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National Basketball Association Scheduling Simulation
National Basketball Association Scheduling Simulation 21-393 Final Project, Fall 2016 Shengqi Chai, Yutong Li, Liyunshu Qian, Ming Yang Department of Mathematics Carnegie Mellon University Pittsburgh, PA 15213 Table of Contents I. Abstract II. Background and Problem Description III. Solution IV. Results V. Conclusion VI. Reference Page 1 of 12 I. Abstract Sport scheduling is a complex task in the presence of a myriad of conflicting requirements and preferences. In this work, our primary goal is to find a feasible and approximately optimal schedule in terms of travel distance for the 30 teams in National Basketball Association. We focus on the schedule for the regular season, which usually spans over a 5-month duration. Existing approaches to build a schedule from scratch tends to suffer from substantial runtime overhead. In particular, it is computationally infeasible to solve the problem directly using linear programming and constraint programming due to the complicate formats and rules for NBA scheduling. Thus for the sake of simplification, we adopted assumptions so that integer programming is applicable. Additionally, we approached the problem using divide and conquer to reduce computational complexity. Apart from Operations Research techniques, methods from Machine Learning and Data Collection are also exploited in finding the solution. Our approach yields reliable schedules in a reasonable runtime, and the algorithm should be applicable, with slight modifications, to any scheduling problems in single-round robin or double-round robin fashion. II. Problem Background National Basketball Association is the preeminent men’s professional basketball league in North America, and is widely considered as one of the best basketball leagues in the world. -
Defense of Baseball
In#Defense#of#Baseball# ! ! On!Thursday!afternoon,!May!21,!Madison!Bumgarner!of!the!Giants!and! Clayton!Kershaw!of!the!Dodgers,!arguably!the!two!premiere!left@handers!in!the! National!League,!faCed!off!in!San!FranCisCo.!The!first!run!of!the!game!Came!in!the! Giants’!third,!when!Bumgarner!led!off!with!a!line!drive!home!run!into!the!left@field! bleaChers.!It!was!Bumgarner’s!seventh!Career!home!run,!and!the!first!Kershaw!had! ever!surrendered!to!another!pitCher.!In!the!top!of!the!fourth,!Kershaw!Came!to!bat! with!two!on!and!two!out.!Bumgarner!obliged!him!with!a!fastball!on!a!2@1!count,!and! Kershaw!lifted!a!fairly!deep,!but!harmless,!fly!ball!to!Center!field.!The!Giants!went!on! to!win,!4@0.!Even!though!the!pitChing!matChup!was!the!main!point!of!interest!in!the! game,!the!result!really!turned!on!that!exchange!of!at@bats.!Kershaw!couldn’t!do!to! Bumgarner!what!Bumgarner!had!done!to!him.! ! ! A!week!later,!the!Atlanta!Braves!were!in!San!FranCisCo,!and!the!Giants!sent! rookie!Chris!Heston!to!the!mound,!against!the!Braves’!Shelby!Miller.!Heston!and! Miller!were!even!better!than!Bumgarner!and!Kershaw!had!been,!and!the!game! remained!sCoreless!until!Brandon!Belt!reaChed!Miller!for!a!solo!home!run!in!the! seventh.!Miller!was!due!to!bat!seCond!in!the!eighth!inning,!and!with!the!Braves! behind!with!only!six!outs!remaining,!manager!Fredi!Gonzalez!elected!to!pinch@hit,! even!though!Miller!had!only!thrown!86!pitches.!The!Braves!failed!to!score,!and!with! the!Braves’!starter!out!of!the!game,!the!Giants!steamrolled!the!Braves’!bullpen!for! six!runs!in!the!bottom!of!the!eighth.!They!won!by!that!7@0!score.! -
NCAA Statistics Policies
Statistics POLICIES AND GUIDELINES CONTENTS Introduction ���������������������������������������������������������������������������������������������������������������������� 3 NCAA Statistics Compilation Guidelines �����������������������������������������������������������������������������������������������3 First Year of Statistics by Sport ���������������������������������������������������������������������������������������������������������������4 School Code ��������������������������������������������������������������������������������������������������������������������������������������������4 Countable Opponents ������������������������������������������������������������������������������������������������������ 5 Definition ������������������������������������������������������������������������������������������������������������������������������������������������5 Non-Countable Opponents ����������������������������������������������������������������������������������������������������������������������5 Sport Implementation ������������������������������������������������������������������������������������������������������������������������������5 Rosters ������������������������������������������������������������������������������������������������������������������������������ 6 Head Coach Determination ���������������������������������������������������������������������������������������������������������������������6 Co-Head Coaches ������������������������������������������������������������������������������������������������������������������������������������7 -
Little League Elbow
Little League Elbow (Elbow, Little League; Medial Apophysitis; Overuse Elbow Injury Related to Throwing) by Laurie LaRusso, MS, ELS En Español (Spanish Version) Definition Little League elbow is pain in the elbow joint due to repetitive throwing. This injury occurs in young baseball pitchers before puberty. The Elbow Joint © 2011 Nucleus Medical Media, Inc. Causes During this injury, the ligament attached to the inner side of the elbow begins to pull one of the growth plates away from the rest of the bone. Because the bones are still growing, the growth plates are weak and susceptible to injury. Certain types of throwing may lead to this condition, such as: Throwing too hard and too often Increasing the number of pitches per week too quickly Throwing too many curves or sliders at a young age Changing to a league where the pitcher's mound is farther away from home plate or the mound is elevated Risk Factors These factors increase your chance of developing Little League elbow. Tell your doctor if you or your child have any of these risk factors: Age: 10-15 years old Sex: male (more boys than girls are baseball pitchers) Page 1 of 3 Copyright © 2011 EBSCO Publishing. All rights reserved. Baseball pitching, especially throwing curve balls or sliders Symptoms Symptoms include: Pain around the bony knob on the inner side of the elbow Swelling (possibly) Pain when throwing overhand Pain with gripping or carrying heavy objects (sometimes) Diagnosis The doctor will ask about: Symptoms How the injury occurred When the pain began Any prior elbow injuries The doctor will also: Examine the elbow for signs of ligament or bone damage Find the source of the pain If needed, have an x-ray or an MRI done to look for damage to the bone Treatment Treatment and recovery depend on the severity of the injury. -
Roy Hobbs Baseball Playing Rules Official Rules of Baseball Plus RH Addendums
Roy Hobbs Baseball Playing Rules Official Rules of Baseball plus RH addendums Roy Hobbs Note I: Roy Hobbs Baseball (RHBB) uses the Official Rules of Baseball as its base, with the following adaptations. The adaptations are for use at the annual Roy Hobbs World Series and any Roy Hobbs- sanctioned event where the promoter chooses to use them. These rules have been distributed to members of the Roy Hobbs Umpires Association. Note II: These rules adaptations apply directly to Open, Veterans, Masters, Legends & Classics age divisions, with further adaptations for Vintage, Timeless, Forever Young and Family ties divisions, which are listed separately as needed. Note III: The Roy Hobbs’ rules amplifications, exceptions and adaptations, updated as of June 1, 2017, supersede any other written copy of Roy Hobbs Rules. Note IV: In case of protest, the Official Rules of Baseball, supplemented by Jaska-Roder’s “The Rules of Professional Baseball: A Comprehensive Interpretation”, will be the basis of rules decisions. u 1.0 Rule interpretations, addendums 1.01 Strike zone: RHBB encourages umpires to call a “full” strike zone as described in Official Rules of Baseball: “. that area over home plate, the upper limit of which is a horizontal line at the midpoint between the top of the shoulders and the top of the uniform pants, and the lower level is a line at the hollow beneath the kneecap. The Strike Zone shall be determined from the batter’s stance as the batter is prepared to swing at a pitched ball.” RHBB notes: 1) Over home plate is strictly a judgment call for each umpire. -
FAIRPORT LITTLE LEAGUE Little League Baseball Was Founded In
FAIRPORT LITTLE LEAGUE Little League baseball was founded in 1939 by Carl Stotz in Williamsport, Pennsylvania, and has been a part of the Perinton and Fairport scene since 1951. In 1950, the Fairport Rotary Club asked several of its members to investigate the possibility of bringing Little League to the community. (East Rochester already had four teams.) It was hoped that teams could be organized to play a short season in the spring and summer of 1950. Sponsors pledged $200 each to supply uniforms and equipment, and a local builder offered to level an area in Potter Park for a diamond. However, residents of Potter Place were not happy with the prospect of screaming children and heavy traffic three to four nights each week and complained to the Village Board. The Board ruled that village property could not be used by any outside organization and since Little League was headquartered in Pennsylvania, they could not use Potter Park. Little League was on hold, but not for long. The next year, 1951, four organizations, Lions, Masons, Rotary, and the Fairport Fire Department formulated plans for bringing baseball to Perinton and Fairport youngsters. The executive committee included Tod Malcolm, Napoleon Mancuso, Gene Malcolm, and Hugh Stevely. The fields would be located in the then unused Fairport Park (today’s Perinton Park). Frank Wood, a local contractor, volunteered to bulldoze the area, and volunteers from the sponsoring organization completed the preparation. That year, Little League began its first season in Fairport/Perinton with four teams and 48 players. The games were popular and had many fans, among them a young man who was, because of crippling rheumatoid arthritis, unable to play. -
2021 Regulations of the US Gaelic Athletic Association USGAA
2021 Regulations of the US Gaelic Athletic Association USGAA (As enacted by USGAA Convention, November 2019, San Diego, CA) USGAA Regulations - Revision 120319 www.usgaa.org 1 1. AFFILIATION AND REGISTRATIONS 3 (i) CLUB 3 (ii) PLAYER 4 2. COMPETITION 8 (a) NAME 8 (b) DIVISIONS 8 (c) MEDALS 8 (d) TROPHY 8 3. SANCTIONED PLAYERS 9 (a) MENS CLUBS ONLY 9 (b) LADIES FOOTBALL and CAMOGIE 9 (c) RETURN TO IRELAND 9 (d) SANCTION PLAYERS’ PASSPORTS 10 (e) ID INSPECTION 10 4. SANCTIONS 11 (a) MENS FOOTBALL 11 (b) HURLING 12 (c) LADIES FOOTBALL 13 (d) CAMOGIE 14 5. HOMEGROWN PLAYERS 15 6. JUNIOR STATUS ELIGIBILITY 15 (a) EXCLUSIVELY JUNIOR DIVISONS 15 7. USGAA PLAYOFF GAMES 16 8. PLAYOFFS – GENERAL RULES 19 9. PLAYOFF ROTATION 20 10. GENERAL 21 11. CONVENTION 22 USGAA Regulations - Revision 120319 www.usgaa.org 2 2021 REGULATIONS 1. AFFILIATION AND REGISTRATIONS (i) CLUB (a) Each club shall affiliate with the USGAA, through the electronic registration system no later than 11:59p.m. PST April 30th. All affiliating and/or registering clubs shall be required to have 13 Playing Members registered at this time. Clubs in the first 3 years of existence, to be classified as “Developmental Clubs”, may register with less than 13 players, but no less than 9 players in the respective code. Each Club shall ensure that its players/members register with the USGAA Registrar through the electronic registration system, or else the player will be deemed ineligible to participate. (b) Club or player registrations that are submitted past the appropriate deadline cannot be accepted. -
EARNING FASTBALLS Fastballs to Hit
EARNING FASTBALLS fastballs to hit. You earn fastballs in this way. You earn them by achieving counts where the Pitchers use fastballs a majority of the time. pitcher needs to throw a strike. We’re talking The fastball is the easiest pitch to locate, and about 1‐0, 2‐0, 2‐1, 3‐1 and 3‐2 counts. If the pitchers need to throw strikes. I’d say pitchers in previous hitter walked, it’s almost a given that Little League baseball throw fastballs 80% of the the first pitch you’ll see will be a fastball. And, time, roughly. I would also estimate that of all after a walk, it’s likely the catcher will set up the strikes thrown in Little League, more than dead‐center behind the plate. You could say 90% of them are fastballs. that the patience of the hitter before you It makes sense for young hitters to go to bat earned you a fastball in your wheelhouse. Take looking for a fastball, visualizing a fastball, advantage. timing up for a fastball. You’ll never hit a good fastball if you’re wondering what the pitcher will A HISTORY LESSON throw. Visualize fastball, time up for the fastball, jump on the fastball in the strike zone. Pitchers and hitters have been battling each I work with my players at recognizing the other forever. In the dead ball era, pitchers had curveball or off‐speed pitch. Not only advantages. One or two balls were used in a recognizing it, but laying off it, taking it. -
Basic Baseball Fundamentals Batting
Basic Baseball Fundamentals Batting Place the players in a circle with plenty of room between each player with the Command Coach in the center. Other coaches should be outside the circle observing. If someone needs additional help or correction take that individual outside the circle. When corrected have them rejoin the circle. Each player should have a bat. Batting: Stance/Knuckles/Ready/Load-up/Sqwish/Swing/Follow Thru/Release Stance: Players should be facing the instructor with their feet spread apart as wide as is comfortable, weight balanced on both feet and in a straight line with the instructor. Knuckles: Players should have the bat in both hands with the front (knocking) knuckles lined up as close as possible. Relaxed Ready: Position that the batter should be in when the pitcher is looking in for signs and is Ready to pitch. In a proper stance with the knocking knuckles lined up, hands in front of the body at armpit height and the bat resting on the shoulder. Relaxed Load-up: Position the batter takes when the pitcher starts to wind up or on the first movement after the stretch position. When the pitcher Loads-up to pitch, the batter Loads-up to hit. Shift weight to the back foot. Pivot on the front foot, which will raise the heel slightly off the ground. Hands go back and up at least to shoulder height (Hands up). By shifting the weight to the back foot, pivoting on the front foot and moving the hands back and up, it will move the batter into an attacking position. -
Good Approach at the Plate
Taking a Good Approach at the Plate !We have all see hitters who we feel overachieve and underachieve their mechanics and physical abilities at the plate. We cannot, for the life of us, figure out why the kid who absolutely crushes the ball in the cage, has solid mechanics, and a quick bat hits 50 points lower than the kid who looks far less impressive in the cage, has slower hands, and has questionable mechanics. If this is the case, look no further than pitch selection and plate approach. !We often hear coaches reminding players to have a proper approach at the plate, but what exactly does that mean? A good approach at the plate means different things depending on the age level you are coaching. Basic Levels !At the most basic levels, a proper approach simply means getting a good pitch to hit in any count and not swinging at pitches far out of the strike zone. Pitchers may not be changing speeds very much, and certainly are not locating pitches very well below the age of 12. At this age level simply emphasize getting a good pitch to hit and protecting the the strike zone with two strikes. Advanced Levels !Once pitchers begin to chance speeds and locate pitches, the concept of taking a quality at bat changes quite a bit. The idea at this level is still to get a good pitch to hit, but the concept of a “good pitch” needs to be refined. The toughest thing to get across to your players is that not every fastball that is a strike is a good pitch to hit. -
The Rules of Scoring
THE RULES OF SCORING 2011 OFFICIAL BASEBALL RULES WITH CHANGES FROM LITTLE LEAGUE BASEBALL’S “WHAT’S THE SCORE” PUBLICATION INTRODUCTION These “Rules of Scoring” are for the use of those managers and coaches who want to score a Juvenile or Minor League game or wish to know how to correctly score a play or a time at bat during a Juvenile or Minor League game. These “Rules of Scoring” address the recording of individual and team actions, runs batted in, base hits and determining their value, stolen bases and caught stealing, sacrifices, put outs and assists, when to charge or not charge a fielder with an error, wild pitches and passed balls, bases on balls and strikeouts, earned runs, and the winning and losing pitcher. Unlike the Official Baseball Rules used by professional baseball and many amateur leagues, the Little League Playing Rules do not address The Rules of Scoring. However, the Little League Rules of Scoring are similar to the scoring rules used in professional baseball found in Rule 10 of the Official Baseball Rules. Consequently, Rule 10 of the Official Baseball Rules is used as the basis for these Rules of Scoring. However, there are differences (e.g., when to charge or not charge a fielder with an error, runs batted in, winning and losing pitcher). These differences are based on Little League Baseball’s “What’s the Score” booklet. Those additional rules and those modified rules from the “What’s the Score” booklet are in italics. The “What’s the Score” booklet assigns the Official Scorer certain duties under Little League Regulation VI concerning pitching limits which have not implemented by the IAB (see Juvenile League Rule 12.08.08). -
First and Third
Cutoffs and Relays • Every player on the field, including the pitcher, has a responsibility and a place to be on every cutoff and relay situation. • The voice commands we use are: We will not say anything if we want the ball to come through to the base we are directing to – we will say the number of the base that we wants the ball “cut and relayed” to (2-2-2,3-3-3,4-4-4) • “Cut” means “cut the ball” and “control the play” • The catcher will direct the play as it develops to home plate. • The third baseman will direct the play as it develops to third base. • On a double, possible triple, the trail infielder will direct the play for the lead infielder. • We want the outfielders to make longer throw and “hit the first cutoff man in the chest.” • Infielders STOP moving when the outfielder picks up the ball. We want the outfielder to throw to a stationary target: open and give with good throws. NEVER jump or short hop relay throw. • All sure doubles, possible triples, with nobody on first base, we line up with a double cut to third. • All SURE doubles, possible triples, with nobody on first base, we ine up with a double cut to home plate. • Trail infielder lines up the play and directs the play. • Infielders must know your outfielders arm strength and position yourself accordingly. • Trail infielder must position yourself to catch a high throw and/or a throw that will short hop the lead infielder so you can catch it on one bounce.