Author Topic: Likelihood Distribution of Number of SpaceX Launches in 2015  (Read 20694 times)

Offline Proponent

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As previously threatened, I'm going to solicit members' views as to the likelihoods of various numbers of SpaceX launches in 2015.  Of course, this does not preclude anybody from starting a traditional single-choice poll as well.  It may be interesting to compare the results of the two.

The advantages I see for this type of poll are 1) it imposes no preconceptions as to the number of flights, and 2) it elicits more information than does a single-choice poll.  We'll see how it goes.

Rules:

1. For ease of tabulation, please use precisely the following format:
Quote
<forum name>: n pn pn+1 pn+2 pn+3 ... pN

<(optional) rationale>

where n is the minimum number of launches to which you assign a non-zero likelihood, pk is 100 times the likelihood assigned to k launches (e.g., a likelihood of 10% should be expressed as "10" [without the quotation marks]), N is the maximum number of launches having non-zero likelihood, and the other two fields are self-explanatory.  Please note that a colon terminates the forum name and that subsequent entries are separate by spaces, not commas or other punctuation.  Please leave a blank line between the first row and any explanatory text.

For example, suppose I think there's a 10% chance of 6 flights, 25% for each of 7-9, 15% for 10 and 5% for 11.  Then my entry would look like

Quote
Proponent: 6 10 25 25 25 15 5

They're probably gonna do better than last year, but I'm not expecting them to completely blow barn doors off.  If nothing else, for the time being there is still just one pad.  And I'm betting that Falcon Heavy isn't going to fly until 2016.

2.  I reserve the right to disregard entries not precisely in the above format as well as to interpret non-conforming entries in what seems a reasonable way.

3.  Likelihoods should sum to 100.  If they don't, they'll be normalized to 100 at my discretion (e.g., if they sum to 99, I may simply normalize; if they sum to 47, I may ask for clarification).

4. I commit tabulating up to 400 entries.  That's not to say I won't process more, but there has to be some limit.  Of course, everybody else is free to process the entries as may seem appropriate.

5. At the close of 2015, I will score each entry according the likelihood assigned to the number of flights which actually occurred.  I will post the results.

6.  A launch shall be deemed to have occurred whenever SpaceX Falcon intended for orbit or beyond leaves the pad in 2015 (GMT).  Whether is successful or not is irrelevant (that way we avoid disputes about the definition of "success").

7.  Entries will be accepted until 15:28:53 GMT 19 January 2015.  Once posted, entries may be modified until the poll closes.

8.  One post per member, please, until the poll closes on 6 January.  Please post questions or comments here (or PM me) rather than posting in the present thread.  This will make tallying the entries easier.

Go for broke with a single number, or play it safe with a nice, broad range -- it's up to you!
« Last Edit: 01/05/2015 08:47 pm by Proponent »

Offline Lar

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Lar: 0 0.05 0.1 0.2 0.45 0.8 1.4 2 4   5 7 9 11   12 14 12   10 6 3 1   0.5 0.5

Rationale: My lower bound is zero. There is a very small, but non zero probability that CRS-5 will fail in such a way that the entire year is shot (note that under Proponent's criteria the recent Antares/Cygnus failure counts as a launch... in order to hit 0 CRS-5 has to "fail" before it even is ignited, and fail so spectacularly that they call off all their launches). I think this a very low probability so I assigned it a .05% chance. The range is broad, it goes up to 20 but the peak is around 12-14 launches. That's what I know they are striving to hit.  The probability of more than 15 starts to fall off really rapidly so I stopped at 20

I fudged a few of the estimates to get it all to come out to 100 (I probably should have pre normalized)

Here's a chart the way Skybum did it

flights      prob        Cum         At least
 0       0.05       0         100.00%
 1       0.1        0.05       99.95%
 2       0.2        0.15       99.85%
 3       0.45       0.35       99.65%
 4       0.8        0.8        99.20%
 5       1.4        1.6        98.40%
 6       2          3          97.00%
 7       4          5          95.00%
 8       5          9          91.00%
 9       7         14          86.00%
10       9         21          79.00%
11      11         30          70.00%
12      12         41          59.00%
13      14         53          47.00%
14      12         67          33.00%
15      10         79          21.00%
16       6         89          11.00%
17       3         95           5.00%
18       1         98           2.00%
19       0.5       99           1.00%
20       0.5       99.5         0.50%
                                0.00%
         


« Last Edit: 12/19/2014 09:04 pm by Lar »
"I think it would be great to be born on Earth and to die on Mars. Just hopefully not at the point of impact." -Elon Musk
"We're a little bit like the dog who caught the bus" - Musk after CRS-8 S1 successfully landed on ASDS OCISLY

Offline saliva_sweet

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saliva_sweet: 4 100

Keeping it simple and pessimistic.
« Last Edit: 12/19/2014 02:37 pm by saliva_sweet »

Offline Garrett

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Garrett: 6 10 20 24 21 14 8 3

rational: no crazy rational. I just hope they'll do at least 6 next year, so that's why I started with that. Last year I said 8, so I'm just hoping for that again, so it gets to be the maximum. I think 12 would be sweet, as it would be an average of 1 per month and that's as far as my expectations go. Also, I played with the numbers so that the distruibution would look kinda Maxwellian ;) (see attached image)

 
- "Nothing shocks me. I'm a scientist." - Indiana Jones

Offline Jimmy Murdok

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Jimmy Murdok: 6 5 12 18 18 20 15 12

Edit/Lar: fix to match requested format.
« Last Edit: 12/19/2014 03:13 pm by Lar »

Offline averagespacejoe

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averagespacejoe: 4 5 7 10 10 10 15 30 10

This is a bizarre format that shows me why I was never an engineer. However here it is.

Edit/Lar: Fix to match requested format
« Last Edit: 12/19/2014 03:19 pm by Lar »

Offline skybum

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skybum: 2 1 1 2 4 6 9 13 20 30 10 3 1

Or expressing this another way:

Number of flightsprobability of achieving
0100%
1100%
2100%
399%
498%
596%
692%
786%
877%
964%
1044%
1114%
124%
131%

Offline CraigLieb

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CraigLieb: 3 1 1 2 6 17 22 25 16 7 2 1

Rationale:
Most likely 9 with more rounded on the low side with a more severe drop off in probability on the high side.
Like showing the chart. I am a fan of bell curves having been a Six Sigma Black Belt, but I don't think this is a situation where there are equal probabilities around the mean.  It will be more skewed to the low side due to "space is hard", "abundance of caution".. etc. Hopeful that they could swing for the fences and hit 12! can't bet that will be the result. 

Edit/Lar: Fix format to match requested format. and yes, I am getting tired of doing this.
« Last Edit: 12/19/2014 04:26 pm by Lar »
Colonize Mars Already!

Offline toruonu

toruonu: 4 3 4 8 11 14 15 13 10 8 6 4 2 1 1

It derives from Poisson distribution for 9 flights, but gets a manual modification trunkage at the higher end shifting some of the probability to lower end due to space being hard etc.
« Last Edit: 12/19/2014 05:21 pm by toruonu »

Offline mheney

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mheney:  7   2 4 6 10 20 25 20 10 2 1

Figuring 50% growth in flights per year is a good pace; I've got 85% of my money on 10-14 flights.
I'd be happy to be wrong on the low side.


Offline Tass

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Tass: 0 0.1 0.2 0.5 1 2 4 8 12 18 23 18 8 5 2 0.9 0.2 0.1

Offline nadreck

nadreck: 0 .5 .5 .5 2 3 5 5 5 5 5 5 10 10 10 20 10 2 1 .5


[edit]Ok Ok, rationale:  Yup I agree that they might stop for a whole year if there is an Anteres event and I consider that a .5% probability right now, and if they launch another 10 in a row without a bauble it is down to about .2 - .3%. Another thing is that while I think they will make 13 launches next year, each successive launch beyond that is really a strain on human (and other) resources for where the company is at right now. By the time they get out to 15 I think payloads will also be an issue. Which is why my odds drop so dramatically at the end. I do think they may launch an essentially "free" bird using a recovered core in the 2nd half of the year and that it will contain either a SpaceX test payload, an Elon or Elon favoured payload for free or cheap, or a "deal" payload for some company that had a standby bird to cover for a failed launch from some other carrier. [/edit]

[2nd Edit] fix my math [/edit]
« Last Edit: 12/19/2014 08:13 pm by nadreck »
It is all well and good to quote those things that made it past your confirmation bias that other people wrote, but this is a discussion board damnit! Let us know what you think! And why!

Offline topsphere

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topsphere: 3 2% 2% 2% 3% 6% 9% 11% 15% 19% 13% 11% 3% 2% 2%

rationale - I figure +-2 from 11 will be very likely, but anything above 13 pretty unlikely. Couldn't be arsed to make it look like a symmetric distribution....
« Last Edit: 12/19/2014 08:18 pm by topsphere »

Offline NaN

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NaN: 0 0.04 0.08 0.16 0.32 0.64 1.28 2.56 5.12 10.24 18 25.96 17 10.24 5.12 2.56 0.64 0.04

Rationale: 9,10,11 carries the bulk of the likelihood. 7-13 as outside possibilities. Beyond that, a longer tail on the bottom than on the top since anything going wrong is more likely than everything going right.

Offline Billium

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Billium: 7, 5.10.10.15.15.15.10.10.5.5

Rational - we have insufficient information to make an accurate prediction buts it's very reasonable to guess 2015 will have more launches than 2015.
« Last Edit: 12/20/2014 04:45 pm by Billium »

Offline cscott

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cscott: 2 0.6 0 0 0 1.9 4.5 11.5 13.5 15.4 11.6 19.2 7.1 7.7 4.5 1.9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.6

Rationale: wisdom of crowds.  This matches the distribution of the votes in the "How many SpaceX flights do you anticipate in 2015?" as of this moment (2014-12-19 22:20 EST)... and happens to match my intuition as well (ie, broad peak between 9 and 12 launches).  For the sake of science (science!) I even included the "more than 35+" joker, including their vote as a vote for 36 launches.

Offline aameise9

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aameise: 6 1.7 3.4 5.8 8.6 11.1 12.8 13.1 12.1 10.1 7.7 5.3 3.3 1.9 1.0

Rationale: Treating each of 50 weeks as independent events and taking the expected mean to be 12, I obtain a binomial distribution with parameters N = 50 and P = 12/50.

I think it would have been sufficient to guess mean and variance ...

Offline arachnitect

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arachnitect: 1 0.5 1 1.5 2 3.5 6 10 19 30 21 4 1 0.5

Offline sdsds

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sdsds: 1 1 2 3 4 5 6 7 8 10 11 12 10 8 6 4 2 1
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Offline MikeAtkinson

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MikeAtkinson: 2 0.1 0.1 0.2 0.6 2 4  7 10 11 12 13 11 10 9 5 2 1  1   1

Low probability of something going really wrong and SpaceX only managing a few flights.

Not much to choose from 9-15 launches, 15 seems the maximum number they can realistically do now. Payload availability and other external influences will likely be the limiting factor.

Low probability of more than 15 launches due to possible multiple reflights of recovered stages, perhaps with customers paying a very low price.


Offline Proponent

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Proponent:  0 0.0  0.0  0.1  0.2  0.3  0.6  1.3  2.8  5.6  9.4 13.3 15.7 15.7 13.3  9.7  6.1 3.3  1.6  0.7  0.2  0.1

Rationale:

I start from SpaceX launches listed by Salo list for 2015, which is more or less consistent with the last with-dates manifest published by SpaceX (attached):

January 6 - Dragon SpX-5 (CRS5) - Falcon 9 v1.1 - Canaveral SLC-40
January 29 - DSCOVR (Triana) - Falcon 9 v1.1 - Canaveral SLC-40
February 17 (TBD) - Eutelsat 115 West B (Satmex 7), ABS 3A - Falcon 9 v1.1 - Canaveral SLC-40
April 8 - Dragon SpX-6 (CRS6) - Falcon 9 v1.1 - Canaveral SLC-40
June 13 - Dragon SpX-7 (CRS7) - Falcon 9 v1.1 - Canaveral SLC-40
1st half - TürkmenÄlem 52.00E (MonacoSat) - Falcon 9 v1.1 - Canaveral SLC-40
2nd quarter - SES-9 - Falcon 9 v1.1 - Canaveral SLC-40
NET 1st quarter midyear - Orbcomm G2 (x11) - Falcon 9 v1.1 - Canaveral SLC-40
August - AMOS 6 - Falcon 9 v1.1 - Canaveral SLC-40 (or 3rd quarter)
September 2 - Dragon SpX-8 (CRS8), BEAM (Bigelow Expandable Activity Module) - Falcon 9 v1.1 - Canaveral SLC-40
2nd half - JCSat-14 - Falcon 9 v1.1 - Canaveral SLC-40
4th quarter - Eutelsat 117 West B (Satmex 9), ABS 2A - Falcon 9 v1.1 - Canaveral SLC-40
December 9 - Dragon SpX-9 (CRS9) - Falcon 9 v1.1 - Canaveral SLC-40

3rd quarter - Demo Flight - Falcon Heavy - Kennedy LC-39A

March 31 - Jason-3 - Falcon 9 v1.1 - Vandenberg SLC-4E
September - SAOCOM-1A - Falcon 9 v1.1 - Vandenberg SLC-4E
late - Iridium Next Flight 1 (x10) - Falcon 9 v1.1 - Vandenberg SLC-4E
late - Iridium Next Flight 2 (x10) - Falcon 9 v1.1 - Vandenberg SLC-4E
TBD - FORMOSAT 5 - Falcon 9 v1.1 - Vandenberg SLC-4E

Let me work backwards through the launch sites, beginning with VAFB.  Two launches there seems feasible, but stuff can easily happen.  I'm going to guess a triangular distribution centered on two and extending from zero to four.  In other words, for VAFB launches I'm assigning likelihoods of

    No. Launches:     0    1    2    3   4
    Likelihood:          11  22 34  22 11%

Then there's the Falcon Heavy from KSC.  I'm pretty sure that's just not going to happen this year, and I'll translate "pretty sure" to 85%.

Now, for the hard part: orbital launches from the Cape's LC-40.  The mean time between Falcon 9 v1.1 launches to date is about 58 days, assuming CRS-5 goes ahead tomorrow (see the plot below, CRS flights are shown in red).
Even if we assume look only at the four most recent flights (and assume CRS-5 goes off as planned), the mean drops just to 44 days.  That would leave time for nine flights in 2015, given CRS-5 early in the year.  But getting the pad abort test off the ground has got to be important, and that will soak up resources (at least vis-a-vis CRS flights), even if it doesn't actually occupy the pad itself.  Maybe, with the burdens of the abort test (I'm guessing there is little chance of the in-flight abort test occuring in 2015), SpaceX could still hope to achieve the same number of orbital launches it pulled of from LC-40 in 2014.  But for the modal case, I'll guess that there are six launches total, again, with just five to orbit.  Again, I'll go with a triangular distribution, this time with a half-width of 3 rather than 2.  So, my LC-40 likelihood distribution looks like:

    No. Launches:    3   4    5   6   7   8  9
    Likelihood:          6  12 19 26 19 12 6 .
I took the launch intervals from the last 5 F9 v1.1 launches and resampled 100,000 times to get a distrubution for the number of launches from LC-40 in the next year, allowing for the fact that one launch has already occurred with 355 days to go in the year.  The result is:

    No. Launches:      2     3     4      5     6      7        8       9    10     11  12   13    14
    Likelihood:          1.0  0.9  1.0  2.3  8.6 17.7  21.8 19.4 13.7  7.7  3.6  1.5  0.5%.

These won't add to precisely 100%, because I've rounded off and have omitted values less than 0.1%.  All values were used, without rounding, in the next and final step.

Convolving all three distributions and rounding to the nearest 1% (thereby eliminating a non-zero likelihood of 14 launches) gives

    No. Launches:     0      1     2     3      4     5      6     7      8    9     10    11    12    13     12  13  14    15   16  17   18
    Likelihood:          0.0  0.0  0.1  0.2  0.3  0.6  1.3  2.8  5.6  9.4 13.3 15.7 15.7 13.3  9.7  6.1 3.3  1.6  0.7  0.2  0.1

There is some possibility that a catastrophic failure early on will shut SpaceX down for the rest of the year.  Accordingly, I steal 1% of likelihood from each of the the two most likely outcomes and redistribute it to the cases of one and two launches:

    No. Launches:     1     2    3       4      5       6        7       8      9     10    11   12   13
    Likelihood:          1% 1% 1%   2%  6%  12%  17% 18% 17% 13% 8% 3%  1% .

There could, of course, be a massive failure before the very first launch, but I put the probability of such a thing at under 1%, so I'm not going to consider it.


I'm guessing that core availablility won't be a problem.  Had I come up with significant likelihoods for, say, 20 launches, I might have pruned the higher numbers to reflect the risk of manufacturing bottlenecks.  But after just six launches in 2014, I'm willing to guess that the supply of cores won't be a limiting factor for ten-ish or fewer launches in 2015.

EDIT:  After updating my calculation quite a bit, I neglected to put the new results on the first line (though they were already in the body of the post).
« Last Edit: 01/19/2015 03:06 pm by Proponent »

Offline schaban

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schaban: 3 2 4 6 7 8 10 15 20 15 10 2 1

They have to attempt to fly at least 3 CRS missions. Almost a given to have more attempts than previous year.



Offline Robert Thompson

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0 1 1 1 3 5 8 11 14 14 14 11 8 5 3 1

Offline Proponent

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The poll is now closed to new entries.

Offline Proponent

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First of all, thanks to everyone who took the time to contribute an entry.

Now that the poll has closed, let's use this thread for discussion rather than the poll's previous discussion thread.  This way, the raw data will be readily at hand should anyone wish to refer to them.

To better reflect the information available at the time of the polls' closing, I have taken the liberty of removing from each any probabilities or votes assigned to zero launches for 2015, since one launch took place before closing.  In the single-vote poll I have interpreted the one vote for 21-25 launches as 0.2 votes for each of 21, 22, 23, 24 and 25 launches.  The one vote for more than 35 is interpreted as a vote for 36.

Firstly, some statistics:

PollSizeMeanEntropy (bits)
Likelihood distribution229.643.60
Single vote66610.833.12

The mean of the likelihood distributions is plotted here, as black bars, along with the single-vote distribution, as red circles.  The vertical dashed lines show the means of the two distributions.  Obviously the single-vote poll is the more optimistic of the two.

One might wonder how much of the "signal" in the likelihood-distribution poll comes from the spike at 4 launches.  That likelihood comes largely from a very manly zero-entropy prediction by saliva_sweet!.  Without saliva_sweet's entry, the mean rises a bit to 9.91 and the entropy falls slightly to 3.54.  Even then, this poll is more skeptical than the single-vote poll.

The table below summarizes individual likelihood distributions, in order of the distribution mean.

MeanEntropy
MEAN9.643.60
saliva_sweet4.000.00
Hernalt7.933.43
arachnitect8.332.79
averagespacejoe8.352.79
Garrett8.452.60
CraigLieb8.472.78
Tass8.613.12
skybum8.752.91
schaban8.903.23
Jimmy Murdok9.292.72
toruonu9.373.47
sdsds9.533.82
NaN9.883.00
topsphere10.173.37
cscott10.893.25
nadreck10.983.66
Billium11.253.21
Proponent11.543.40
mheney11.662.81
MikeAtkinson11.773.60
Lar11.953.65
aameise12.003.52

Now it's up to SpaceX to deliver the results!
« Last Edit: 01/20/2015 10:22 pm by Proponent »

Offline Proponent

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Now that the number of SpaceX launches intended to reach LEO or beyond in 2015 is known, scores can be assigned.  The columns in the following table respectively show the mean of each participant's likelihood distribution, the entropy of the distribution (zero meaning that all likelihood was assigned to a single number of launches, while larger values indicate greater uncertainty), the likelihood (L) assigned to the actual number of launches (7), and the natural logarithm of that likelihood (lnL).  The table is sorted by likelihood.  Not only is there a row for each participant, but results are also shown for the mean of all likelihood distributions and for the single-value poll (not included in the mean).

MeanEntropyLlnL
Garrett8.4502.6040.200-1.609
CraigLieb8.4702.7750.170-1.772
Hernalt7.9293.4300.141-1.956
Jimmy Murdok9.2902.7160.120-2.120
Tass8.6143.1200.117-2.149
toruonu9.3703.4680.110-2.207
averagespacejoe8.3512.7860.103-2.272
arachnitect8.3302.7930.100-2.303
skybum8.7502.9060.090-2.408
schaban8.9003.2310.080-2.526
MEAN9.7223.5910.075-2.588
sdsds9.5303.8180.070-2.659
topsphere10.1703.3730.060-2.813
NaN9.8802.9970.051-2.972
nadreck10.9803.6590.050-2.991
Billium11.2503.2090.050-2.996
cscott10.8923.2460.045-3.101
Lar11.9513.6540.040-3.218
MikeAtkinson11.7733.6050.040-3.219
SINGLE-NUMBER POLL10.8263.1220.036-3.323
aameise12.0033.5180.035-3.360
Proponent11.5453.3980.028-3.576
mheney11.6602.8150.020-3.912
saliva_sweet4.0000.0000.000 -Inf

The winner is Garrett, who assigned a likelihood of 20.0% to seven launches.  Not only is his likelihood highest, but the entropy of his likelihood distribution is one of the lowest, meaning that he made a relatively precise prediction.  I'm one of the worst performers, having assigned a likelihood of just 2.8% to seven launches.

It's interesting that despite having just 22 participants, this poll assigned a much higher mean likelihood (7.5%) to seven launches than did the single-vote poll (3.6%), which had 667 participants.

Offline sdsds

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A mere "thumbs up" doesn't adequately convey how much I like this! Thanks for putting it together!

I note that the distribution with mean closest to the actual seven launches was that offered by Hernalt. Though that's not a victory, it deserves recognition. (On a personal note, my guess was about as "middle of the road" as possible, with 10 guesses "better" and 11 guesses "worse" than mine.)
— 𝐬𝐝𝐒𝐝𝐬 —

Tags: SpaceX Predictions 
 

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