Pasha Nayda Mathematics in Hockey. Pasha Nayda Math in Hockey April 26, / 34

Transcription

1 Pasha Nayda Mathematics in Hockey Pasha Nayda Math in Hockey April 26, / 34

2 Introduction Math can be found in many everyday life activites: walking, running, swimming; Ice Hockey is all about math and numbers: Rules (Periods, Players, Length); Statistic and Analytics Discovers Weaknesses and Strength; Helps to approach the best result; For Example: Most efficient spot for the shot; Right hockey position How much time goalies have time for the shot. Pasha Nayda Math in Hockey April 26, / 34

3 History and Facts First official indoor hockey game, Montreal, Canada. Pasha Nayda Math in Hockey April 26, / 34

4 History and Facts was etablished NHL (National Hockey Game) Prior to the 1960s, hockey sticks were straight. Stan Mikita, a Chicago Blackhawks introduced a first stick with the curve in the 60s. Pasha Nayda Math in Hockey April 26, / 34

5 History and Facts The greatest player of all time, Wayne Gretzky, has 61 NHL records. Nobody else comes close to his many records. Pasha Nayda Math in Hockey April 26, / 34

6 History and Facts The first NHL million dollar contract went to Bobby Orr in It was a $200,000, five year term contract. Pasha Nayda Math in Hockey April 26, / 34

7 Rules Regular hockey game in professional and collegiate level is 60 minutes; Each game is divided into three seperateparts called periods (20 mintues each); There 5 players and 1 goalie one ice per each time; Penalty - if player commits it, he must go to penalty box for 2 minutes; Team is shorthanded for 10 % of the period. Pasha Nayda Math in Hockey April 26, / 34

8 Ice Rink Ice rink has basic geometry shape, which looks like square box with rounded corners; There 5 lines on the ice: 2 red goal lines ( each side one); 2 blue lines - determines the offside; 1 red line - center of the ice. Pasha Nayda Math in Hockey April 26, / 34

9 Ice Rink The rink has 5 same size faceoffs circles, with the diametr of 30 feet; There are goal creases from each side with the radius of 6 feet; Trapezoid line - is located behind the each goal. Pasha Nayda Math in Hockey April 26, / 34

10 Scoring The main goal of a hockey is to score more goals than your opponent will, and knowing math can help to increase the effectiveness; Pass of the boards; Understanding of angles; Example: Pasha Nayda Math in Hockey April 26, / 34

11 Scoring 40 The angle is 40, which is right in the middle where we could see the net in front of us. This position is really dangerous for the goalie, since a player has more open spots to shot. Pasha Nayda Math in Hockey April 26, / 34

12 Scoring 15 The angle is 15, which is right in the middle where we could see the net in front of us. This position is really dangerous for the goalie, since a player has more open spots to shot. Pasha Nayda Math in Hockey April 26, / 34

13 Growing of Hockey Ice hockey is growing worldwide according to the International Ice Hockey Federation s annual survey of players.the Inernational Ice Hockey Federation published the results of their 2013 survey, pointing out that worldwide, the total number of hockey players from 2012 to 2013 has increased 2.47 % and 1.64 million people in the world play organized hockey (SB Nation) Pasha Nayda Math in Hockey April 26, / 34

14 Top 10 Hockey Coutries Pasha Nayda Math in Hockey April 26, / 34

15 Top 5 countries, Players Hockey Players (t) Finland Czech USA Canada Russia Countries Pasha Nayda Math in Hockey April 26, / 34

16 Top 5 countries, Rinks 7,631 Hockey Rinks 1,983 2, Czech 274 USA Canada Russia Finland Countries Pasha Nayda Math in Hockey April 26, / 34

17 ELO of the Hockey Teams ELO - is a rating systeam of the NHL. used for comparing the relative skill level of competitors in 1-on-1 or team-on-team games; rating starts from the previous number for two competitors and than updates based on the outcome of the game Pasha Nayda Math in Hockey April 26, / 34

18 ELO Model Rating changes depends on the final score of the game, and some details that also are taking on consideration like: home or away game, and is it regular game or playoffs ; Rating can go up and down, it is also based against what ranked team you are playing against, if your team beat very high ranked team, that s mean that you will get more points that usually; A tie is considered to be half a win and will cost the ELO-favourite some points; The zero-sum system - is teams trade points based on game outcomes. If Team A gains 5 points, Team B loses 5 points Pasha Nayda Math in Hockey April 26, / 34

19 ELO Model Formulas In Hockey it is considered that average rating is target at 1,500. Formula for expected outcome ( probability of winning) for the home Team H (when playing visitng Team V) is: E H = (ELO H ELO V +Home) /400 ELO H and ELO V are the ELO ratings for teams H and V; Home is an adjustment to account for home ice effects, since a team who is playing home has higher expectation to win. Pasha Nayda Math in Hockey April 26, / 34

20 Example of some team s Statistics ELO Rating Winning Percentage Points in Standing Goals difference (Season) Goals difference (Per game) 1,350 30% ,400 36% ,450 43% ,500 50% ,550 57% ,600 64% ,650 70% ,700 76% Table: The table shows that ELO differentials Pasha Nayda Math in Hockey April 26, / 34

21 ELO Formulas After a game is played, the change in the ELO rating of the home team is easy to calculate, using these formulas: ELOChange = K I M (Outcome H E H ) ELO H = ELO H Old + ELOChange E H - is expected outcome of the game (the probability of a win for the home team) Outcome H - is very simply to determine, if home team wins that 1, if lose - 0, if it is a tie than it s 0.5 Pasha Nayda Math in Hockey April 26, / 34

22 ELO Formulas K - is the velocity of change. A high K says that we think that a single game adds a lot of information. A low K implies that a single game outcome adds little news. I - is the importance of the game. Usually in hockey we use I=1 for regular game and I=1.5 for the playoffs M - is the margin of victory factor. A higher M gives ELO more information about the relative quality of the two teams. However, once a game is won, the score becomes less meaningful. M is also designed to reflect expectations. Pasha Nayda Math in Hockey April 26, / 34

23 Margin of Victory Formula ( ( M = MAX(1, LN ABS GD H 0.85 ELO ) ) H ELO V + Home + e 1 ) 100 GD H - is the goal differential in the game, from the perspective of the home team. Pasha Nayda Math in Hockey April 26, / 34

24 Greatest NHL teams Based on the ELO Rating model, the highest rating score of ELO in NHL histroy was established by Montreal Canadiends in , who reached 1700 points that season, and was dominated for 10 years. Here is little example of the best 6 ELO Ranked NHL teams from Pasha Nayda Math in Hockey April 26, / 34

25 Greatest NHL teams Pasha Nayda Math in Hockey April 26, / 34

26 Sidney Crosby vs. Alex Ovechkin Experts believe that Alex Ovechkin and Sidney Crosby are the best hockey player in last 10 years; Crosby has increadiable puck control and great vision, which makes him unique; Ovechkin has great shot, which goalie s can not even see sometimes. Pasha Nayda Math in Hockey April 26, / 34

27 Comparison Goals Compare Points Assits Pasha Nayda Math in Hockey April 26, / 34

28 Statistics Pasha Nayda Math in Hockey April 26, / 34

29 Rigid body dynamics First year at the NHL both got over 100 points. Average per player in a leage is 23.3 points In Ovechkin received Calder Memorial Trophy, which is awarded to the rookie of the year In Crosby received Hart Memorial Trophy which is awarded to the most valuable palyer of the year. During next 10 years Crosby and Ovechkin together received around 12 Trophies in total. Pasha Nayda Math in Hockey April 26, / 34

30 Goals Comparison Graph 60 Crosby Ovechkin Goals ,006 2,008 2,010 2,012 2,014 Season Pasha Nayda Math in Hockey April 26, / 34

31 Assists Comparison Graph 80 Crosby Ovechkin Assists ,006 2,008 2,010 2,012 2,014 Season Pasha Nayda Math in Hockey April 26, / 34

32 Points Comparison Graph 120 Crosby Ovechkin 100 P oints ,006 2,008 2,010 2,012 2,014 Season Pasha Nayda Math in Hockey April 26, / 34

33 So who is better? Some hockey experts argue that Ovechkin is a selfish player and he never passes the puck, when Crosby has a great puck control is more fully balanced player; Others, believe that Ovechkin is the greatest sniper of all time and noone will come even close to his scoring goals achivments in next 30 years; Therefore, it is really hard to compare these two great hockey players and probably many fans will argue about this topic for many more years. Pasha Nayda Math in Hockey April 26, / 34

34 Conclusion Based on this research we could of seen how math and hockey are close related. Used to calculate the most effective ways to achieve certain physical or visual results. Used to understand hockey rules and it s consepts. Used to indentify weaknesses and strength: like percentage of faceoffs winning, amount of hits and shots on goal. Therefore, I believe that with even more developed technology, hockey would be using ever more mathematics in a future, because the receipe of success is hiding under accurately calculated numbers. Pasha Nayda Math in Hockey April 26, / 34