Chance of Precipitation

I heard the term POP on the radio. It stands for "Probability of Precipitation". The explanation of it was pretty simple, but there is a little more to it than I thought. What it measures, of course, is the chance you are going to get rain, snow or whatever, falling on you that day. A fairly simple formula: 

POP = (probability any precipitation falls in the area) x (predicted area of coverage).

Examples: 

The meteorologist thinks about half the region will get wet. There is a 20% chance it rains somewhere in that area. So, 0.50 x 0.20 = 10% chance of rain.

There is a 70% chance of rain falling somewhere in the region. The coverage is almost total, say 90%. So, 0.70 x 0.90 = 63% chance of rain. That is, a 63% chance that it will rain on you.

By the way, that number doesn't tell you anything about how much it might rain. Although by "precipitation" they do seem to hold to there being at least a hundredth of an inch falling.  

I missed out. I think I would have liked to have been a meteorologist.

 I wrote something a few weeks ago about measuring the height of Mount Everest. Now you simply use GPS? The article says that its more complicated than that.

Initially, it was the Trigonometric Survey of India in which they marched across the sub-continent, measuring angles angles and finding distance until being able to measure the height of Mount Everest. George Everest, a surveyor, was an important part of the efforts to measure it. 

Some interesting facts that it came out:

• There was a recent earthquake that lowered its height, but it was only by one inch.
• A legend states that the measurement came out to be exactly 29,000 feet. They figured people would suspect a figure like that, so they tacked on a couple more feet so they published the height as 29,000 feet.
• For GPS you need a receiver. There is one near the top. The official height is from a survey done in the fifties.

There are complications I wasn't aware of. The elevation is the height above sea level. But what exactly is sea level. To begin with, the earth isn't completely round. Sea level is not level due to the tides. It is basically the average of the high and low tides, but that gets a little tricky to measure. That can also differ because other mountains in the area can alter the gravity, which then alters the tide height.

As the article stated, "All of our elevations have an error."

 

Wilt's Free Throws

 Wilt Chamberlain is the second leading scorer of all time. Right behind Michael Jordan. But, he couldn't shoot free throws. He once missed 22 straight free throws. That seems worth investigating. First what are the chances? He made 51.1% of his free-throws during his career. In other words he has a 48.9% chance of missing. So to miss two straight would be .489 x .489 = .239121 or a 23.9% chance. Twenty-two in a row? That would be .489 to the 22nd power. That comes out to 0.000000146. 

Just for fun, I took the reciprocal. That is almost seven million. He shot over eleven thousand free throws in his career. I thought missing 22 in a row might be somewhat likely. But no, it isn't. There is a lot of math here a person could play with. Wilt wasn't the worst ever. Andre Drummond makes 38.6% of his free throws. You could figure the probability for him missing 22 in a row.

Could a typical player do this? Lets suppose we want to find out, what percent would you normally have to shoot to have a 50% probability of of missing 22 in a row.  The equation would be x^22 = .50. Using the log and inverse log on your calculator, you come up with 96.9%. That is the chance you miss a shot. So, that means your free throw success rate would be 3.1%. Not good.

Election Results

 There was an important Senate election in Georgia (on the website I was looking at it was "Georiga"). I saw this :

Candidate A   51.5%  -  1,957,641

Candidate B   48.5%  -  1,844,815

That was with 87% of the vote counted.

If the vote is split evenly the rest of the way, Candidate A wins, obviously. What percent would be needed? I figured it was my duty as a citizen to find out.

There are a total of 3,802,456 votes so far with 87 % in. That means there must be a total of:

0.87x = 3,802,456

x = 4,370,639

Candidate A needs at least half of that, which is 2,185,319.

With a little subtraction there are 586,183 votes left and he need 227,678 of them. Candidate A needs 40.1% of the remaining votes. That sounds about right. Certain sections get counted at different times. So its not over. 

Update - Its not decided yet, but Candidate A now has 50.02% of the vote. About as close as it can get.

Increases

 I heard a news report that there were 111 deaths among the homeless due to Covid. This was a 23% increase. Sad news of course, but it made me think of what that meant if you wanted to know what the amount was previously. A little algebra would do the trick.

Assume there were "x" deaths previously, so the equation would be:

                        x deaths plus a 23% increase is 111

                        x + 0.23x = 111        

                         1.23x = 111

                         x = 111/1.23

                         x = 90

A practical, every day application

Measuring Mountains

Here is an interesting item I saw online

"Accurately measuring miniscule changes in a mountain that is more than 5 miles us is no easy feat, but surprisingly, measurements rely on geometric formulas and surveying techniques that haven't changed all that much since the 1800's, said Peter Molnar, a geologist at the university of Colorado, Boulder.

At heart, measuring a mountain relies on basic ninth-grade math. To calculate the elevation of a mountain, scientists would measure the distance. between two points on the ground and then measure the angles between the top of the mountain and each point. 

"if you have two angles, you know the third, because the sum of the angles is 180 [degrees], Molnar told Live Science. 

To carry out these measurements, surveyors must identify a horizontal surface using a level (which, like the kind at a hardware store, relies on a trapped air bubble that, under the influence of gravity, slides closer to or farther away from a central region as it tilts". From there, surveyors eye the summit and measure the angle with the assistance of a glorified highly accurate protractor - a telescopic device known as a theodolite. With two angles and one side of  a triangle, trigonometry reveals the lengths of the other sides, and thereby, the height of the triangle (the mountain)."

If I'm getting the picture they are trying to convey, this method (I assume the Law of Sines) would not give the height. It would give distances from each of the individuals to the top of the mountain. .From there, you could use one of those distances and set up a vertical right triangle and measure the angle of elevation to the summit. Then you could simply use: Sin(measure of angle of elevation) = opposite side / hypotenuse. Solve the equation for  the opposite side and that is the height of the mountain.

There were other interesting things in the article. That can be for another time. 

Virus Probabilities

 I saw something on the news about the coronavirus. Wearing a mask is 70% effective in blocking the droplets that can cause you to be sick. If you and the other person is wearing a mask, you only have a 9% of getting infected. (Those numbers are what I heard, but I'm not certain of the context because I wasn't totally paying attention, but we'll run with it.) Those numbers seem right, mathematically. You have person A and person B. You want either one's mask to block the germs.

Probablility of A or B is happening is 

Pr(A) + Pr(B) - Pr(A) x Pr(B).=  0.7  +  0.7  - 0.7 x 0.7 = 1.4 - 0.49 = 0.91. 

Thus,a 9% chance germs get through.

Looking at it another way, start directly with the probability germs get through.

C and D are now the events that germs aren't blocked.

Pr(C) x Pr(D) = 0.3 x 0.3 = 0.09

Again a 9% chance.

Pr(B) - Pr(A) x Pr(B).=  0.3 +  0.  - 0.7 x 0.7 = 1.4 - 0.49 = 0.91. 

Leaves

 I looked out upon my lawn covered with leaves and wondered how many there were. The brute force method is to go count them. Lets say I don't have the time or inclination to do that. I could take some smaller areas of the lawn, count the leaves there, and compare them to the whole.

This is the same kind of thing that is done in surveys. DVD sales, TV ratings, unemployment numbers, all survey to get their results. We recently had a presidential election. It took a while, a long while, because they said they were getting to a 99.5%. That doesn't give you certainty of a number. It just means you are 99.5% certain of being within a range of numbers. Almost all nationwide statistics are surveys. When we don't do that - the census every 10 years - it takes months and months to get to everyone.

I'm sure you know how this kind of thing works, but I took the time to do it, so I feel obligated to share.

I (roughly) marked one yard by one yard squares. There were three of them and they averaged having 125 leaves in each. Then I found the area of the entire yard. Nicely, it is pretty much a trapezoid. The bases about 7 and 14 yards with a height of 7 yards. That gives an area of 73.5 square yards.

Next, a proportion would be 125/1 = x/73.5. So, x = 9187.5 leaves. 

So, a nice problem for maybe an Algebra I or general math class. It can lead into the idea of the surveys that go on every day.

The Lighthouse at Alexandria

I was watching a video about the Lighthouse at Alexandria. It no longer exists, but was one of the seven wonders of the world. The video said it could be seen from thirty miles away. They didn't mention how tall it was. That can be figured out, though. There is a formula. To the right is a diagram of the situation.

Suppose v is the height of the lighthouse. OH is the distance to the horizon from the top of the lighthouse. Using a geometry thereom, the diameter squared = (diameter+h)h. You could also come up with a formula by using the Pythagorean Theorem. In that case, (v+r)squared = r squared + OH squared. And then the radius or diameter of the earth could be substituted in. Another extension could be to find formulas for distance to the horizon for other other planets. Formulas that are then derived usually are simplified by the fact that the value of v is so small compared to r. 

Those formulas can be found on-line. Using one of them, by my calculation, to have the horizon be 30 miles away you would have to be 605 feet up in the air. Pretty tall. The Eiffel Tower is 984 feet. But the tallest now are less than 300 feet. So the video, or I seem to be off. But maybe not. It's certainly possible. You don't get picked as a wonder of the world if you're not pretty impressive.

Going for Two

Seems like I wrote something like this before, but things have changed now, so it is time to revisit. In the NFL, after you score a touchdown, you can go for a one-point conversion, by kicking, or go for a two-point conversion, by running or passing. The two pointers are harder to make, though. So which should you do? The kicks pretty much always went through. Because of that, the NFL decided they needed to make things a little more interesting and moved the kick back a ways. It still almost always goes through, but the percent is down a little bit - to a success rate of 93.8% of the time. The pass or throw option is roughly half - a success rate of 50.1%.

We should find the expected value for each. 

For a kick, you can get one point, 93.8% of the time:

                    1 x .938 = .938 points per try

For running or passing, you get two points, 47.9% of the time:

                    2 x .501 = 1.02 points per try

Is that even worth messing with? It depends on how good your team is, but typically a team scores something around 60 touchdowns in a season. That would mean roughly (.938 x 60 =) 56.28 points if you kick all the time. And (1.02 x 60 =) 61.2 when running or passing. So about five point over the course of a season. So not a lot, but then again, it only takes one point to lose a game.

And of course your decision could depend on the situation in any particular game. If you score a touchdown near the end of the game and you are now behind by two, you definitely would go for the two-point attempt. 

By the way, I don't know if this was in the book, but Scorecasting is a great little book about sports and how coaches don't always do what makes the most sense. 

Moving Averages

 

Moving averages are in the news thanks to the Corona virus. They takes the major fluctuations out of data that might otherwise jump around a lot. The following graph shows this. There are fluctuations during the week because of the nature of the work week. I'm not exactly sure why, but maybe Mondays usually show more positive cases than Fridays. The following graph shows this situation in Georgia, but I think this kind of thing can be found in pretty much any state. And after that is some information from Investopedia. 

Understanding Moving Average (MA)

Moving average is a simple, technical analysis tool. Moving averages are usually calculated to identify the trend direction of a stock or to determine its support and resistance levels. It is a trend-following, or lagging, indicator because it is based on past prices.

The longer the time period for the moving average, the greater the lag. The 50-day and 200-day moving average figures for stocks are widely followed by investors and traders and are considered to be important trading signals. 

Moving averages are a totally customizable indicator, which means that an investor can freely choose whatever time frame they want when calculating an average. The most common time periods used in MA's are 15, 20, 30, 50, 100, and 200 days. The longer the time span, the less sensitive the average will be.

There is no correct time frame to use when setting up your MA's. The best way to figure out which one works best for you is to experiment with a number of different time periods until you find one that fits your strategy.

Moving averages, a.k.a. running or rolling averages, that I've see, usually use 3 or 7 data points at at time. I had no idea as many as 200 were ever used.

I randomly picked a baseball player from the past and found his number of home runs each season. Incidentally, I once heard a baseball stat man say it would take about three seasons to get an accurate picture of how good a batter is. Now that I think about it, that makes sense, At about 500 at-bats a season, that would be 1,500 at-bats total. I saw on-line that the Pew Research center will typically survey 1,500 people at a time.

Anyway - here are Mickey Mantle's home run totals each season. Then a rolling average, three years at a time, then five years at a time. Notice, it gets a little less bumpy each time.

13, 23, 21, 27, 37, 52, 34, 42, 31, 40, 54, 30, 15, 35, 19, 23, 22, 18

            19, 24, 28, 39, 41, 43, 36, 38, 42, 41, 33, 27, 23, 26, 21, 21

                        24, 34, 34, 38, 39, 40, 40, 39, 34, 35, 31, 24, 23, 23

Fires

There has been a lot of fire action in the West the last couple of weeks. And as time went by there was a lot of smoke. I got an air quality app. I was wondering why the graph chopped off at 500. My app said we were well into the 500's. I learned that that was as high as the chart goes. We were literally off the chart. I guess they assume you aren't going to have numbers like that. Our house was never in imminent danger of fire. They had a map on the news that had green areas meaning "Get prepared to maybe leave", and yellow was "Get ready to go, and red was "Go now". Our house looked to be 5 to 10 miles from the green and maybe 10 to 15 from the yellow. So, a bit concerning, but not too bad. I figured we're in a city, not a forest. I guess I never really paid attention to how many trees there are on our street. There are a disturbing number.

But everything is much better now. When I was in high school / college I had a summer crap job of working in a youth parks program. That is when I learned I was not cut out for manual labor. We built trails and dug ditches and paved a parking lot. Yes, I was literally part of paving paradise and putting up a parking lot. Its not as much fun as it looks like. My job in paving was to be above where the tar comes from the dump truck, down a chute. I was standing above that bin and was to keep the tar moving along with some kind of stick they gave me. It was about 105 degrees those days and the tar itself was about a billion degrees. And if you've smelled fresh tar before you know its not pleasant. I spent hours right on top of that heat and smell.

Anyway, for about a week there was a big forest fire that they used us for to help "mop up". That was kind of fun. One time we were kind of on the front lines, but otherwise we just had a hoe or shovel and found smoldering places and put those out. We also had back pack filled with water and a squirt gun thing attached. That was super fun.

I'll never forget the lunches. I hope they've improved. Some kind of meat sandwich with almost no mayonnaise and an 8 oz can of unsweetened grapefruit juice. That was nasty. I was maybe the thirstiest I'd ever been. But, I lived and had an adventure, so that was cool. 

Tipping

 We'll I've gotten back on the horse and ready to do more math application blogs. I took a few months off. Not for any particularly good reason, although I did move. Piece of advice - Try not to move. Or at least make enough money to afford to pay one of those companies that will do everything for you.

Speaking of that, how much should you tip them? I don't know if you actually tip moving people, but its a transition (no idea how to spell "segway") into my post. 

First of all, I have a thing about tipping. The really important people don't get tipped - doctors, emt's, teachers, firemen. Its mostly people in a restaurant that take your order and your money. As restaurant workers go, they really aren't the hardest workers there. The cooks aren't getting tipped. The bus boy isn't getting tipped. The night time custodian isn't getting tipped. Plus, I'm even more annoyed when the credit card machine asks you how much you want to tip. I had that happen at a place where I got my own drink and all the server did was hand me a donut (that someone else made). Does that really deserve a tip?

Anyway, they say 10% isn't enough anymore. So now I'm not just bothered, I'm mathematically bothered. Apparently, tipping needs to go up to at least 15% because of inflation. That is either greed or a lack of understanding of how percentages work. 

Something used to cost $100 dollars, and lets say now it costs $140. A 10% tip would have meant a $10 tip. Present day, your 10% tip is $14. Yes, there is inflation, but the percent takes care of that. If prices go up and you still tip at 10%, the amount of your tip goes up. And what would 15% of $140 be? $21.

At cash registers that give you choices of tips, 15% seems to be the low end. It should still be 10% if it even exists at all. 

Whose idea was this? I'm guessing the people getting the tips. I don't want to be rude, but I you did betting in school you probably would understand percentages better and you wouldn't be working as a server in a restaurant to begin with.

Note - Future blogs will not be as mean spirited.

A Final Word

I'm closing up this math applications blog for now. I may come back to it at some point. I was writing this as a tie-in to my book. However, I've got another job now. Its a long story. I have had fun doing this, but its time has come. The past postings still exist, of course, and you can check out any of them for ideas regarding applications of mathematics. Even if a particular one is not exactly what you were looking for, it might cause you to think along the lines of something else that better suits your purpose.

And here is something kind of interesting. This happens to be my 99th posting. That made me think that maybe I needed to do a 100th. No, I'll think I'll leave it as it is because 99 represents the incompleteness that... OK, I've got nothing, but there is probably something profound in ending on 99. Maybe I'll figure that out and make it my 100th post some day.

Absolute Value

Absolute value is a tricky thing. Students love it because it is so easy. They probably come away thinking, "Could I have done this right? That just felt way to easy. And even if I did do it right, it seams pretty pointless." There actually are mathematics applications to absolute value. Here are a few.

Average Deviation – There are a number of formulas that measure the variability of data. A common one is the standard deviation. However, average deviation is similar and easier to compute. The average deviation simply finds the average distance each number is from the mean. To find the average deviation, the distance from the mean is found for each piece of data in the set. Those distances are added and then divided by the number of pieces of data. If the mean is 32, we would want 28 and 36 to both be considered positive 4 units away from the mean. Absolute value is used so there are no negative values for those distances.

Example: 

- A set of data is {21, 28, 31, 34, 46}. The mean average is 32.The average deviation is 6.4.

Statistical Margin of Error – As mandated by the U.S. Constitution, every ten years the government is required to take a census counting every person in the United States. It is a huge undertaking and involves months of work. So how are national television ratings, movie box office results, and unemployment rates figured so quickly – often weekly or even daily? Most national statistics are based on collecting data from a sample. Many statistics that are said to be national in scope are actually data taken from a sample of a few thousand. Any statistic that is part of a sample is subject to a margin of error. (In 1998, President Clinton attempted to incorporate sampling in conducting the 2000 census, but this was ruled as unconstitutional.)

Example:

- On October 3, 2014 the government released its unemployment numbers for the month. Overall unemployment was listed at 5.9%. The report also stated that the margin of error was 0.2%. Government typically uses a level of confidence of 90%. Thus there is a 90% chance that the actual unemployment rate for the month was x, where |x-5.9| ≤ 0.2.

Richter Scale Error – The Richter scale is used to measure the intensity of an earthquake. However, like many measurements, there is a margin of error that needs to be considered. Scientists figure that the actual magnitude of an earthquake is likely 0.3 units above or below the reported value. If an earthquake is reported to have a magnitude of x, the difference between that and its actual magnitude, y, can be expressed using absolute value:  |x-y| ≤ 0.3.

Body Temperature – “Normal” body temperature is assumed to be 98.6° F. For any student that has made the case that anything other than 98.6° prevents their attendance at school, there is good news. There is a range surrounding that 98.6 value that is still considered in the normal range and will allow your attendance at school. Your 99.1° temperature is probably just fine. Supposing plus or minus one degree is safe, an expression could be written |x-98.6| ≤ 1.0, which would represent the safe range. Why is the absolute value a necessary part of this inequality? Without it, a temperature of 50 degrees would be considered within the normal range, since 50-98.6 = -48.6, which is, in fact, well less than 1.0.

Ten Cool Things about Laplace

I thought it was time to look at another interesting mathematician. This week it is Pierre-Simon LaPlace.

1. Lived from 1749 to 1827, all in France.
2. Married at age 39 to an 18 year old.
3. Made important contributions to the method of least squares - used to find a best fitting line.
4. Wrote the five volume Celestial Mechanics contributing greatly to a theory of the origins of the universe.
5. Appointed by Napoleon Bonaparte to be Minister of the Interior of France.
6. Later regretting this, Napoleon later stated, "Laplace was not long in showing himself a worse than average administrator."
7. Very possible apocryphal, but Napoleon was speaking to Laplace on the influence of God on a a particular situation to which he replied, "I had no need of that hypothesis."
8. Commenting on this story, Stephen Hawking said, "I don't think that Laplace was claiming that God does not exist. It's just that he doesn't intervene, to break the laws of science."
9. When he died, his brain was removed and displayed.
10. He is buried in Paris in the Pere Lachaise Cemetery along side other star-studded famous residents Balzac, Sarah Bernhardt, Bizet, Maria Callas, Chopin, Joseph Fourier, Yves Montand, Jim Morrison, Marcel Proust, Rossini, and Oscar Wilde.

Sermon Stats

In sermon notes in a church bulletin it stated, "The probability Jesus could have fulfilled even eight of these prophesies is 1 in 10 to the 17th power (1 in 100,000,000,000,000,000)". This was a statistic taken from a book, although I don't know the title. I thought there is a math application in there somewhere.

I thought that small a number might be almost incomprehensible to most. Maybe to everyone. It

reminds my of something David Letterman said once regarding buying a lottery ticket. A particular lottery was at a near record amount and lots of people were buying them. He wanted people to consider that if you buy a ticket, your chance of winning is only slightly more than if you don't buy one. Incidentally, I was in the audience for one of his shows during his final month. Hilarious. I am including a picture for no other reason than I love Dave. Back to math.

I considered a couple of ways to tie this probability to other situations. How does this probability compare with chances in rolling a die? In flipping a coin?

Well, the chances of rolling a "6" are one in six. How many consecutive rolls would correspond to the above probability?

1 / 10¹⁷ = 1 / 6^x
10¹⁷ = 6^x
Taking the common log of each side, we get:
17 = x(log6)
x = 21.85

So, at least 21 consecutive rolls coming of 6.

Similarly with flipping the coin. The coin has only two outcomes, so:

1 / 10¹⁷ = 1/2^x
After a few steps we get x = 56.47

56 heads in a row. Unlikely.

If worried about church vs state issues, a teacher could come up with other kinds of problems. The actually probablility of winning a certain lottery, winning the grand prize in the McDonald's Monopoly Game. For example, I just looked up on-line that the probability of getting the Boardwalk piece - 1 in 602,000,000.

Good Luck.

Evaporation

When I was a lad, I remember looking a drops of rain that had plopped on the sidewalk. It was a light rain so I could make out the individual drops. They gradually evaporated. I noticed that if I used my finger and spread the raindrops, out they evaporated faster. At my tender age I had no idea why. Still not 100% certain, but my guess now is that if you have a drop of water it is losing molecules, i.e., evaporating, from its surface. If you take a drop of water, it is evaporating at a certain rate. If you separate that drop into two drops, it will evaporate faster because there is much more surface area for which it can use to evaporate.

So, let's examine this as a math application. Suppose a drop of water is spherical and has a volume of 10 whatevers. Then suppose we separate that drop into two drops of volume 5 whatevers each. Then we look at their total surface areas. Will they come out the same?

We start with the fact that it has a volume of 10:  (4/3)πr³ = 10
If we solve for r we get a value of r = 1.3365
We can then find its surface area: 4π(1.3365)² = 22.446

Now what if we now have two spheres of 5 each.
Their radii would be:  (4/3)πr³ = 5, so r = 1.0608
The surface area of one drop is 14.140. There are two drops, though, so the total surface area of them would be 28.28

Comparing the two situations, we can in fact state that, since 28.28/22.466 = 1.26, there is 26% more surface area, and so I will postulate a 26% faster drying time for the two drops over the one drop.

That was to be the end of the story, but I thought what if you separate one spherical drop into two? Is it always going to be a 26% greater surface area.

Unfortunately this is beyond my skill level to show all this. You might recall that I only recently found how to write integer exponents. This process involves having the cube root of a fraction all taken to a power of two and other assorted difficulties. So let me map this out leaving a few gaps for you or students to work through. It really is a great problem, though, with the opportunity to review simplifying - some major simplifying.

• Let us say that  (4/3)πr³ = V
• Solve for r
• Substitute this expression into 4πr²
• Now, find the radius for a sphere that his half the original volume:    (4/3)πr³ = (v/2)
• Substitute this r into 4πr²
• Make a ratio of the two radii and simplify 
• You end up with cube root of 16 divided by 2, which is 1.26
• Ta-da. An increase of 26%

Satisfying

Predicting Win Percentages

Continuing on from last weeks post regarding the website fivethirtyeight.com and how they come up with their information. Last week was about how they look at various political polls and how they rank them. I found that quite interesting.

Even more interesting to me is how they come up with in-game percentages as to who is going to win. We all do that to some degree. Five minutes to go and your team has a ten point lead. You are probably going to win. So it is over 50%. But is it 60%? 85%? They know. At least I would say that their guess is as good as it gets.

I want to give Jay Boice and Nate Silver credit because I'm just relaying what they say is how their group comes up with those percentage win chances. I will try to do their explanation justice. So with a bit of paraphrasing, here we go,

• You you are ahead by 10 a with five minutes to go. The question becomes - How often have teams in that same situation done that in the past?
• They use regression analysis based on various game situations in the past. "The past" being the scores from all of the NCAA games over the past five years. 
• It makes a difference if that team that is ahead is really the better team, so they also factor in the pre-game win probabilities. That team currently in the lead may be more lucky than good.
• Finally, what is the current situation? It's five minutes to go. But who has the ball. Is one of the teams getting ready to shoot free throws?
• They don't account for everything, e.g., a player has fouled out and won't be available the rest of the game. That certainly could have an impact. 
• There probably are a number of factors that are just too much to deal with, so they don't.

Their results are pretty impressive. I haven't checked them out in real time. Its always after a game has been played. I'll have to remember to do that. Looking at them after the fact, though, their results seem pretty impressive. You can see some of their March Madness work here: 2017 March Madness Predictions

Rating the Polls

I was going to call this week's post "March Mathness" and talk a little about the NCAA tournament. Let's do that next week. Let me go ahead, though, and apologize for the title now. I'm sure I'm not the only one to use this type of play on "March Madness". That still doesn't make it right.

There is a nice website by the name of fivethirtyeight.com. It presents information regarding polls and polling data (The 538 part comes from the fact that there are 538 electors in the electoral college.) One interesting part of the website is looking at various polls (there are a lot more than I would have imagined - they rate over three hundred polling firms).

The reason I got there is because I was trying to figure out how their site, can come up with in-game information like Arizona is ahead of St. Johns 55 to 46 with 3:38 left to play, thus Arizona has an 89% chance of winning. Wow. It's clear Arizona would probably win, but how do they come up with a percent like that? Anyway, we'll look at that next week.

I got side-tracked with a section that speaks to how they rate various polls. For example the Trump/Clinton election did not come out as most had predicted. Some polls are better than others. They rate them all. For example, one of the best seems to be the ABC News/Washington Post poll. On the other had, an organization called Research 2000 is not. An overview of their methodology is at:

https://fivethirtyeight.com/features/how-fivethirtyeight-calculates-pollster-ratings/

They don't really give enough information to show exactly how they do it. That would probably be beyond me anyway. Let me tell you something they have used in the past. It is an especially cool math application since it has a square root stuck in there.

Total Error = Square Root of (Sampling Error + Temporal Error + Pollster Induced Error)

Why don't polls come out exactly right:

1. Sampling Error:  Sampling not enough people or not getting a representative sample
2. Temporal Error:  The farther away it time a poll is from the event; the more error
3. Pollster Induced Error:  Seems to be kind of a catch-all category for other things that can go wrong, such as assuming a too high or too low voter turnout.

Something else interesting they talk about is the concept of "herding". The companies that do the polling want to look good. It does not look good if they've wandered too fall away from the rest of the herd. If most every other poll has candidate A having around 55% of the vote and you predict he'll have 73%, you might make an "adjustment" to your results. Or you simply chose to not publish those results in which your company seems to be way off. 

That and other factors make it pretty complicated. Polling itself is complicated and then ranking the pollster even more so. 

I hope I've done justice to what they do. If you read what they have to see on their website you can see the complexity involved.

Next week, March Madness. Don't worry it will still be going on. In fact, it is actually March and slopping over into a little bit if April Madness.