Kyle Shewfelt who was in fourth place. Two judges had given Dragulescu a 9.5 on his second vault, when there were clearly more than 0.5 in errors.

Adrian Stoica, a Romanian, was the FIG's Men's Technical Director at the time, and many believe that Dragulescu's score was a show of partisanship.

About today's results, Coach Rick on GymnasticsCoaching.com has said:

This is worse than the Uchimura pommel dismount scandal at the 2012 Olympics. 

On par with the Dragalescu 2nd Vault scandal at the 2004 Olympics. Four judges were sanctioned that time.

I had many feelings about this, as well.

China wins with a fall on floor and a pancake splat on p-bars. W.T.F.
— Uncle Tim (@uncletimmensgym) October 7, 2014

Had Kato not messed up his Tak 1/1…………………………………………………………………………………………………………………………………… GAH!
— Uncle Tim (@uncletimmensgym) October 7, 2014

Overall, Japan was the more consistent team. But, with some distance between myself and the event, I can say that Japan had their fair share of mistakes and missed opportunities. Let's take a look at some numbers… 

As you can see, China performed more difficulty than Japan, especially on rings.

Event	CHN D-Score Avg.	JPN D-Score Avg.
Floor	6.633	6.900
Pommels	6.233	6.333
Rings	6.833	6.300
Vault	6.000	5.867
Parallel Bars	6.900	6.633
High Bar	7.100	6.733
Overall	6.617	6.461

Dang! The Chinese on rings are hot.

What the Japanese lacked in difficulty they made up in execution. Correction: almost made up in execution.

Event	CHN E-Score Avg.	JPN E-Score Avg.
Floor	8.289	8.677
Pommels	8.341	8.780
Rings	8.677	8.544
Vault	9.355	9.389
Parallel Bars	8.541	8.711
High Bar	8.219	8.222
Overall	8.571	8.721

Japan's execution scores, though better than China's, just weren't enough to overcome China's difficulty. Unfortunately, that's not where this story ends.

Like moths to a flame, gymnastics fans are attracted to the faintest whiff of controversy. If you look closely at the high bar execution scores, they are awfully close: an 8.219 average for China and an 8.222 average for Japan. On top of that, Zhang Chenglong's execution score was only 0.044 behind Kohei Uchimura's. (8.466 to 8.500.)

So, we sit down at our laptops and compare high bar routines in slow motion. We watch Kohei's routine:

Then, we watch Zhang Chenglong's routine:

And we compare pirouetting skills. How much did they twist? How crooked and whackadoodle were their swings out of the pirouettes?

vs.

And we'll compare release catches. How early did they catch? How bent were their arms? Did they almost kiss some pipe?

vs.

And, in the end, we, the couch gymnasts of the world, blame the judges.

(And some of us open up old wounds because we are masochistic like that. We remember that time, in 2011, when Zhang Chenglong was last to go on high bar. He managed to beat Epke Zonderland in Rotterdam. And we get our tighty whities in a bundle because "the judges really messed that one up.")

But we don't blame the gymnasts. We're reluctant to blame the gymnasts – when, to be quite frank, the Chinese team left the door wide open for Japan. And Japan tripped walking up the stairs.

Shirai Kenzo stepped out of bounds on floor. There went three tenths right there.

Ryohei Kato competed a 5.6 vault instead of his 6.0 vault. There go another four tenths right there. (Though, he did score a 14.966 in finals compared to his 14.866 in prelims.)

Yusuke Tanaka "bombed" parallel bars. He scored a 15.700 in prelims and only a 15.166 in finals. That's 0.534. (Personally, I would die a happy man if I scored a 15.166 on p-bars.)

Ryohei Kato missed his Adler 1/1 into his Yamawaki, dropping his difficulty score from a 6.4 to a 6.3. There's another tenth.

As I said on the Worlds preview show of GymCastic, the team title was Japan's to lose, and lost it they did.

That's right. The judges did not lose the meet. The gymnasts did.

Contrary to what we might believe, gymnasts do have agency in competitions. Contrary to what we might believe, gymnasts are not the marionettes of some maniacal puppeteer judges.

Sure, judges will mess up from time to time. They are human – just like the gymnasts. When it is crystal clear that the judges did mess up, they should be castigated.

But was Zhang Chenglong's high bar score as painfully wrong as the Marian Dragulescu's 2004 vault score situation?

No. De ninguna manera.

Don't be so dramatic.

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