Longing for the days when...

I will do it 5 times on the weekend and post my results. Everyone else is invited to do it as well, if they are interested.
Scottbdoug.

I will tell you that you have nearly a 50 percent chance of "proving" yourself right!

You see, the chances of your results coming out exactly even are very small, but there is a chance. Thus, your odds of "success" are just under half. However, your chances of "proving yourself wrong" are also nearly 50 percent.

So enjoy your test, but I think your time would be better spent by having a nice chat with a mathematics instructor.

Im laughing on the inside

Perhaps im not being very clear in that people are questioning my math skills.

I know if one card has a 1-5 automatic hit and a second card has a 1-5, 1-10 hit or flyout 11-20 with the same on a 2-5 is mathematically the same.

Perhaps a different approach is needed to explain variation in chance. Meaning that a 100% chance one time and a 0% a second time is not the same as a 50% chance twice although both are mathematically the same.

The simple reason for this that the first will always get 50%. The second will not. The 2nd will result in 50% in most cases but not all. Sometimes the result will be 0% or 100%. The more times you do the 2nd the closer you will get to 50% but the 1st is always 50%.

Thats all im saying. The second deviates from the mathematical norm of 50%. The first never does. Therefore if your result you want to reflect something to be exactly 50% the better option is the first not the 2nd. And if accuracy is what you want which strat obviously is supposed to want, the more accurate stats to what the player did in the mlb that season, then an automatic hit rather than a chance hit is more accurate ans should be used as much as possible. The less chance hit and the more automatic hits should be the norm as much as possible taking into account the limitations of roles available on the card.

Let's say over the course of the season, you can expect on average to roll ten 1-5s and ten 2-5s. (You can pick any number you want but ten makes it easier to follow.)

On the surface, your argument makes sense but only if you make the assumption that 1-5 and 2-5 are being rolled equally on both cards. For a moment let's make that assumption that 1-5 and 2-5 are each rolled 10 times for each batter over the course of a season.

With hitter number one, it will always be 5 hits and 5 outs. With hitter number two, it could be anything (although, on average, still 5 and 5). So, it looks like you have a point because player 2 has more variation...

However, let's say the dice are really streaky and 16 1-5s are rolled and only four 2-5s. Now player 1 will have 16 hits whereas player 2--on average--will have 10 hits. Player 2 will be close the expected average, whereas player 1 will be six over average every time. Who has more variation now?

While a non-straight result--when rolled--has more variation than a straight one, the variation is balanced out by how many times the result comes up in the first place. Thus, strangely enough, the variation will work out--on average--exactly the same for both hitters.

One more try to make it clear...

Hitter and pitcher "A" each have a 1-10 chance for a hit on every dice roll. Expected average: .500.
Hitter and pitcher "B" each have 50 percent straight hits and 50 percent straight outs each. Expected average: .500.

Expected average is the same for both, and expected variation for "A" and "B" is also exactly the same. The variation is achieved with "A" by whether a 1-10 chance is achieved or not. The variation in "B" is achieved whether a hit or not is rolled in the first place.

Yes you are correct. I cant argue with that. The two chance rolls will be closer to 50% than the automatic roll when there are other rolls other than the two. You could never hit the two rolls or them hit more often than an easier roll. I did not think of it in that way. So with that arguement it means the more spread out the chance rolls there are the more it will reflect the actual stats because the less often you will miss a chance than you do an automatic hit.

Now that is a great argument. And I must say that i stand corrected. In fact my arguement is actually the opposite of what i thought.

This is what i enjoy about arguments you always learn some new and become better elightened.

I still think the cards are a mess to look at but now i understand the reason why.

Thanks coyote

Scott.

Three business men stop at a hotel and get a room for $30. The manager later realizes that the room is only $25 and sends the bellhop to return $5. The bellhop figures the 3 business men can't evenly split it so he gives them $3 back and keeps $2. Each business man therefore only paid $9 each or $27 and the bellhop has $2 and that's $29. What happen to the other dollar?
My point is you have to believe the math not the words. A 50% chance is a 50% chance. Which player would hit more HRs with 500 at bats? One with a 1-4 Homerun or someone with a 2-7 1-10 split? Math says they both hit the same all other things being equal.

The three business men as a group paid $27 for the $25 room and the bellhop kept the other $2 for himself. You were trying to add up to $30 when you should have been subtracting down to the $25 price of the room.

Perhaps a different approach is needed to explain variation in chance. Meaning that a 100% chance one time and a 0% a second time is not the same as a 50% chance twice although both are mathematically the same.

The simple reason for this that the first will always get 50%. The second will not. The 2nd will result in 50% in most cases but not all. Sometimes the result will be 0% or 100%. The more times you do the 2nd the closer you will get to 50% but the 1st is always 50%.

Thats all im saying. The second deviates from the mathematical norm of 50%. The first never does. Therefore if your result you want to reflect something to be exactly 50% the better option is the first not the 2nd. And if accuracy is what you want which strat obviously is supposed to want, the more accurate stats to what the player did in the mlb that season, then an automatic hit rather than a chance hit is more accurate ans should be used as much as possible. The less chance hit and the more automatic hits should be the norm as much as possible taking into account the limitations of roles available on the card.

The problem is that you averaged the two when they should be multiplied. If you flip a coin there is a 50% chance it will land on heads, flip it two times there is not a 50% chance it will land on heads both times but a 25% chance. There are four scenarios (Heads/Heads, Heads/Tails, Tails/Heads then Tails/Tails) and Heads/Heads in only one of the four.

The advantage of the splits is the precision it gives. If there are no splits the most precise a roll can be is 1/108 or just under 1% (0.00926...) for any single player card 1/108 where the 108 comes from 2 dice times half of one die. If the powers that be determine that they wish to assign a percent chance of a player getting a single on his card is 7% they would need to have a roll with a 7.56 chances out of 108. The closest you could get is the combination of 1-2, 1-7 and 1-12) which is 8 (1+6+1) chances out of 108. This is 5.8% off the required value.

The total chances you have with the splits is 108*20 or 2160. With this you can achieve precision of 1/2160 (0.00046296...). The closest you can now get to the 7% required for the single is 6.99% (151/2160) which is a lot closer to the 7% than the 7.56 that you were limited to without the splits. This is done by using the same combination of 1-2, 1-7 and 1-12. The 1-2 now gives 20 chances and 1-7 gives 120 for a total of 140. We are now 11 short of our goal of 151. We know the 1-12 would give us another 20 but that is too much. Of course, if we put a 1-11 split on the 1-12 roll we get and add that 11 to the 120 we get the 151 we are looking for..

Over a few hundred at-bats that player's single count will be much more accurate by using the splits as the odds of getting the single per at-bat are more accurate than without the splits.

This is the beauty of math; the randomization of dice; and dumb LUCK.

It's kind of like real life, isn't it?