T206 Demmitt & O'Hara....are they 350-only Series cards ?

[Matt]

Originally Posted by egbeachley

For example, if 10% of the 350/460-series cards sampled as a pop 4 or 5, then there would be a 10% chance that 1 target of pop 5 would be 350/460-series. But since both targets are a pop 5, then the possibility would be 10% of 10% or a 1% chance that based on this methodology that the 2 cards are really 350/460-series.

We're moving away from cards now, but I don't believe you are correct here (any statisticians in the house?). Multiplying probabilities to arrive at the probability that both A and B are true only works in scenarios where A and B are exclusive of each other - if A is true it has no bearing on if B is true. (i.e. the odds that both you and I have birthdays on January 1st is 1/365 * 1/365) That clearly isn't the case here as we all agree whatever is true for Demitt is true for O'Hara (i.e. the odds that twins have a birthday on January 1st is 1/365) .
To illustrate this point better, consider the inverse of your argument. Using your numbers, there is a 90% chance Demitt is a 350 only back and a 90% chance O'Hara is a 350 only back. By your logic (multiplying the probabilities), therefore, there is an 81% chance that they are 350 only backs which contradicts your finding above (of it being a 99% probability).
A such, I don't think you can multiply the probabilities in this case.

I certainly could be off with what I just wrote, so if anyone out there knows probability logic, please chime in.

[egbeachley]

Originally Posted by Matt

To illustrate this point better, consider the inverse of your argument. Using your numbers, there is a 90% chance Demitt is a 350 only back and a 90% chance O'Hara is a 350 only back. By your logic (multiplying the probabilities), therefore, there is an 81% chance that they are 350 only backs which contradicts your finding above (of it being a 99% probability).
A such, I don't think you can multiply the probabilities in this case.
.

Simple statistics error. Never add or multiply the chance of something happening, rather multiply the chance something won't happen.

[Matt]

Originally Posted by egbeachley

Simple statistics error. Never add or multiply the chance of something happening, rather multiply the chance something won't happen.

It's inverse so it doesn't matter - the probability it is a 350 only is the inverse of the probability it's not a 350/460. The probability is is a 350/460 is the inverse of the probability it is not a 350 only. Here it is reworded:

"To illustrate this point better, consider the inverse of your argument. Using your numbers, there is a 90% chance Demitt is not a 350/460 back and a 90% chance O'Hara is not a 350/460 back. By your logic (multiplying the probabilities), therefore, there is an 81% chance that they are not 350/460 backs which contradicts your finding above (of it being a 99% probability).
A such, I don't think you can multiply the probabilities in this case."

Also - didn't you multiply probabilities of something occurring?
"For example, if 10% of the 350/460-series cards sampled as a pop 4 or 5, then there would be a 10% chance that 1 target of pop 5 would be 350/460-series. But since both targets are a pop 5, then the possibility would be 10% of 10% or a 1% chance that based on this methodology that the 2 cards are really 350/460-series."


Consider this - say Demitt was a 5 population but O'Hara showed 7 times in the survey. We can all agree then that it should be about 50/50 since Demitt would look like a 350 only card (which averaged 4.8) and O'Hara would look like a 350/460 card (which averaged a 7.4) and knowing both are the same, we couldn't use that data to say any one was more likely then the other. But multiplying the probabilities, as you have done, would lead you to the wrong conclusion:

We would have a 10% probability that Demitt would be a 350/460 series (or not a 350 only series) and say a 50% probability that O'Hara would be a 350/460 series (that percentage doesn't really matter to make the point, but assuming a normal distribution 50% is a reasonable number). So, you've got .10 * .50 = a 5% chance that they are 350/460 series and 95% chance they are 350 only series, even though we all agreed above that with those numbers it's 50/50.

[tedzan]

Matt
I think egbeachley has clarified what I meant by......
"This argument of yours, Matt, is not a statistically valid one."

A weighting factor must be considered in interpreting the data from these T206 surveys.

The range of the 350-only PB cards in these surveys was from 1 to 8.
HOWEVER, ONLY 5 OF THE 638 SAMPLES WERE 8.

The range of the 350/460 PB cards in these surveys was from 4 to 23.
HOWEVER, ONLY 8 OF THE 451 SAMPLES WERE 4

I think you will agree that these extrem #s represent the 3 SIGMA points on a Bell curve; and, further reinforce
my contention that a very high probability exists that the Demmitt and O'Hara (St Louis vars.) were printed and
issued during the 350-only POLAR BEAR run.


TED Z

[Matt]

Originally Posted by tedzan

Matt
I think egbeachley has clarified what I meant by......
"This argument of yours, Matt, is not a statistically valid one."

As I've shown above I believe his logic to be incorrect.

Originally Posted by tedzan

A weighting factor must be considered in interpreting the data from these T206 surveys.

Agree - 100%

Originally Posted by tedzan

The range of the 350/460 PB cards in these surveys was from 4 to 23.
HOWEVER, ONLY 8 OF THE 451 SAMPLES WERE 4

How many 350/460 backs were 5 populations since that's the population number we're dealing with? And while we are there, how many of the 350 only cards are 5 populations?

Originally Posted by tedzan

I think you will agree that these extrem #s represent the 3 SIGMA points on a Bell curve; and, further reinforce
my contention that a very high probability exists that the Demmitt and O'Hara (St Louis vars.) were printed and issued during the 350-only POLAR BEAR run.

I don't have the raw data so I can't say exactly, but my guess based on the numbers you have shared here is that it's somewhere in the neighborhood of 70%-80% likely.

[E93]

The area of a circle is πr2
JimB

P.S. I vote for 350 series only.

[tedzan]

Hey guy, it was great meeting you at the National.

We don't always agree on things; but, we do on this subject



TED Z

[tedzan]

In response to several requests, I'm listing here all the players in the T206 set whose trades or reassignments are
reflected in their repeated cards with respect to each series.

....................150 series..............350 series................350/460 series................460 series

Ball...................NYA........................ .................................................. ...........Clev
G. Brown...........Cubs.....................Was
Dahlen..............Bos N....................Brkl
Elberfeld............NYA.....................Was
Herzog..............NYA........................... .................................................. ........Bos
Lake.................NYA.......................... .......................St Lo A...........................St Lo A
Kleinow.............NYA......................NYA.. .................................................. ......Bos A
Lundgren...........Cubs.....................KC
McIntyre...........Brkl........................... .......................Brkl & Cubs
Schaefer...........Det............................ .................................................. ........Was
F. Smith............Chi.......................Chi.... .................................................. ......Chi & Bos A
Willis.................Pitt....................... ...........................St Lo N

Designed as a 350/460 subject....but, not issued since Nicholls retired May 1910 upon being traded to Cleveland.

Nicholls.............A's.......................... ....................(would be Baltimore)



Demmitt..................................NYA & St Lo A

O'Hara....................................NYG & St Lo N

If the Demmitt & O'Hara variations were printed and issued during the 350/460 series (Summer/Fall 1910 release),
American Litho. would have identified them with these teams......

Demmitt.......................................NYA. ......................Montreal

O'Hara.........................................NYG .......................Toronto



Hopefully, this info provides you with an overall perspective on how the T206 designers kept pace with the player
changes during the T206 production era (1909-1911).



TED Z

[Matt]

One last follow up for the sake of correctness (I'll continue the OT probability discussion with ebeachley offline unless it's of interest to others):

One flaw in the logic we've both been using: Say 10% of 350/460 cards have a population of 5. That doesn't mean there's a 10% chance that a given card with a survey population of 5 is a 350/460 card. Rather, it means if a card IS a 350/460 card it has a 10% chance of being a 5 pop. In order to do a correct statistical analysis for our example, we need to compare the 10% chance of a 350/460 being a pop 5 to the % of a 350 series being a pop 5. Let's say the probability that a 350 only card is a pop 5 is 50%. Now, knowing we have a pop 5 card, we can say it is 10%/%10+%50 or a 1 in 6 probability it is a 350/460 card.