Which of the following is most likely? Is Justin Verlander able to throw 100 consecutive strikes?

  • Steph Curry made a streak of 100 consecutive free throws.
  • Justin Tucker made 100 consecutive field goal tries from 40 yards.

 

Given that Verlander is going to be difficult to predict, let’s finish with him last.

Steph Curry has a free throw percentage of 93.10 percent in the 2019/2020 season with the Golden State Warriors (source: Basketball Reference).

The average percentage for a 40-yard field goal in the NFL is 85.83 percent. In Tucker’s case, though, I would say that he is better than average. The NFL average for field goals in the 30 to 39 yard area is 89.32 percent, while Tucker’s rate is 96.63 percent in the same range. According to my calculations, Tucker’s chance of converting a 40-yard field goal is 85.85 percent (96.63 percent /89.32 percent), which is 92.86 percent when applied to the NFL average (see table below).

When it comes to baseball, things may become complicated. It is necessary to inquire as to whether we are discussing genuine pitches in actual games or a controlled exhibition. The reason why this is important is because in actual games, pitchers do not try to throw a strike on every pitch they throw. A pitcher’s goal is to throw towards the edge of the strike zone as often as possible, making it more difficult for the hitter to obtain a clean hit.

I don’t have any statistics to back this up, but I’ve seen pitchers in the bullpen during minor league games who appear to consistently place the ball directly in the catcher’s mitt, without the catcher having to move. It is reasonable to assume that a pitcher such as Verlander would be successful in throwing a strike at least 95 percent of the time in a controlled test environment. Verlander’s strikeout percentage in real games, on the other hand, is just 68.50 percent.

To get the chance of 100 consecutive successful trials, disregarding the effect of tiredness, multiply the probability of a single successful trial by the 100th power of the probability of a single successful trial.

On a more serious note, I believe that Verlander is the better pitcher in a controlled experiment; but, I believe that Curry is the better pitcher under game circumstances.

This question was first posed on Barstool Sports, where it was answered. In addition, there has been a lot of debate about it in my forum at Wizard of Vegas.

If you want to stack cannonballs in a pyramid with a square foundation, like the pyramids of Egypt, or triangular, like tetrahedrons, which method is more efficient: a pyramid with a square base, like the pyramids of Egypt, or triangular?

Some formulae that may be of use to readers are included below:

  • 12 + 22 + 32 + 42 + 52 + 62 +… + n2 = n*(n+1)*(2n+1)/6 = n*(n+1)*(2n+1)/6 = n*(n+1)*(2n+1)/6 = n*(n+1)*(2n+1)/6 = n*(n+1)*(2n+1)/6 = n*(n+1)*(2n+1)/6 = n*
  • 1, 3, 6, 10, 15, and so on add up to n*(n+1)/2, which equals n*(n+1)*(n+2)/6.

 

I’m going to presume you mean the one with the least amount of wasted space between cannonballs when you say “efficient.”

Keep things easy by defining the volume of any pyramid’s volume by using the centers of the balls that are placed at each of the pyramid’s four corners. Let us suppose that n is the number of cannonballs that may be found in a side of each pyramid’s base.

First, let’s have a look at the pyramid with a square base:

  • The total number of cannonballs in the pyramid is 12 + 22 + 32 + 42 + 52 + 62 +… + n2 = n*(n+1)*(2n+1)/6. The number of cannonballs in the pyramid is 12 + 22 + 32 + 42 + 52 + 62 +… + n2.

After that, let’s figure out the height of this square pyramid whose base has a side length of n. Other than a square base, as can be seen in the illustration, the sides of this triangle are all equilateral triangles. As a result, the slant height is likewise equal to n. The distance between one corner of the base and the opposing corner is given by the formula n*sqrt (2). So the distance between a corner of the base and the center of the base is equal to n*square (2)/2. Let’s say the height is h. Imagine a right triangle created by three variables: height, distance from a corner of a base to its center of gravity, and the angle of the slant height.

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