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 | |
---|---|---|---|---|---|

B_{0} | 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 | |
---|---|---|---|---|---|

B_{0} | 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.

I am curious if the preference towards D score would still be as strong on the mens' side if Mr. I Am 9 Million Miles Ahead Of My Closest Competition Uchimura were not included in the calculations. It could just be that the men are better at hitting and thus less likely to have major errors that affect their placement in the all-around as severely? But since we've determined both sides of the score are significant, can Bruno Grandi please shut up about halving the D score to "make the E score actually matter" now?

ReplyDeleteYou need to change the line "For the women, it's not the size of the D that matters. It's what you do with it." because it contradicts your claim that both D and E are statistically significant. Also, what data are you using? Worlds AA finals?

ReplyDeleteFair. It has been changed to: "For the women, the size of the D matters. But what you do with it matters even more."

DeleteAnd, yes, Worlds AA Finals, 2014.

I ran the data with the 2013 Worlds AA Finals, too. The values were slightly different, but the conclusions were the same: E scores are stronger predictors for the women.

Oh, and out of curiosity, I ran the numbers for the top 10 all-around finishers on the women's side. E-scores were still the strongest predictor.

Deletep value for D: 0.0197

p value for E: 5.73e-05

Beta value for D: -0.3012759

Beta value for E: -0.8612570

Compare that to the results for the top 24:

p value for D: 3.30e-11

p value for E: 2.54e-12

Beta value for D: -0.5798

Beta value for E: -0.6640

Outstanding. You should write this up as a paper and spread it around. Also, these "relative importance" statistics are new to me — can you take a look at this? Is this the same thing, just more specific? http://musicatechnica.com/CorrelationsOfSums.pdf

DeleteOh, and out of curiosity, I ran the numbers for the top 10 all-around finishers on the women's side. E-scores were still the strongest predictor.

Deletep value for D: 0.0197

p value for E: 5.73e-05

Beta value for D: -0.3012759

Beta value for E: -0.8612570

Compare that to the results for the top 24:

p value for D: 3.30e-11

p value for E: 2.54e-12

Beta value for D: -0.5798

Beta value for E: -0.6640

Fair. It has been changed to: "For the women, the size of the D matters. But what you do with it matters even more."

DeleteAnd, yes, Worlds AA Finals, 2014.

I ran the data with the 2013 Worlds AA Finals, too. The values were slightly different, but the conclusions were the same: E scores are stronger predictors for the women.

Hi Dennis,

DeleteThis week is kind of crazy. I'll try to take a look at your article later. In the meantime, if you use R, you might want to play around with the "relaimpo" package.

Here's the R code for Relative Importance:

# Calculate Relative Importance for Each Predictor

library(relaimpo)

calc.relimp(model,type=c("lmg","last","first","pratt"),

rela=TRUE)

# Bootstrap Measures of Relative Importance (1000 samples)

boot <- boot.relimp(model, b = 1000, type = c("lmg",

"last", "first", "pratt"), rank = TRUE,

diff = TRUE, rela = TRUE)

booteval.relimp(boot) # print result

plot(booteval.relimp(boot,sort=TRUE)) # plot result

Hi Dennis,

DeleteThis week is kind of crazy. I'll try to take a look at your article later. In the meantime, if you use R, you might want to play around with the "relaimpo" package.

Here's the R code for Relative Importance:

# Calculate Relative Importance for Each Predictor

library(relaimpo)

calc.relimp(model,type=c("lmg","last","first","pratt"),

rela=TRUE)

# Bootstrap Measures of Relative Importance (1000 samples)

boot <- boot.relimp(model, b = 1000, type = c("lmg",

"last", "first", "pratt"), rank = TRUE,

diff = TRUE, rela = TRUE)

booteval.relimp(boot) # print result

plot(booteval.relimp(boot,sort=TRUE)) # plot result

However, thank you for doing the work on this — the data repeatedly show that people have a misconception about the extent to which difficulty influences final placement.

ReplyDeleteI was thinking about the D's in bed last night. Could it possibly have to do with the variety of vaults performed for the women vs. men? There isn't too much variety amongst WAG AAers right now--they're all Yurchenko's of a varying number. That means there's a smaller range of difficulty, since, many of them are starting vault from a similar number. What would differentiate them, then, would be execution.

ReplyDeleteFor MAG, there's a much bigger variety of vaults that used by the AAers, with a bigger range of scores, and you add five more scores to the total (as opposed to three for the WAG). That's going to add up.

Do my thoughts make sense? I think it boils down to vault.

I think E scores matter more for women than men because there are 4 events for women vs. 6 events for men. Falls have the biggest effect on E-score variance. For women, one fall in the AA is disastrous (Example: Aliya in 2014). When there are only 4 events, a gymnast cannot recover from a fall. With men, they have more events to pull up their E-scores.

ReplyDeleteA fall always affects the E-score. However, a fall only sometimes affects the D-score.

That could definitely be a part of it. But part of it is the lack of variation in the men's E-scores.

DeleteSteve Butcher mentions it briefly in his interview on GymCastic: http://gymcastic.com/139-steve-butcher-president-of-the-fig-mens-technical-committee/