--- In STMFC@..., Tim O'Connor <timboconnor@...> wrote:
Ok, you have 120 trains, 7000 cars, 2400 box cars right? Or 20 box
cars per train (on average)?
Here's a simple, straightforward probability calculation --
Let's say 4 out of 100 box cars is owned by SP or T&NO. (I checked my 1940
ORER, the two combined owned 27,740 box, automobile & furniture cars.)
So what is the random chance of a 20 box car freight train with ZERO
SP/TNO box cars?
It's just .96**20 or .44 -- a 44% random chance. Or in other words, with the
SP/TNO owning 4% of the fleet, a 20 box car train has a 56% chance that it will
have -at least one- SP/TNO box car. (It could have 2 or more of course.)
The statistic that we have been discussing is "expectation" -- what is the
"expected" (or average number) of SP box cars. G-N says it is 0.8 (.04*20),
but in your data set of 120 trains it is 1.6 (200/120). Now recall that
probability of at least 1 car -- 56%. The population -difference- between the
observed and expected number in your sample (of 4.5% of freight trains) is
less than 1 car per train. This is why I said it -could- be explained by
random chance, especially since the data set is so small. We both agree
that the recession of 1938 also could skew the data.
Yes, it is highly frustrating to us because we have so little data. We can
certainly learn a lot from conductor's reports -- about cargos, destinations,
composition of individual freight trains, all kinds of operational stuff that
is wonderful to know. I have an SP conductor's book, and it's great. But I'm
just not so comfortable with trying to extrapolate a lot about distribution
of box cars in the USA from a small number of these books. I know Dave and
Tim Gilbert used a lot of other sources.
The actual percentage of SP cars from the ORER in 1938 is 3.3%, not the 4% you assume. There are 1,308 non-UP box cars, which I believe is the relevant number, not your 2,400. This gives an average number of non-UP box cars per train of about 11, not 20. Based on G-N the expected number of SP cars in the train books is 44, versus the 201 actually found. Thus each of the 120 trains would have to have at least one additional car.
Getting that extra car in each train isn't as easy as it seems. If the process is random, as you hypothesize, 83 of the trains won't have any SP car at all; 31 will have one SP car, 5 or 6 will have two, 1 will have 3. Having more than 3 is too remote to consider. (We can discuss how I obtained these numbers off list if you want – I expect it is of little interest to the group.)
The easiest way to get an extra car (i.e., the way with the greatest likelihood of success) is to add one to each of the 83 trains with no car at all because it is analogous to winning a bet in which the odds are only 83 to 31 against you. Other conversions give you worse odds. Of course winning each and every time for 83 times in succession is highly unlikely – it would be far easier to come up with heads every time in 83 coin tosses – but even if you were to do so you would only have 83 more cars, for a total of 127 SP box cars. You would still need another 74. It can't be done in a million years.