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# crossfit: useful

EMBO Practical Course: Bioinformatics and Genome Analysis, 5–17 June 2017.

# $k$ index: a crossfit and weightlifting benchmark

I want to diverge from my traditional scope of topics and propose a new benchmark for weightlifting and CrossFit: the $k$ index.

The $k$ index is brainy and fun and gives you a new way to structure your goals. At high values, it's very hard to increase, making each increment a huge challenge.

Going around with a t-shirt that says "$k=40$ at everything" is maximally geeky and athletic.

## definition of $k$ index

For a given movement (e.g. squat, deadlift, press), you achieve index rank $k$ if you can perform $k$ unbroken reps at $k$% of your current one rep max (1RM).

Unbroken means no more than 1–2 seconds of pause between each rep. Exact standards would need to be established for competition.

## example of $k$ index

Suppose an athlete's one rep max (1RM) squat is 100 kg (220 lb).

The athlete will have a $k$ index rating of $k=10$ for squats if they can perform 10 unbroken reps at 10% 1RM, which is 10 kg (22 lb).

The athlete will have a $k$ index rating of $k=20$ for squats if they can perform 20 unbroken reps at 20% 1RM, which is 20 kg (44 lb).

The athlete will have an independent $k$ index rating for other movements like deadlift and press. These ratings are likely to be different for each movement.

## range of values

The minimum $k$ index is $k=0$ and it's a value we're born with.

The maximum theoretical $k$ index is trivially $k=100$ because, by definition, you cannot lift more than your current 1RM.

The maximum practical $k$ index is much lower than $k=100$ and probably in the range of $k = 50$.

## expected $k$ value

If you perform $r$ reps at weight $w$ you can estimate your 1RM using the Epley formula $w(1+r/30)$ assuming $r>1$. In other words, for each rep at a weight $w$ your estimate of your 1RM increases by ~3.3% above $w$.

There are various 1RM estimate equations and generally they are designed for fewer than 20 reps.

In some estimates, like by Mayhew et al. and by Wathan, the rep counts appear as $e^{-xr}$ for small $x$ such as $x=0.055$ which makes the formula converge to a value when $r$ is large like $r>15$. For example, Mayhew et al. converges to to a maximum of 1.91× of the weight being tested and Wathan converges to 2.05× of the weight being tested.

Other estimates, like McGlothin, generate unreasonable values for high rep count (e.g. 185 lb at 25 reps suggests a 1RM of 535 lb, which is insanely high) and for $r>37$ gives negative estimates.

Therefore, while I'm reluctant to apply any of these equations to get a rough idea of an expected $k$ value, I'm going to go ahead any way and use the Epley formula.

But let's try it anyway. If you lift $k$ reps at $k$% 1RM and we assume Epley applies, $$k/100 * 1RM * (1+k/30) = 1RM$$

which gives $k$ to the nearest rep $$k = 41$$

Again, if Epley applies (which it probably doesn't), this means that if your $k > 41$ you have more endurance relative to your level of strength.

Similarly, if your $k < 41$ then your strength is higher relative to your level of endurance.

In the table below I provide the 1RM estimate for each $k$ index value, which should give you an idea of how difficult it is to increase the $k$ index.

From personal experience—I haven't tried this yet—achieving $k=30$ is going to be hard and $k=40$ feels to me like it would be extremely challenging.

## testing $k$ index

The $k$ index requires more preparation and thought than testing your 1RM.

To accurately assess your $k$ index you need to first have an accurate assessment of your 1RM. Thus, a proper 1RM test is a prerequisite.

Second, you need to pick a value of $k$ to attempt to achieve and then attempt to perform the $k$ reps at the required weight. If this is your first $k$ index test, you need to pick $k$ conservatively.

I suggest trying for $k=20$ (20 reps at 20% 1RM). This should be doable for most people. Depending on how the 20th rep felt, you might want to take a 5 min rest and then try for $k=25$ (25 reps at 25% 1RM). This should be exponentially harder than testing for $k=20$.

Everytime you retest your 1RM you need to retest your $k$ index.

## $k$ index as a benchmark

The $k$ index is a measure of muscle endurance and movement efficiency.

It is not a measure of raw strength, since it is not strictly a function of your 1RM—an athelete with a lower 1RM may have a higher $k$ index for that movement.

It attempts to simplify multi-rep benchmarks like 3RM, 5RM, 10RM and so on. Although these themselves are very useful and I would not advocate forgetting about them, the $k$ index adds a measure of grit into the mix.

As a single number, the $k$ index can be used to visualize performance, especially in combination with 1RM. A plot of $k$ vs 1RM would very nicely distinguish different training regimes, such as powerlifting (low $k$ high 1RM) and CrossFit (high $k$ lower 1RM).

Your $k$ index may change independently of your 1RM, or vice versa. For example, you can get stronger and increase your 1RM but now find that your $k$ index is lower.

I think most people can get $k=20$, or close to it, on their first try. The range between $k=30$ and $k=50$ is where things get interesting and very painful.

## $h$ index

The $k$ index is similar to the h index, a metric commonly used in academic publishing.

The h index is defined as follows. "A scholar with an index of $h$ has published $h$ papers each of which has been cited in other papers at least $h$ times.". For example, if I have an $h=10$ then I have 10 papers that have at least 10 citations each.

To increase my $h$ index to 11, it is not enough to publish a paper with 11 citations. Now, the other 10 papers also have to have an extra citation each.

## $k$ total WOD

In 1 hour, establish your $k$ index for squats, deadlift and strict press, in that order. The total of your $k$ index values is your $k$ total.

Beginner athletes: attempt $k=20$, $k=24$ and $k=27$.

Intermediate athletes: attempt $k=24$, $k=27$ and $k=30$.

Elite athletes: attempt $k=30$, $k=32$ and $k=34$.

The goal of this workout is to test all three $k$ indexes in one session. You can test the individual movements on separate days and compare.

## scope of use

The $k$ index is only applicable for movements in which an athelete moves weight and for which a 1RM can be measured.

It does not apply to body weight movements like unweighted pushups or pullups. It can, however, apply to weighted forms of those movements.

Achieving the same $k$ index for different movements may not be equally easy. For example, it's probably easier to have a $k=30$ for deadlift than for strict press, since the latter uses smaller muscles.

## usage and notation

All of the following are equivalent.

squat $k30$

$k30$ (squat)

squat $k=30$

A squat $k$ index of 30.

## rep scheme table for $k$ index

The table below shows the requirement for achieving each index assuming a 1RM of 100 kg.

The performance column gives the 1RM estimate using the Epley formula based on your rep count relative to the actual 1RM used to calculate the weight. For example, for $k=30$ your 1RM estimate is $30/100 * (1+30/30) = 0.6$ of your 1RM, which is lower than you estimated and you can said to be underperforming. On the other hand, if you manage $k=50$ then your 1RM estimate based on your rep scheme is 1.33× the value used to calculate the weight.

As I mentioned above, the use of the Epley formula here is almost definitely wrong. However, I haven't done enough research in this field to know what formula to use for accurate 1RM estimation from a very high rep count. It's possible that no such accurate assessment can be made and I need to try to at least try it for myself in the gym.

krepsperformance
1 1 @ 1% 1RM (1 kg) 0.01
2 2 @ 2% 1RM (2 kg) 0.02
3 3 @ 3% 1RM (3 kg) 0.03
4 4 @ 4% 1RM (4 kg) 0.05
5 5 @ 5% 1RM (5 kg) 0.06
6 6 @ 6% 1RM (6 kg) 0.07
7 7 @ 7% 1RM (7 kg) 0.09
8 8 @ 8% 1RM (8 kg) 0.10
9 9 @ 9% 1RM (9 kg) 0.12
10 10 @ 10% 1RM (10 kg) 0.13
11 11 @ 11% 1RM (11 kg) 0.15
12 12 @ 12% 1RM (12 kg) 0.17
13 13 @ 13% 1RM (13 kg) 0.19
14 14 @ 14% 1RM (14 kg) 0.21
15 15 @ 15% 1RM (15 kg) 0.22
16 16 @ 16% 1RM (16 kg) 0.25
17 17 @ 17% 1RM (17 kg) 0.27
18 18 @ 18% 1RM (18 kg) 0.29
19 19 @ 19% 1RM (19 kg) 0.31
20 20 @ 20% 1RM (20 kg) 0.33
21 21 @ 21% 1RM (21 kg) 0.36
22 22 @ 22% 1RM (22 kg) 0.38
23 23 @ 23% 1RM (23 kg) 0.41
24 24 @ 24% 1RM (24 kg) 0.43
25 25 @ 25% 1RM (25 kg) 0.46
26 26 @ 26% 1RM (26 kg) 0.49
27 27 @ 27% 1RM (27 kg) 0.51
28 28 @ 28% 1RM (28 kg) 0.54
29 29 @ 29% 1RM (29 kg) 0.57
30 30 @ 30% 1RM (30 kg) 0.60
31 31 @ 31% 1RM (31 kg) 0.63
32 32 @ 32% 1RM (32 kg) 0.66
33 33 @ 33% 1RM (33 kg) 0.69
34 34 @ 34% 1RM (34 kg) 0.73
35 35 @ 35% 1RM (35 kg) 0.76
36 36 @ 36% 1RM (36 kg) 0.79
37 37 @ 37% 1RM (37 kg) 0.83
38 38 @ 38% 1RM (38 kg) 0.86
39 39 @ 39% 1RM (39 kg) 0.90
40 40 @ 40% 1RM (40 kg) 0.93
41 41 @ 41% 1RM (41 kg) 0.97
42 42 @ 42% 1RM (42 kg) 1.01
43 43 @ 43% 1RM (43 kg) 1.05
44 44 @ 44% 1RM (44 kg) 1.09
45 45 @ 45% 1RM (45 kg) 1.12
46 46 @ 46% 1RM (46 kg) 1.17
47 47 @ 47% 1RM (47 kg) 1.21
48 48 @ 48% 1RM (48 kg) 1.25
49 49 @ 49% 1RM (49 kg) 1.29
50 50 @ 50% 1RM (50 kg) 1.33
krepsperformance
51 51 @ 51% 1RM (51 kg) 1.38
52 52 @ 52% 1RM (52 kg) 1.42
53 53 @ 53% 1RM (53 kg) 1.47
54 54 @ 54% 1RM (54 kg) 1.51
55 55 @ 55% 1RM (55 kg) 1.56
56 56 @ 56% 1RM (56 kg) 1.61
57 57 @ 57% 1RM (57 kg) 1.65
58 58 @ 58% 1RM (58 kg) 1.70
59 59 @ 59% 1RM (59 kg) 1.75
60 60 @ 60% 1RM (60 kg) 1.80
61 61 @ 61% 1RM (61 kg) 1.85
62 62 @ 62% 1RM (62 kg) 1.90
63 63 @ 63% 1RM (63 kg) 1.95
64 64 @ 64% 1RM (64 kg) 2.01
65 65 @ 65% 1RM (65 kg) 2.06
66 66 @ 66% 1RM (66 kg) 2.11
67 67 @ 67% 1RM (67 kg) 2.17
68 68 @ 68% 1RM (68 kg) 2.22
69 69 @ 69% 1RM (69 kg) 2.28
70 70 @ 70% 1RM (70 kg) 2.33
71 71 @ 71% 1RM (71 kg) 2.39
72 72 @ 72% 1RM (72 kg) 2.45
73 73 @ 73% 1RM (73 kg) 2.51
74 74 @ 74% 1RM (74 kg) 2.57
75 75 @ 75% 1RM (75 kg) 2.62
76 76 @ 76% 1RM (76 kg) 2.69
77 77 @ 77% 1RM (77 kg) 2.75
78 78 @ 78% 1RM (78 kg) 2.81
79 79 @ 79% 1RM (79 kg) 2.87
80 80 @ 80% 1RM (80 kg) 2.93
81 81 @ 81% 1RM (81 kg) 3.00
82 82 @ 82% 1RM (82 kg) 3.06
83 83 @ 83% 1RM (83 kg) 3.13
84 84 @ 84% 1RM (84 kg) 3.19
85 85 @ 85% 1RM (85 kg) 3.26
86 86 @ 86% 1RM (86 kg) 3.33
87 87 @ 87% 1RM (87 kg) 3.39
88 88 @ 88% 1RM (88 kg) 3.46
89 89 @ 89% 1RM (89 kg) 3.53
90 90 @ 90% 1RM (90 kg) 3.60
91 91 @ 91% 1RM (91 kg) 3.67
92 92 @ 92% 1RM (92 kg) 3.74
93 93 @ 93% 1RM (93 kg) 3.81
94 94 @ 94% 1RM (94 kg) 3.89
95 95 @ 95% 1RM (95 kg) 3.96
96 96 @ 96% 1RM (96 kg) 4.03
97 97 @ 97% 1RM (97 kg) 4.11
98 98 @ 98% 1RM (98 kg) 4.18
99 99 @ 99% 1RM (99 kg) 4.26
100 100 @ 100% 1RM (100 kg) 4.33

VIEW ALL

# Classification and regression trees

Fri 28-07-2017
Decision trees are a powerful but simple prediction method.

Decision trees classify data by splitting it along the predictor axes into partitions with homogeneous values of the dependent variable. Unlike logistic or linear regression, CART does not develop a prediction equation. Instead, data are predicted by a series of binary decisions based on the boundaries of the splits. Decision trees are very effective and the resulting rules are readily interpreted.

Trees can be built using different metrics that measure how well the splits divide up the data classes: Gini index, entropy or misclassification error.

Nature Methods Points of Significance column: Classification and decision trees. (read)

When the predictor variable is quantitative and not categorical, regression trees are used. Here, the data are still split but now the predictor variable is estimated by the average within the split boundaries. Tree growth can be controlled using the complexity parameter, a measure of the relative improvement of each new split.

Individual trees can be very sensitive to minor changes in the data and even better prediction can be achieved by exploiting this variability. Using ensemble methods, we can grow multiple trees from the same data.

Krzywinski, M. & Altman, N. (2017) Points of Significance: Classification and regression trees. Nature Methods 14:757–758.

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Logistic regression. Nature Methods 13:541-542.

Altman, N. & Krzywinski, M. (2015) Points of Significance: Multiple Linear Regression Nature Methods 12:1103-1104.

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Classifier evaluation. Nature Methods 13:603-604.

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Model Selection and Overfitting. Nature Methods 13:703-704.

Lever, J., Krzywinski, M. & Altman, N. (2016) Points of Significance: Regularization. Nature Methods 13:803-804.

# Personal Oncogenomics Program 5 Year Anniversary Art

Wed 26-07-2017

The artwork was created in collaboration with my colleagues at the Genome Sciences Center to celebrate the 5 year anniversary of the Personalized Oncogenomics Program (POG).

5 Years of Personalized Oncogenomics Program at Canada's Michael Smith Genome Sciences Centre. The poster shows 545 cancer cases. (left) Cases ordered chronologically by case number. (right) Cases grouped by diagnosis (tissue type) and then by similarity within group.

The Personal Oncogenomics Program (POG) is a collaborative research study including many BC Cancer Agency oncologists, pathologists and other clinicians along with Canada's Michael Smith Genome Sciences Centre with support from BC Cancer Foundation.

The aim of the program is to sequence, analyze and compare the genome of each patient's cancer—the entire DNA and RNA inside tumor cells— in order to understand what is enabling it to identify less toxic and more effective treatment options.

# Principal component analysis

Thu 06-07-2017
PCA helps you interpret your data, but it will not always find the important patterns.

Principal component analysis (PCA) simplifies the complexity in high-dimensional data by reducing its number of dimensions.

Nature Methods Points of Significance column: Principal component analysis. (read)

To retain trend and patterns in the reduced representation, PCA finds linear combinations of canonical dimensions that maximize the variance of the projection of the data.

PCA is helpful in visualizing high-dimensional data and scatter plots based on 2-dimensional PCA can reveal clusters.

Altman, N. & Krzywinski, M. (2017) Points of Significance: Principal component analysis. Nature Methods 14:641–642.

Altman, N. & Krzywinski, M. (2017) Points of Significance: Clustering. Nature Methods 14:545–546.

# $k$ index: a weightlighting and Crossfit performance measure

Wed 07-06-2017

Similar to the $h$ index in publishing, the $k$ index is a measure of fitness performance.

To achieve a $k$ index for a movement you must perform $k$ unbroken reps at $k$% 1RM.

The expected value for the $k$ index is probably somewhere in the range of $k = 26$ to $k=35$, with higher values progressively more difficult to achieve.

In my $k$ index introduction article I provide detailed explanation, rep scheme table and WOD example.

# Dark Matter of the English Language—the unwords

Wed 07-06-2017

I've applied the char-rnn recurrent neural network to generate new words, names of drugs and countries.

The effect is intriguing and facetious—yes, those are real words.

But these are not: necronology, abobionalism, gabdologist, and nonerify.

These places only exist in the mind: Conchar and Pobacia, Hzuuland, New Kain, Rabibus and Megee Islands, Sentip and Sitina, Sinistan and Urzenia.

And these are the imaginary afflictions of the imagination: ictophobia, myconomascophobia, and talmatomania.

And these, of the body: ophalosis, icabulosis, mediatopathy and bellotalgia.

Want to name your baby? Or someone else's baby? Try Ginavietta Xilly Anganelel or Ferandulde Hommanloco Kictortick.

When taking new therapeutics, never mix salivac and labromine. And don't forget that abadarone is best taken on an empty stomach.

And nothing increases the chance of getting that grant funded than proposing the study of a new –ome! We really need someone to looking into the femome and manome.

# Dark Matter of the Genome—the nullomers

Wed 31-05-2017

An exploration of things that are missing in the human genome. The nullomers.

Julia Herold, Stefan Kurtz and Robert Giegerich. Efficient computation of absent words in genomic sequences. BMC Bioinformatics (2008) 9:167