Math and Sports By ：黄一舜 郭丽峰 余昊航

FOOTBALL

From the pictures we see, we can easily find that every football is made up of pentagons and hexagons. Each pentagon is surrounded by hexagons. There are 32 pieces of skin on each football.

Penalty

4/5 80% 3/3 100% 3/4 75% 8/10 80% 2/5 40% 6/9 66.7%

From the paper written by Steve Levitt. If the goalkeeper choose the correct way. When we kick left % When we kick right %

Football lottery How do bookmakers judge who will win the game?

1. Elo prediction 2. Scroing rate prediction 3. Six prediction

Elo prediction The possibility of the host 44.8%+0.53*X The possibility of the away 24.5%+0.39*X X is the difference between the two teams points

Scroing rate prediction Y>0.3 The higher will win. 0.1<Y<0.3 If the host is higher, the host will win. If the host is lower, the host will win or draw. Y<0.1 The host will win or draw. Y is the average scoring rate

Six prediction Z>5 The higher will win. Z=5 If the host is higher, the host will win. If the host is lower, the host will win or draw. 1<Z<5 The higher will win. Z<2 The host will win or draw. Z is the difference between the two team points in 6 recent games.

how to apply math in basketball

Understand shooting implications When you shoot you are involving three factors: angles, the impulse, and the position of your arms. You should apply a greater angle if you make a field shoot, but a smaller one when you shoot from inside the free throw zone. You may shoot higher when you have some defenders in front of you, also I recommend to shoot from a 45 or greater angle, cause that helps the ball to enter softer and cleaner to the basket. Your elbow should be the closest possible to your face so the ball goes in straight line and extend your arm as far as you can so you have greater force.

Understand the parabola in shoots The parabola is the downside curve that's made in every shoot. As you are shooting you may realize that as higher the parabola the cleaner or easier the ball gets inside the hoop, and as lower, the more chances there are the ball hits the rim. For the parabola effect to be completed you should apply the "follow through" with your wrist, that means you shall give the ball a back flip effect at the end of your shot using your hand.

Apply math in rebounding Whenever the ball is shot from one side, from a field shoot, it will end on the other side, the most of the times; when shot from the free throw zone it will mostly rebound on the same side. When more force is applied the rebound will get further, when little force implied, the ball will fall in the same place it hit. So familiarize yourself with rebounding implications so you can guess every time where the ball's going.

Get an assistant to record percentages You have to know how many rebounds, shoots, steals, and counter attacks you are making, so you can improve on the areas where you have low performance. Record the attempted and made shoots. The offensive and defensive rebounds. The total steals and counter attacks on the game. The second chance points you made and the team's shooting tendencies.

SYMMETRY

snooker P Q AB C D

Snooker P Q AB C D

P Q P’ AB C D

Snooker A B C D Q P

A B C D P Q P’ Q’Q’

Snooker A B CD P Q

QUESTION What can we do under the condition as bellow ？ AB CD Q P