What hits more often heads or tails?

According to Diaconis' research, a spinning penny will land tails side up roughly 80 per cent of the time. This is because the heads side of the penny, the one with the portrait of Abraham Lincoln on it, is slightly heavier than the tail side.

business-standard.com - Guessing heads or tails isn't really a 50-50 game: study

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If a coin is flipped with its heads side facing up, it will land the same way 51 out of 100 times, a Stanford researcher has claimed. According to math professor Persi Diaconis, the probability of flipping a coin and guessing which side lands up correctly is not really 50-50. He claims that a natural bias occurs when coins are flipped, which results in the side that was originally facing up returning to that same position 51 per cent of the time, the 'Daily Mail' reported. Diaconis came to this conclusion after determining that no matter how hard a coin is flipped, the side that started up will spend more time facing up most of the time. One way of thinking about this, as noted in an article from Coding Wheel, is to look at the ratio of even and odd numbers starting from one. What you'll discover is that no matter what number you stop at, there will never be more even numbers than odd numbers in that sequence, the paper said.

The coin flips work in much the same way.

Diaconis first realised that coin flips were not random after he and his colleagues managed to rig a coin-flipping machine to get a coin to land heads every time. He and his team then asked humans subjects do the same thing over and over, recording the results with a high speed camera. Though the results were a little more random, they still ended up with the 51-49 per cent margin. Diaconis noted that the randomness is attributed to the fact that when humans flip coins, there are a number of different motions the coin is likely to make. For instance, he showed how coins don't just move end to end, but also in a circular motion, like a tossed pizza. He also found that there are ways to flip a coin where it looks like it is tumbling in the air, but in reality, it doesn't move at all. Diaconis proved this by tying a ribbon to a coin and showing how in four of 10 cases the ribbon would remain flat after the coin was caught. In another startling discovery, Diaconis determined that the probability of guessing which side comes up of a spinning penny is also skewed more in one direction. According to Diaconis' research, a spinning penny will land tails side up roughly 80 per cent of the time. This is because the heads side of the penny, the one with the portrait of Abraham Lincoln on it, is slightly heavier than the tail side. This causes the coin's centre of mass to lie more toward the head side than the tail. So when it is spun, the penny will naturally fall toward its heavier size, which means there is considerably higher chance that it will land with the tail side up.

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Where should you bat your best hitter?

Your best hitters should bat in the number three and number four spots in the order. Put the speedier (and/or higher on-base) of the two in the number three slot. Follow that up with your next best on-base guys in the number one and two spots.

billjamesonline.com - Where should your best hitters bat? | Articles - Bill James Online

Where should your best hitters bat? One school of thought is to put your best hitter at the top of the order because he'll get more at-bats that way over the course of the season. Your second best hitter bats second. And so on down the order. Here are the average plate appearances per lineup position based on the 2006 MLB season: Lineup Position Plate Appearances 1 767 2 749 3 732 4 714 5 697 6 680 7 661 8 643 9 625 As you can see, each higher spot in the order means 15 to 20 or more plate appearances over the course of the season.

But let's look at another element. How often does each lineup position come up with men on base?

Lineup Position Number of Times With Men on Base 1 259 2 323 3 351 4 363 5 333 6 314 7 304 8 293 9 288 The number four position has the most over the course of a season. In fact, it's 104 times more than the leadoff position, quite a significant difference. The third spot in the order is not far behind. What does this tell me? Your best hitters should bat in the number three and number four spots in the order. Put the speedier (and/or higher on-base) of the two in the number three slot. Follow that up with your next best on-base guys in the number one and two spots. Five through eight (or nine)? Go with the best to worst with the remaining players. It's the formula I've used playing Strat-O-Matic baseball for the last 25 years. The studies say it doesn't matter that much and maybe it doesn't. But it matters to me, and to about 98% of all baseball fans.

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