The significance of Thunder's Place PE Data stats

Here is the percentile rank of the circumference of TP PE data (at 2.5% intervals):

———— | - inclusive - | - exclusive -|

— pop - | start | -end- | start | end -|

- 100.0% | 1.000 | 1.000 | 1.000 | 1.000

— 97.5% | 4.000 | 4.000 | 4.000 | 4.250

— 95.0% | 4.000 | 4.250 | 4.188 | 4.500

— 92.5% | 4.250 | 4.375 | 4.250 | 4.500

— 90.0% | 4.375 | 4.500 | 4.375 | 4.625

— 87.5% | 4.500 | 4.500 | 4.500 | 4.720

— 85.0% | 4.500 | 4.500 | 4.500 | 4.750

— 82.5% | 4.500 | 4.625 | 4.500 | 4.800

— 80.0% | 4.500 | 4.750 | 4.500 | 4.875

— 77.5% | 4.625 | 4.750 | 4.563 | 4.920

— 75.0% | 4.700 | 4.800 | 4.688 | 5.000

— 72.5% | 4.750 | 4.875 | 4.720 | 5.000

— 70.0% | 4.750 | 4.938 | 4.750 | 5.000

— 67.5% | 4.750 | 5.000 | 4.750 | 5.000

— 65.0% | 4.813 | 5.000 | 4.750 | 5.000

— 62.5% | 4.900 | 5.000 | 4.800 | 5.100

— 60.0% | 5.000 | 5.000 | 4.875 | 5.120

— 57.5% | 5.000 | 5.000 | 4.900 | 5.125

— 55.0% | 5.000 | 5.000 | 4.960 | 5.200

— 52.5% | 5.000 | 5.063 | 5.000 | 5.250

— 50.0% | 5.000 | 5.110 | 5.000 | 5.250

— 47.5% | 5.000 | 5.125 | 5.000 | 5.250

— 45.0% | 5.000 | 5.200 | 5.000 | 5.313

— 42.5% | 5.000 | 5.250 | 5.000 | 5.375

— 40.0% | 5.100 | 5.250 | 5.000 | 5.500

— 37.5% | 5.125 | 5.310 | 5.100 | 5.500

— 35.0% | 5.200 | 5.400 | 5.125 | 5.500

— 32.5% | 5.250 | 5.500 | 5.196 | 5.500

— 30.0% | 5.250 | 5.500 | 5.250 | 5.500

— 27.5% | 5.350 | 5.500 | 5.250 | 5.600

— 25.0% | 5.438 | 5.500 | 5.250 | 5.625

— 22.5% | 5.500 | 5.550 | 5.350 | 5.750

— 20.0% | 5.500 | 5.625 | 5.438 | 5.750

— 17.5% | 5.500 | 5.750 | 5.500 | 5.800

— 15.0% | 5.510 | 5.750 | 5.500 | 5.880

— 12.5% | 5.700 | 5.900 | 5.500 | 6.000

— 10.0% | 5.750 | 6.000 | 5.625 | 6.000

—- 7.5% | 6.000 | 6.000 | 5.750 | 6.125

—- 5.0% | 6.000 | 6.200 | 6.000 | 6.250

—- 2.5% | 6.250 | 6.500 | 6.063 | 6.500

—- 0.0% | 8.875 | 8.875 | 8.000 | 8.250

with the graphs for inclusive and exclusive sets.

Thanks for taking the time to do this slipstream.

Is it possible to extrapolate a prediction of the average growth rate?

You seem to know what is coming next, marinera… :)

Well, almost next.

Here’s the Thunder’s Place PE Data volume estimations by percentile ranking:

———— | — inclusive — | — exclusive — |

— pop - | start -|- end - | start -|- end - |

- 100.0% | 00.080 | 00.080 | 00.080 | 00.080

— 97.5% | 06.048 | 06.446 | 06.770 | 08.057

— 95.0% | 07.187 | 07.639 | 07.474 | 09.266

— 92.5% | 07.906 | 08.541 | 08.049 | 10.103

— 90.0% | 08.460 | 09.055 | 08.568 | 10.773

— 87.5% | 08.863 | 09.669 | 08.863 | 11.131

— 85.0% | 09.266 | 09.988 | 09.266 | 11.490

— 82.5% | 09.668 | 10.445 | 09.508 | 11.937

— 80.0% | 09.870 | 10.773 | 09.702 | 12.136

— 77.5% | 10.072 | 11.001 | 09.947 | 12.434

— 75.0% | 10.324 | 11.439 | 10.233 | 12.645

— 72.5% | 10.548 | 11.729 | 10.345 | 12.931

— 70.0% | 10.832 | 11.937 | 10.480 | 13.259

— 67.5% | 10.979 | 12.119 | 10.773 | 13.566

— 65.0% | 11.280 | 12.419 | 10.942 | 13.852

— 62.5% | 11.515 | 12.633 | 11.191 | 14.006

— 60.0% | 11.835 | 12.931 | 11.426 | 14.282

— 57.5% | 11.937 | 13.160 | 11.585 | 14.530

— 55.0% | 12.063 | 13.454 | 11.850 | 14.805

— 52.5% | 12.368 | 13.718 | 11.937 | 15.062

— 50.0% | 12.612 | 13.926 | 12.119 | 15.353

— 47.5% | 12.931 | 14.224 | 12.434 | 15.628

— 45.0% | 13.083 | 14.443 | 12.651 | 15.937

— 42.5% | 13.429 | 14.744 | 12.931 | 16.249

— 40.0% | 13.677 | 15.045 | 13.142 | 16.558

— 37.5% | 13.926 | 15.418 | 13.429 | 16.851

— 35.0% | 14.125 | 15.737 | 13.708 | 17.214

— 32.5% | 14.443 | 16.249 | 13.923 | 17.530

— 30.0% | 14.684 | 16.835 | 14.203 | 18.054

— 27.5% | 15.045 | 17.102 | 14.443 | 18.417

— 25.0% | 15.547 | 17.452 | 14.847 | 18.776

— 22.5% | 15.902 | 18.054 | 15.079 | 19.258

— 20.0% | 16.513 | 18.507 | 15.647 | 19.828

— 17.5% | 17.102 | 18.959 | 15.988 | 20.257

— 15.0% | 17.698 | 19.680 | 16.473 | 20.931

— 12.5% | 18.392 | 20.275 | 17.100 | 21.764

— 10.0% | 19.114 | 21.416 | 17.940 | 22.918

—- 7.5% | 20.167 | 22.537 | 18.957 | 23.780

—- 5.0% | 21.951 | 23.920 | 20.390 | 25.596

—- 2.5% | 24.281 | 26.561 | 23.269 | 28.578

—- 0.0% | 66.208 | 66.208 | 42.017 | 54.157

Again, this is something valuable about our data. Since we have the corresponding measurements for length and circumference, we can calculate a (cylindrically estimated) volume distribution that doesn’t assume a correlation between the two measurements. There are the line graphs. We can also calculate the true correlation (R squared) between length and circumference as seen in this scatter chart.

That last graph indicates more valuable data for our PE purposes. So, I’ll follow up with some growth trends.

:) Yes, I am used to generating my own data and analyzing those. To work with only the mean and SD and having to assume normalcy, even when I know the data are probably not normal, was vexing.

Agreed. I made that analysis predominantly to address the 96 per cent of men who are either 2 SD above or below the mean, not the extreme tails (yes, marinera, I am thinking of your 13.5” penis question :D ).

No worries. I am happy to see this theme and dialogue continued and expanded upon.

Shucks… now you are making me blush. ;)

Seriously - nice work. I look forward to seeing the rest of your analyses.

Pri

I started out the with basics when analyzing growth. I’ll describe each column in the tables below:

First, as above, I have two sets of each measurement are either inclusive or exclusive. Inclusive counts all contributors, and exclusive counts only those contributors that made more than one entry.

The next column is “startX”, where X = L (length), C (circumference), and V (volume). Similarly “end X” is the last measurement provided by a contributor by date.

Then I have “∆X”, ∆ being the character delta, signifying “change in”. So, ∆L, ∆C and ∆V are just the absolute differences between start and end measurements. example: 7” - 6.5” = 0.5”

To understand how long growth takes, I have ∆X/day. I track hours in addition to days in my logs, as many others do. It would be nice to have hours here, but I can only work with the data we have.

I also added percent change in measurements, as “%∆X”, to see if there was any relative growth phenomena that is obscured by absolute growth. There is also a corresponding percent growth rate “%∆X/day”.

The last column is “days”: the total duration of the measurements provided by the contributors. Again, a “time under load” metric in hours would have been nice to have, but hindsight is 20/20. This is only so valuable because so many folks (like me) have taken time off and I haven’t tried to make my scripts smart enough to spit out a more intelligent duration when it can be inferred from the entries.

Finally, all measurements are in inches (length and circumference), cubic inches (volume), or percentage (where indicated).

Length stats:
inclusive | startL | end L -| ∆L ——| ∆L/day| %∆L ——| %∆L/day| days
- average | 06.384 | 06.682 | 00.297 | 0.044 | 004.92% | 00.03% | 235
— median | 06.300 | 06.700 | 00.000 | 0.000 | 000.00% | 00.00% | 0
- minimum | 01.000 | 01.000 | -1.500 | 0.000 | -21.43% | -0.61% | 0
- maximum | 13.000 | 13.000 | 03.625 | 8.375 | 077.78% | 04.76% | 5344
- std dev | 00.919 | 00.978 | 00.512 | 0.293 | 008.81% | 00.11% | 640

exclusive | startL| end L | ∆L ——| ∆L/day | %∆L ——| %∆L/day| days
- average | 6.312 | 7.008 | 00.696 | 00.005 | 011.52% | 00.08% | 550
— median | 6.250 | 7.000 | 00.596 | 00.002 | 009.26% | 00.04% | 225
- minimum | 1.000 | 1.000 | -1.500 | -0.043 | -21.43% | -0.61% | 1
- maximum | 9.770 | 9.999 | 03.625 | 00.250 | 077.78% | 04.76% | 5344
- std dev | 0.858 | 0.906 | 00.580 | 00.009 | 010.29% | 00.16% | 887

Observations:

The inclusive startL is slightly larger than the exclusive startL, which you can interpret to mean that some portion of larger guys didn’t make a second entry because they were already large enough.

The absolute change in length for the exclusive group averages 0.696” and the median is 0.596” - both over half an inch. You have a 50% chance of growing at least half an inch if you stick with it long enough to make more than one entry into the db.

The median absolute change in length in the inclusive group is zero, telling us that fewer than half the guys are in the exclusive group.

The absolute change in length per day is 0.044” for the inclusive group with an average of 235 days duration. The same exclusive metric is 0.005” with an average of 550 days. This says that 2x longer duration slows your growth rate 10X over the duration. More fun graphs on this, later.

The max and mins are way out there, but I have generally stopped using the absolute measurements as a filter and started using the growth rate changes. They seem more indicative of foul play. I’ve started to take the good with the bad because the sample size is so big, they don’t have a huge impact, anyway. example: I can throw out everyone that has positive or negative growth rates of more than 0.1” or 1% per day. This can be a post all to itself, but every time I filter it, I double the amount of data I get to compare. (ugh)

You’d be hard-pressed to convince me that it is possible to grow more than the maximum change in length shown here; either absolute or relative. 3.625” or 77.78% seems incredible, but there are guys that pop up all the time asking if it is possible to double their length in 6 months. This makes it clear that isn’t likely to happen in any amount of time, but later analysis will show the real likelihoods.

Looking at the exclusive relative growth rates (%∆L/day) next to days is pretty revealing. The average is 0.08%/day and median is 0.04%/day, while the durations are flipped with 550 days average and 225 days median. This says to me that most guys get their gains quickly and stop. i.e.: The 0.08%/day corresponds to the lower 225 median days, while the 0.04%/day is due to the longer average 550 day duration.

Average duration for the exclusive set is 550 days - over a year. Median is 225 days - just over seven months. I think this median is long enough to get some respectable gains and then watch gains slow to a frustrating crawl.

Girth stats:
inclusive | startC| end C | ∆C ——| ∆C/day| %∆C ——| %∆C/day| days
- average | 5.025 | 5.161 | 00.136 | 0.034 | 002.83% | 00.02% | 0235
— median | 5.000 | 5.114 | 00.000 | 0.000 | 000.00% | 00.00% | 0
- minimum | 1.000 | 1.000 | -0.750 | 0.000 | -12.00% | -0.36% | 0
- maximum | 8.875 | 8.875 | 02.750 | 6.313 | 063.33% | 14.29% | 5344
- std dev | 0.660 | 0.688 | 00.286 | 0.219 | 006.14% | 00.24% | 640

exclusive | startC| end C | ∆C ——| ∆C/day | %∆C ——| %∆C/day| days
- average | 4.985 | 5.303 | 00.318 | 00.003 | 006.62% | 00.05% | 550
— median | 5.000 | 5.250 | 00.250 | 00.001 | 004.89% | 00.02% | 225
- minimum | 1.000 | 1.000 | -0.750 | -0.020 | -12.00% | -0.36% | 1
- maximum | 8.000 | 8.250 | 02.750 | 00.750 | 063.33% | 14.29% | 5344
- std dev | 0.570 | 0.617 | 00.365 | 00.019 | 007.95% | 00.37% | 887

Observations:

Same as above - inclusive is larger than exclusive start.

Absolute and relative change in girth is roughly half that of length. Girth is either harder to gain, a less important objective to most members, or both.

The max absolute end measurement in this set is 8.25”, the max absolute change is 2.750” and the max relative change is 63.33%. If someone asks how likely it is to gain more than that, you can have high confidence in saying “zero”.

The inclusive start and end medians are lower than the average, so there are more above average guys than below before and after. The exclusive data flips the start state, so it goes from more below average guys before to more above average guys after. (duh, it works)

Volume stats:
inclusive | startV | end V -| ∆V ——| ∆V/day | %∆V ——| %∆V/day| days
- average | 13.315 | 14.732 | 01.417 | 00.010 | 012.20% | 00.09% | 0235
— median | 12.612 | 13.926 | 00.000 | 00.000 | 000.00% | 00.00% | 0
- minimum | 00.080 | 00.080 | -4.956 | -0.099 | -18.56% | -0.38% | 0
- maximum | 66.208 | 66.208 | 30.317 | 04.868 | 359.18% | 30.61% | 5344
- std dev | 04.738 | 05.314 | 02.705 | 00.084 | 025.27% | 00.55% | 0640

exclusive | startV | end V -| ∆V ——| ∆V/day | %∆V ——| %∆V/day| days
- average | 12.877 | 16.194 | 03.317 | 00.024 | 028.56% | 00.20% | 550
— median | 12.119 | 15.353 | 02.538 | 00.011 | 020.66% | 00.09% | 225
- minimum | 00.080 | 00.080 | -4.956 | -0.099 | -18.56% | -0.38% | 1
- maximum | 42.017 | 54.157 | 30.317 | 04.868 | 359.18% | 30.61% | 5344
- std dev | 04.218 | 05.286 | 03.290 | 00.127 | 032.07% | 00.83% | 887

The exclusive average absolute change in volume is 3.317 cubic inches and the relative change is 28.56%!!! That is amazing.

The median relative change is +20.66%. More guys get smaller gains, but a few guys must be gaining a lot.

So, the basics of growth are revealing and interesting. Things get more interesting when we look at growth distributions and rank.

This table is the percentile rank of absolute (inches) and relative (%) length growth. This also includes a duration column, but it is directly related to the rank column, not the rank change columns. There is a lot of data to look at, so I’m dropping the inclusive group to simplify things, for now.

- rank | - ∆L -|- %∆L -| days
100.0% | 0.000 | 00.0% | 0000
097.5% | 0.000 | 00.0% | 0011
095.0% | 0.000 | 00.0% | 0020
092.5% | 0.000 | 00.0% | 0028
090.0% | 0.000 | 00.0% | 0031
087.5% | 0.125 | 01.7% | 0036
085.0% | 0.150 | 02.3% | 0046
082.5% | 0.200 | 03.2% | 0056
080.0% | 0.250 | 03.6% | 0061
077.5% | 0.250 | 03.8% | 0068
075.0% | 0.250 | 04.3% | 0077
072.5% | 0.300 | 04.7% | 0090
070.0% | 0.350 | 05.4% | 0099
067.5% | 0.375 | 05.8% | 0116
065.0% | 0.400 | 06.4% | 0124
062.5% | 0.450 | 06.9% | 0136
060.0% | 0.500 | 07.4% | 0149
057.5% | 0.500 | 07.7% | 0164
055.0% | 0.500 | 08.2% | 0183
052.5% | 0.500 | 08.7% | 0207
050.0% | 0.591 | 09.3% | 0225
047.5% | 0.625 | 09.8% | 0245
045.0% | 0.625 | 10.4% | 0276
042.5% | 0.700 | 11.0% | 0302
040.0% | 0.750 | 11.7% | 0331
037.5% | 0.750 | 12.1% | 0365
035.0% | 0.787 | 13.0% | 0388
032.5% | 0.850 | 13.8% | 0423
030.0% | 0.920 | 14.6% | 0468
027.5% | 1.000 | 15.5% | 0510
025.0% | 1.000 | 16.7% | 0583
022.5% | 1.000 | 17.1% | 0653
020.0% | 1.120 | 18.2% | 0731
017.5% | 1.187 | 19.2% | 0844
015.0% | 1.250 | 20.0% | 0957
012.5% | 1.300 | 22.3% | 1089
010.0% | 1.437 | 24.0% | 1308
007.5% | 1.600 | 27.1% | 1691
005.0% | 1.770 | 31.8% | 2491
002.5% | 2.000 | 36.4% | 3831
000.0% | 3.625 | 77.8% | 5344

Despite making multiple entries, the first 10% of the contributors did not experience any growth. Though it is not shown here, there were some definite clusters of very low (single digit days) and very high durations (>3000 days) in this subset of the data making up about 4% of the 10%. I think this may be suspect data.

There are other clusters around small denominator increments, pointing to retirement after achievable milestones or perhaps low fidelity measurement.

I’ve used this view a few times now when advising members on growth expectations. When someone asks, is half an inch possible, it appears almost likely assuming you can make it beyond the mean duration. Each increment becomes harder and harder to achieve. I can give you a few likelihoods of achieving a certain growth target given a duration of commitment.

Here are a couple of evenly incremented absolute length distributions and their corresponding ranks.

∆L -|- rank -| |- ∆L -|- rank -|
0.0 | 100.0% | | 0.00 | 100.0% |
0.1 | 087.8% | | 0.05 | 089.5% |
0.2 | 082.2% | | 0.10 | 087.8% |
0.3 | 071.8% | | 0.15 | 085.1% |
0.4 | 064.5% | | 0.20 | 082.2% |
0.5 | 052.4% | | 0.25 | 073.4% |
0.6 | 048.6% | | 0.30 | 071.8% |
0.7 | 042.1% | | 0.35 | 069.5% |
0.8 | 034.0% | | 0.40 | 064.5% |
0.9 | 030.1% | | 0.45 | 062.3% |
1.0 | 022.1% | | 0.50 | 052.4% |
1.1 | 020.2% | | 0.55 | 051.4% |
1.2 | 016.6% | | 0.60 | 048.6% |
1.3 | 012.3% | | 0.65 | 044.3% |
1.4 | 010.1% | | 0.70 | 042.1% |
1.5 | 008.1% | | 0.75 | 035.5% |
1.6 | 007.3% | | 0.80 | 034.0% |
1.7 | 006.3% | | 0.85 | 032.5% |
1.8 | 004.8% | | 0.90 | 030.1% |
1.9 | 004.1% | | 0.95 | 029.0% |
2.0 | 002.4% | | 1.00 | 022.1% |
2.1 | 002.4% | | 1.05 | 021.5% |
2.2 | 002.0% | | 1.10 | 020.2% |
2.3 | 001.4% | | 1.15 | 018.4% |
2.4 | 001.1% | | 1.20 | 016.6% |
2.5 | 001.0% | | 1.25 | 013.1% |
2.6 | 000.9% | | 1.30 | 012.3% |
2.7 | 000.8% | | 1.35 | 011.4% |
2.8 | 000.6% | | 1.40 | 010.1% |
2.9 | 000.5% | | 1.45 | 009.8% |
3.0 | 000.4% | | 1.50 | 008.1% |
3.1 | 000.4% | | 1.55 | 007.9% |
3.2 | 000.4% | | 1.60 | 007.3% |
3.3 | 000.3% | | 1.65 | 006.5% |
3.4 | 000.3% | | 1.70 | 006.3% |
3.5 | 000.1% | | 1.75 | 005.1% |
3.6 | 000.1% | | 1.80 | 004.8% |
3.7 | 000.0% | | 1.85 | 004.5% |
3.8 | 000.0% | | 1.90 | 004.1% |
3.9 | 000.0% | | 1.95 | 004.0% |
4.0 | 000.0% | | 2.00 | 002.4%

I wanted to view the single significant decimal of the full population in the first set. You can see how long the tail is, and how it clusters 98% of the contributors in the first half.

The second set is just a tighter zoom on the first half of the prior set. It still shows a pretty long tail, but reveals more fidelity about the distribution within the most significant part of the population.

Here are a couple of sets that show the rank of relative growth increments. The second set looks at the top half of the prior set in greater fidelity.

%∆L |- rank -| | %∆L |- rank
00% | 100.0% | | 00% | 100.0%
02% | 086.2% | | 01% | 089.0%
04% | 076.5% | | 02% | 086.2%
06% | 066.6% | | 03% | 083.3%
08% | 055.8% | | 04% | 076.5%
10% | 046.5% | | 05% | 071.4%
12% | 037.9% | | 06% | 066.6%
14% | 032.0% | | 07% | 062.3%
16% | 026.4% | | 08% | 055.8%
18% | 020.4% | | 09% | 051.8%
20% | 014.9% | | 10% | 046.5%
22% | 012.7% | | 11% | 042.6%
24% | 010.0% | | 12% | 037.9%
26% | 008.7% | | 13% | 035.1%
28% | 006.6% | | 14% | 032.0%
30% | 005.4% | | 15% | 029.0%
32% | 004.7% | | 16% | 026.4%
34% | 003.5% | | 17% | 022.7%
36% | 002.8% | | 18% | 020.4%
38% | 002.2% | | 19% | 018.2%
40% | 001.7% | | 20% | 014.9%
42% | 001.6% | | 21% | 014.2%
44% | 001.3% | | 22% | 012.7%
46% | 001.1% | | 23% | 011.3%
48% | 000.9% | | 24% | 010.0%
50% | 000.8% | | 25% | 009.2%
52% | 000.6% | | 26% | 008.7%
54% | 000.6% | | 27% | 007.8%
56% | 000.4% | | 28% | 006.6%
58% | 000.4% | | 29% | 006.2%
60% | 000.3% | | 30% | 005.4%
62% | 000.3% | | 31% | 005.2%
64% | 000.3% | | 32% | 004.7%
66% | 000.2% | | 33% | 004.3%
68% | 000.2% | | 34% | 003.5%
70% | 000.1% | | 35% | 002.9%
72% | 000.1% | | 36% | 002.8%
74% | 000.1% | | 37% | 002.3%
76% | 000.1% | | 38% | 002.2%
78% | 000.0% | | 39% | 001.9%
80% | 000.0% | | 40% | 001.7%

Great posts, slipstream! I was planning to do similar ones myself.

Nice clean illustrations, slipstream :up: Thanks for taking the time to do this.

Fantastic effort- a real service to all the members here. And excellent aproach/method/explanation for those who are less mathematically inclined than the tech crowd.

Completely awesome!

I think we can call this the new best poll right? It definitely trumps Lifestyles poll sample size.

Wonderful work. This is why TP is the best PE site around: we have the best people.

Now we have a standard answer for about 50% of newbies questions (no, I’m not going to show how I calculate it ;) ).

Would be perfect to know if there is a difference in % growth between s.c. “small starters”, “big starters”, and “average starters”. One day in the future, don’t burn out.

For now, 1,000 thanks. :up: :up:

I agree. The dedication to encouragement and study of understanding this the best we can is awesome. Many thanks to the vets and mods.

I already have these graphs and will be posting them later (once I catch up on work a bit). Preview: not much correlation.

I’ve been doing it anyway. I’m glad to share as I have time.

Para-Goomba, docrob, fantom, BHB - Thanks.

As smart as I think I am (and humble ;) ), I value the opinions of the community. I’m better with data than physiology. I’d like to see more comments and interpretation of the previously posted data and graphs. What do YOU think?