If you have read my writing before, you know that I like to write about games that people play, especially games that other people pay them to play. I also like to use numbers to talk about these games. Sometimes I use numbers that other people made up, but sometimes nobody else has made up numbers that can help me find out the things I want to know about the games I am writing about, so I make up my own numbers. I have a lot of fun seeing what my numbers say about the games I am watching, but the numbers can sometimes be hard for other people to understand.
So I am trying a new thing right now, using an idea from a man who used to help our country build boats that fly into space, and now makes funny drawings that people look at on their computers. He decided to draw a picture of an important space boat and write about what all of the parts do, but in words that most people can understand. He decided to use only the ten hundred words used most often in the language we use in my country. The drawing he made helped people learn about the space boat, and it was also very funny. The people who saw the drawing liked it so much that he decided to make a whole book of pictures of hard-to-understand things that were explained in simple words. (It is called Thing Explainer and it is a very good book.)
This man also made a place that helps other people write using the same words that he did. That is what I am doing now. I am going to explain some of the numbers I have made up using only the ten hundred words people use the most in this language.
One of the games I like to write about has a name that sounds like Ten Is. (Its name is also used in the name of something that can go wrong with the part of your arm that bends, because people who play the game have this problem with their arms more than other people.) It is usually played by two people who stand on a flat piece of ground with straight lines drawn around it. (You can also play the game with four people, but it is harder to make numbers about that way of playing, and not as many people want to watch it, so I am writing about the two-person way.) In the middle of the ground is a wall made of several lines of stuff that can also be used to tie things together. The wall looks like what people use to catch a lot of fish at a time and has the same name. This wall goes all the way across the space where the game is played and is about half as tall as a person.
One person stands on each side of the wall and they hit a ball to each other. They hit the ball using sticks that have an empty circle on one end. The circle is about as wide as a person’s foot is long. There are lines across the circle that are about as far from each other as a person’s finger is wide, and the people try to hit the ball with the lines. (If they hit it with the circle instead, it will usually go somewhere they do not want it to go.) These sticks were made of wood when people first made up the game, but now they are usually made of metal or plastic or both. The newer sticks let people hit the ball harder without breaking the stick or sending the ball where you don’t want it to go. (Sometimes when players get angry they break their sticks on the ground or over their legs. When they do this they get in trouble.)
The ball is a bright yellow or green color so people can see it. It is about as big as a person’s hand when all the fingers are pushed into a ball shape (like if the person wants to hit someone and have it really hurt). The ball is made of the same stuff as car tires and is very full of air, and if you drop it on hard ground it will jump up again to be almost as high as where it was dropped from. If you hit the ball too many times some of the air will come out and it will not jump as well anymore, so you have to get a new one.
The first person who doesn’t get the ball over the wall before it bounces two times or hits it outside the lines on the ground loses a point, but that’s all right, because they do it again many times to decide who wins at the game on that day. (There are lots of other laws to the game that tell the players where they can stand and where they are allowed to hit the ball at the beginning of the point, but we don’t need to talk about all of those right now.)
The players take turns hitting the ball first; a player’s turn is over when one of them gets at least four points and has at least two more points than the other player. The player who does this gets a more important point that is called a “game.” The players keep taking turns until one of them has won six games and has at least two more games than the other player; when that happens, he gets an even more important point called a “set.” If both players win six games before the end of the set, most of the time they will use a special kind of game to break the tie so that the set does not go on forever. (At some places they don’t always use this tie-breaking game, and one time two players had to play for more than ten hours before someone was ahead by two games in their last set.)
Even after they finish a set, the players still aren’t done! Most of the time they play until someone wins two sets, but sometimes they play until someone wins three sets. The first player to win that number of sets wins for the day. The whole event has the same name as a small stick with a red end that people use to start fires.
This is a fun game that a lot of people play all over the world. Some people are very good at it and other people will pay money to watch them play. (For a while, the people who played the game didn’t get any of the money that other people were paying to watch them, but they do now. The best players get a lot!)
There are two groups of people who run the game. One is called the Group of People Who Play the Game That Sounds Like Ten Is and Get Paid For It. The other is called the Group of People From Lots of Countries Who Like the Game That Sounds Like Ten Is. (The second group used to run the game by themselves, but a little over twenty years ago the best players decided they didn’t like how that group was doing things so they made their own group. The group that the players made runs most of the events now, but the other group still runs the very biggest ones. There is also another group that sets up events in the game for women; it is called the Group of Women Who Play the Game That Sounds Like Ten Is. Even though the name of their group does not say so, the women also get paid.)
The two groups tell the players all the places where the game will be played each week, and a lot of players (usually about thirty, sometimes more) will come to each place and play against each other. The people who win get to keep playing; the people who lose go home, or go to a different place where they can play next week. At the end there are only two people left and the person who wins between them wins the whole event and gets the most money.
The most important events in the game last two weeks and have over a hundred players. The people who win get paid a whole lot of money and the people who watch the game will remember them for a long time. These events have a name that means (Big and Important) (Hit Very Hard). (It is the same name as when a player in another kind of game hits a ball over a wall far away, when three of the other players on his team are on the safe bags.)
Most of the time, the people who win the most important events are the best players in the world. But almost half a hundred years ago, the people who run the game decided that they wanted another way to find out who the best players are. They also needed a way to tell which players should get to play in each of the events, because if they let everyone play then the events would take much longer.
So they decided to make a computer system that they could use to say how good the players are. (This is important because the computers don’t care about who the players are, only what they do in the game. If you ask people to say how good the players are, they might change their answers if they don’t like one of the players.) The system looks at how well the players have played in each event for the last year. People tell the computers which events are the most important so the computers will care about them more, but almost every event that is played is used to see who the best players are.
The system usually does a good job at finding the best players, but it is not always as good at putting the players in the right order outside of the ten best in the world. One problem with it is that the computers do not care who each person played against during the year, so if someone had to play the best players in the world more than they should have (and lost to them most of the time), that will make his computer number worse even though it does not mean he played worse. Another problem is that people decide how important each event should be to the computers before it happens. Sometimes a lot of the best players will show up to play one event, and none of them will play another event that the computer thinks is just as important (or even more important). A third problem is that the computers do not care how easy it was for someone to win. If a player beats someone without losing any games, he is doing better than if he almost lost to the same person before beating him, but the computer will think both of those wins are the same.
So I decided to make my own computer numbers to figure out who the best players are at this game. I put a whole lot of information into my computer about who played at different events, who they played against, whether they won or lost, and how easy it was for them to win or lose. (At first I had to put in the information by myself, one event at a time. This took a long time and it was hard to be sure that I wasn’t putting any of the numbers in wrong. But later another man who also likes to look at numbers about this game put a lot of information out where anyone with a computer can get it! You don’t even have to pay for the numbers, and they can help you learn all kinds of things about the game. This is pretty cool. You can get the information yourself by pushing on these words with your computer. The only laws about it are that you can’t sell the numbers to other people, and if you use them you have to say where they came from. That is what I am doing now.)
The system I used to make my numbers is kind of like the system that people use to say who the best players are at a board game that has some pieces that look like horses and some that look like parts of old big stone houses and lots of other pieces that all move in different ways. The system only looks at who a player played against, and how many games both players won. I did not tell the computer which events were the most important – but because the best players usually play the most important events and those events take more sets to pick who wins, the computer can figure out which events are important without my help!
There is one important change I make to the board-game number system. The change is about people who do not play very much during the year. Most of the time, if a player is very good at this game, people will ask him to play in their events a lot. If a player does not play very many events during a year, it usually tells us one of two things. The player might be hurt and not able to play very much, or the people who run the events might not think he is good enough to have there.
Sometimes players who do not play very much will look very good in the events they do play. Five years ago, there was a player who only played in one event that I have numbers for. He beat the first person he played very easily, and then decided he was too hurt to play the next person. Since the only numbers I had for him made him look like a very good player, my changed board-game system decided he was the best player in the world for that year. But we know that he was not the best player in the world, because he played some other events that I don’t have information from (there are too many of them – if I had the numbers for all of them my computer would not be fast enough to make the numbers I want it to make), and did not play as well in those events.
So I change the board game number for players who play in less than ten events during the year. I do this by looking at all of the players who played a certain number of events and seeing how well they did as a group. The players who played only one event are usually the worst group, which makes sense, because if they were better, people would ask them to play more events. (Most people who only play one event are asked to play that event because they live in the country where it is held and the other people who live there might like to watch someone from their own country play the game.) After I have the numbers for each group of players, I move the numbers for each player who played less than ten events toward the number for his group. People who played eight events don’t have their numbers moved very much, but people who played one or two have them moved a lot, because we don't know as much about them.
The changed board-game number should be a good way to find out who has the best chance to play well in the future. But we also want to know who played well in the past, and the board game number can only answer part of that question. The other part has to do with how much each person played. The more you play, the harder it is to play like one of the best players in the world. This is in part because people who play this game often get hurt – not always enough that they can’t play at all, but enough to keep them from playing their best. If you can still play really well when you are hurt a little, or if you don’t get hurt as often, that makes you a better player. It is also in part because someone might play really well for a few events because the other players don’t know where they like to hit the ball. As a player plays more, the other players will learn where he likes to hit the ball and be ready for it, and an important part of being a good player is being able to change your plans when the other player figures out your first one.
So once I have the board-game number for each player, I take one more step. I look at the players each person faced during the year, and find the chances of another player doing better than him against the same people. To do this, I use a number picture. (A number picture is a picture that people make with numbers instead of lines and colors. Just like other pictures, it is often a good way to explain things that are hard to explain with words.) This number picture has a name made of long words, but which we will call the Two Answer Chance Number Picture.
The Two Answer Chance Number Picture is used when looking at a large number of yes-or-no questions, usually the same question asked over and over. One question you might ask would be, “When you threw that round metal piece of money in the air and it landed on the ground, did the side that looks like a person’s face point up when it landed?” The Two Answer Chance Number Picture tells us what can happen when you throw the round metal money piece in the air a whole lot of times, and what the chances are of the face on the money looking up a certain number of times out of all the times you threw it.
With computers, we can also use the Two Answer Chance Number Picture to look at questions where the chances of yes and no are not the same. This is important when looking at games, because the question we will be asking over and over to make these numbers is “Did you win the game,” and if you are asking that question about the best player in the world, the answer usually has a better chance of being yes than it does of being no.
I said earlier that I look at the chances of another player doing better than the person whose number I am making. A question that you may be asking yourself right now is, “What other player?” This is a very important question because if you use different players, it can make big changes in the order of the players you end up with in the final number. (We will call the player we use to look at all the other players the “Ground Player,” because all of the players whose board-game number is below his will have Two Answer Chance Numbers that look like they are under the ground.)
When I was first making these numbers, I decided I would choose a number that would stay the same for every year I looked at, and use the player whose board game number was in that place in the order as the Ground Player. I tried a few numbers and ended up choosing the one that is right between seven tens and eight tens.
This number worked for most things, but I never liked the fact that there was not a good reason for me to pick it, so now I have changed how I choose the Ground Player. I decided to use the player whose board-game number is right in the middle.
There are a few ways to find the middle of a group of numbers. One way that people use a lot is to add all the numbers together, then break the answer into as many parts as there were numbers in the group. This middle number is called the “mean.” (I can use its real name here, which I can’t do for most words about numbers, because “mean” also means other things, which you can tell because I just used one of the other meanings.)
The other way that is used most often is to put all of the numbers in the group in order from smallest to biggest, then start from one end of the group and go through the numbers until you have passed exactly half of them. The number at that point is what we will be using as the middle number. (If there is no number at the half point, you take the two numbers closest to it, add them, and break the answer in half.)
However, I did not just find the middle number of everyone’s board-game numbers for the year. Instead, I put all of their board game numbers in a group, but put each player’s number in the group more than once. The number of times each player is in the group is the same as the number of games he played during the year. I made this change to make sure that I was looking at the middle player who would be playing at any given time; without this change, the middle would probably be someone who played only a few events and everyone interesting would be much better than him.
The middle player found this way usually ends up outside of the hundred best board-game numbers, but inside the one-and-a-half hundred best. (In the year that is about to end, the middle player is in place one hundred added to two twenties and two.) This means that the Ground Player I’m using now is worse than the Ground Player I was using before, so more players have numbers that are over the ground and the ones who were already over the ground are further over it now than they used to be. The lower Ground Player also means that players who played more events will sometimes pass players who played fewer events and were ahead of them before. That happened in the numbers for the year that is about to end, as the second-best player I found using the old Ground Player is different than the one I found using the new Ground Player.
The one other change I made to my numbers was to add information from a few more events. There are a few weeks each year when lots of countries put their best players in this game on a team and have them play against a team of the best players from another country. I used to count only the games played in the most important part of this event, which is called the World Group. I checked and found out that the players in the next group down, which is called Group One, are also mostly players that already have numbers in my system, so it helps to add more information about them. The group below that, Group Two, is mostly made of players who don’t play any other events that I count in my numbers, so adding the information from that group would not help as much. (In these events, some of the games are played after the country who wins is already decided. I don’t count these because the players don’t care about them, and a lot of the time they don’t try their hardest when the games don’t matter.)
Once you have picked your Ground Player, you can see what his chances are of doing better than any other player against the same people. For the best players in the world, the Ground Player’s chances of doing better than them are very small.
The best player at this game in the world right now is a man from a country that used to be part of a bigger country; that bigger country broke into several smaller countries about twenty years ago. He is very good at hitting the ball back after the other player hits it first. He has been the best player in the world for about five years now.
The chance of this year’s Ground Player (remember, his board-game number was number one hundred and two twenties and two) doing better than the best player against the same people are less than one out of ten times ten times ten… one hundred times (or ten to the power of one hundred), or at least that’s what the Two Answer Chance Number Picture says. That is such a small number that it is hard to understand, so let’s see if we can explain it better.
People who study space and the stars think that the huge space we live in that holds everything we know about is around ten to the power of ten years old. They also think that everything we know about is made up of tiny pieces that all have different numbers of the same parts, but act very different if they have different numbers of those parts. They think there are about ten to the power of (eight times ten) of these tiny pieces.
If we made one of the Ground Player from this year for every tiny piece that we know about in the huge space we live in, and each of those Ground Players played ten hundred full years of this game in every second since the huge space began, we would expect one of them to have one year as good as the year that the best player in the world just had.
The numbers that come out of the Two Answer Chance Number Picture are so large (or so small) that I make one more change to them. One way of thinking about the size of a number is to look at how long the number is when you write it down. If you count all of the numbers it takes to write down a large number, this will give you a smaller number to work with. (The name for this, like most words about numbers, is long and sounds strange, but people sometimes use just the first part of it, and that part is the same as the name for thick parts of trees that are cut up for people to use to make fires.) So instead of writing down (ten to the power of one hundred) for the best player in the world, we can take the (cut up tree part) of that number and give this player a number of one hundred. The same tree-part-sounding thing works for players whose Two Answer numbers are less than one, except that the way we think about how long those numbers are gives them tree-part-sounding numbers that are less than none.
I am going to stop writing about these numbers for now, because all that is left to do is to give the numbers for the year that is about to end, and the names of the players are not among the words I am allowed to use. So I will put those numbers and the players’ names up in my next writing. During the year that is about to start, I will try to make new numbers every two or three weeks as people keep playing the Game that Sounds Like Ten Is, so we can see how the numbers change during the year.