8. Sports betting

Sports betting Volume 1, Issue 8 Supervising teachers: Alexandros Markoulakis 2nd General Lyceum Eugenia Potiriadou of Kamatero The e-Twinning Group: SPORT SCIENCE STORIES 2017—18 1

Contents Volume 1, Issue 8 Alexandros Markoulakis Supervising teachers: 2nd General Lyceum Eugenia Potiriadou of Kamatero Inside this issue: Front Cover 1 Contents 2 The European Football Market 3 Football Betting 4 Data 5 Data Analysis 9 Probability 21 Sport Science Stories 41 Back Cover 48 2

The European Football Market Volume 1, Issue 8 2nd General Lyceum of Kamatero MARKET SIZE OF THE EUROPEAN PRO- FESSIONAL FOOTBALL MARKET FROM 2006/07 TO 2015/16 (IN BILLION EUROS) The statistic shows the total revenue of the European professional soccer market from 2006/07 to 2015/16. In the 2010/11 season, the total revenue of the European profes- sional soccer market was estimated at 16.9 billion euros. Many people around the world depend on this industry to make a living, including play- ers, coaches, referees, marketing companies, the media and, last but not least, book- makers. 3

Football Betting Volume 1, Issue 8 Alexandros Markoulakis Supervising teachers: 2nd General Lyceum Eugenia Potiriadou of Kamatero Football betting worth £1.4BILLION to gambl ing industry in one year, new figures reveal. Stats have revealed that bookmakers have made a profit of over £330million be- tween October 2015 and Sep- tember 2016. It is a record profit over a 12 month period for bookmakers, while the entire gambling industry scored a gross gambling yield of £13.8bn. The statistics come amid increased attention surrounding gambling in football. Bookmakers’ work involves predicting whether a team will win or lose and cal- culating betting odds on this basis. A successful bookmaker needs not only luck but also acute mathematical skills in order to analyse complex sets of data, tak- ing into consideration a variety of combinatory factors and complex variables. 4

What the Students Do Volume 1, Issue 8 Data 2nd General Lyceum of Kamatero Objectives: The students make a spreadsheet with the results of The most important games. This spreadsheet (next page) is based on the skill that students Greek Football Championship in the season 2016/17. first need to develop is to become familiar with designing and The names of all the teams are listed in the left column building a database (home team) and upper row (away team) in alphabeti- using spreadsheets. cal order. Students can take the desired data sets The results of each game are included in the two cor- from these sources responding cells: the left cell indicates the number of and import them into goals scored by the home team, and the right cell indi- their own spread- sheets. cates the number of goals scored by the away team. 5

What the Students Do Volume 1, Issue 8 Data 2nd General Lyceum of Kamatero GREEK HANDBALL CHAMPIOSHIP_ 2016-17 6

What the Students Do Volume 1, Issue 8 Data 2nd General Lyceum of Kamatero GREEK FOOTBALL CHAMPIONSHIP_ 2016-17 7

What the Students Do Volume 1, Issue 8 Data 2nd General Lyceum of Kamatero Results of the Games_Greek Football Championship 2016 - 17 Pan- Plata- Olym- Pane- Levadia Pas Panathi- Asteras away Iraklis Veria PAOK Larissa Kerkyra AEK Xanthi Atro- piakos naikos ionios nias Giannina tolikos Tripolis kos home mitos 1 Olympiakos 2 1 3 0 3 0 0 1 2 0 2 1 2 0 5 0 3 0 3 1 2 1 2 0 4 0 3 0 6 1 2 PAOK 2 0 3 0 1 0 1 0 0 0 3 0 3 4 0 1 5 1 2 1 3 2 2 0 3 0 1 0 4 0 3 Panathinaikos 1 0 1 0 0 0 1 0 1 2 2 1 1 0 4 0 1 0 4 0 3 1 2 1 0 0 2 0 5 0 4 AEK 1 0 3 0 2 3 0 0 4 1 3 0 2 2 1 1 5 0 0 0 2 0 3 0 4 0 0 0 6 0 5 Panionios 0 2 1 0 1 1 1 1 2 0 1 1 2 1 1 1 1 0 2 0 3 0 1 0 1 3 1 0 1 2 6 Xanthi 0 2 0 0 1 0 0 0 0 2 1 0 0 0 2 0 0 0 3 0 3 1 1 0 2 2 3 1 3 0 7 Platanias 2 2 1 3 1 0 0 2 1 1 0 1 3 0 3 3 2 1 0 0 3 0 3 2 3 2 1 0 1 0 8 Atromitos 0 1 0 2 0 1 0 1 1 2 2 1 4 1 1 1 1 4 0 2 1 0 0 0 2 0 1 0 1 0 9 Pas Giannina 0 2 0 1 1 1 1 1 1 0 1 1 0 0 3 0 1 0 0 0 1 2 4 0 0 0 1 2 2 0 10 Kerkyra 0 2 0 5 1 1 1 1 1 0 1 0 0 1 1 1 0 1 0 0 2 0 2 0 1 0 0 3 2 0 11 Panetolikos 0 2 0 1 0 0 3 2 0 2 2 3 1 2 2 0 1 2 4 0 1 1 2 1 2 0 2 0 1 0 12 Asteras Tripolis 0 0 1 2 0 5 3 2 1 1 0 0 2 0 0 1 1 1 1 2 4 1 1 1 1 0 2 2 1 0 13 Larissa 1 0 0 2 0 0 1 2 2 0 1 0 0 0 1 2 1 1 1 1 1 0 1 4 2 1 2 2 0 0 14 Levadiakos 1 1 0 1 0 3 0 2 1 4 1 1 1 2 1 1 2 1 2 1 2 1 1 1 1 1 3 0 3 1 15 Iraklis 1 2 1 1 1 1 2 2 1 2 0 1 1 1 1 2 2 1 0 0 2 1 1 1 1 1 1 0 1 1 16 Veria 1 2 0 0 1 1 0 2 0 1 0 4 0 0 0 1 3 0 4 0 1 1 4 3 1 1 2 0 0 2 8

What the Students Do Volume 1, Issue 8 Data Analysis 2nd General Lyceum of Kamatero 1. 1. The students developed a formula to calculate the number of games that were played in the whole season in the Greek Championship. The number of the teams that played against each other was 16). Each team has 15 opponents that have all played both home and away games. So, each team plays 2 ∙ 15 = 30 games. 15 of them are at home and 15 away [15 games at home / 15 games away]. Since there are 16 teams, and each team played 15 games either away or at home, therefore, in total, 16∙15 = 240 matches were played in the season. 2. Then, the students calculated the goal statistics (goals scored and conceded) for each team for the whole season. The data table as well as the graph are displayed on the next page. The students decided to make the graph accordingly to the ranking table and then identified the connection between the shape of the graph and the ranking in the final table. After the calculations, some students compared the results from their spreadsheet with the real data from online databases in order to check their calculations. 9

What the Students Do Volume 1, Issue 8 Scored goals Conceded goals 1 Olympiakos 60 16 PAOK 49 19 2 2nd General Lyceum of 3 Panathinaikos 45 20 Kamatero 4 AEK 54 23 5 Panionios 34 23 6 Xanthi 34 25 7 Platanias 34 38 Data 8 Atromitos 29 38 Pas Giannina 30 10 9 10 Kerkyra 22 46 11 Panetolikos 29 40 Analysis 12 Asteras Tripolis 35 49 13 Larissa 22 41 14 Levadiakos 39 28 15 Iraklis 27 49 16 Veria 22 55 Scored and Conceded goals for each team, Superleague Greece, 2016-17 60 50 40 30 20 10 0 Scored goals Conceded goals 10

What the Students Do Volume 1, Issue 8 Data Analysis 2nd General Lyceum of Kamatero 3. The students calculated the average number of goals per game in the whole season. Scored Total number of Average number of goals scored goals goals per game 1 Olympiakos 60 2 PAOK 49 3 Panathinaikos 45 4 AEK 54 5 Panionios 34 6 Xanthi 34 7 Platanias 34 8 Atromitos 29 9 Pas Giannina 30 554 2.31 10 Kerkyra 22 11 Panetolikos 29 12 Asteras Tripolis 35 13 Larissa 22 14 Levadiakos 27 15 Iraklis 28 16 Veria 22 Answer: 2.31 goals/game 11

What the Students Do Volume 1, Issue 8 2nd General Lyceum of Kamatero Data Analysis 3. The students calculated the relative frequency p(n) of the number of goals per game. Relative Frequencies p(n) Olympiakos PAOK Panathinaikos AEK n N*p(n) p(n) N*p(n) p(n) N*p(n) p(n) N*p(n) p(n) 0 6 0.20 7 0.23 8 0.27 7 0.23 1 2 0.07 8 0.27 12 0.40 6 0.20 2 14 0.47 6 0.20 3 0.10 10 0.33 3 5 0.17 6 0.20 3 0.10 3 0.10 4 1 0.03 1 0.03 2 0.07 2 0.07 5 1 0.03 2 0.07 2 0.07 1 0.03 6 1 0.03 0 0.00 0 0.00 1 0.03 30 1 30 1 30 1 30 1 Relative frequency versus goals per game for the following four teams 0.50 p(n) p(n) 0.45 p(n) 0.40 0.35 p(n) 0.30 Relative frequencies 0.25 0.20 0.15 0.10 0.05 6 6, 0.03, 0.03 0.00 6 6, 0.00, 0.00 0 1 2 3 4 5 6 7 Number of goals per game 12

What the Students Do Volume 1, Issue 8 2nd General Lyceum of Kamatero Data Analysis Relative Frequencies p(n) Panionios Xanthi Platanias Atromitos n N*p(n) p(n) N*p(n) p(n) N*p(n) p(n) N*p(n) p(n) 0 7 0.23 12 0.40 10 0.33 12 0.40 1 14 0.47 9 0.30 11 0.37 11 0.37 2 7 0.23 3 0.10 4 0.13 5 0.17 3 1 0.03 5 0.17 5 0.17 0 0.00 4 1 0.03 1 0.03 0 0.00 2 0.07 5 0 0.00 0 0.00 0 0.00 0 0.00 6 0 0.00 0 0.00 0 0.00 0 0.00 30 1 30 1 30 1 30 1 Relative frequencies versus goals per game for the following four teams 0.50 0.45 p(n) 0.40 p(n) 0.35 p(n) Relative frequencies 0.30 p(n) 0.25 0.20 0.15 0.10 0.05 0.00 0 1 2 3 4 5 6 7 Number of goals per game 13

What the Students Do Volume 1, Issue 8 Data Analysis 2nd General Lyceum of Kamatero Relative Frequencies p(n) Pas Giannina Kerkyra Panetolikos Asteras Tripolis n N*p(n) p(n) N*p(n) p(n) N*p(n) p(n) N*p(n) p(n) 0 9 0.30 15 0.5 12 0.40 9 0.30 1 16 0.53 10 0.33 10 0.33 13 0.43 2 2 0.07 4 0.13 6 0.20 4 0.13 3 2 0.07 0 0.00 1 0.03 2 0.07 4 1 0.03 1 0.03 1 0.03 2 0.07 5 0 0.00 0 0.00 0 0.00 0 0.00 6 0 0.00 0 0.00 0 0.00 0 0.00 30 1 30 1 30 1 30 1 Relative frequencies versus number of goals per games for the following four teams 0.60 0.50 p(n) p(n) Relative frequencies 0.40 p(n) 0.30 p(n) 0.20 0.10 0.00 1 2 3 4 5 6 7 Number of goals per game 14

What the Students Do Volume 1, Issue 8 Data Analysis 2nd General Lyceum of Kamatero Relative Frequencies p(n) Larissa Levadiakos Iraklis Veria n N*p(n) p(n) N*p(n) p(n) N*p(n) p(n) N*p(n) p(n) 0 12 0.40 14 0.47 11 0.37 18 0.60 1 14 0.47 8 0.27 11 0.37 7 0.23 2 4 0.13 5 0.17 7 0.23 2 0.07 3 0 0.00 3 0.10 1 0.03 1 0.03 4 0 0.00 0 0.00 0 0.00 2 0.07 5 0 0.00 0 0.00 0 0.00 0 0.00 6 0 0.00 0 0.00 0 0.00 0 0.00 30 1 30 1 30 1 30 1 Relative frequency versus number of goals per game for the following four teams 0.70 0.60 p(n) 0.50 p(n) 0.40 p(n) Relative frequencies 0.30 p(n) 0.20 0.10 0.00 0 1 2 3 4 5 6 7 Number of goals per game 15

What the Students Do Volume 1, Issue 8 Data Analysis 2nd General Lyceum of Kamatero 4. The students multiplied the number of goals n with corresponding relative frequency p(n) on each row of the table. Then summarise all products. What is the information we get? Average number of goals each team scored per season Panionios Xanthi Platanias Atromitos n p(n) n∙p(n) p(n) n∙p(n) p(n) n∙p(n) p(n) n∙p(n) 0 0.23 0.00 0.40 0.00 0.33 0.00 0.40 0.00 1 0.47 0.47 0.30 0.30 0.37 0.37 0.37 0.37 2 0.23 0.47 0.10 0.20 0.13 0.27 0.17 0.33 3 0.03 0.10 0.17 0.50 0.17 0.50 0.00 0.00 4 0.03 0.13 0.03 0.13 0.00 0.00 0.07 0.27 5 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 6 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.17 1.13 1.13 0.97 Average number of goals each team scored per season Olympiakos PAOK Panathinaikos AEK n p(n) n∙p(n) p(n) n∙p(n) p(n) n∙p(n) p(n) n∙p(n) 0 0.20 0.00 0.23 0.00 0.27 0.00 0.23 0.00 1 0.07 0.07 0.27 0.27 0.40 0.40 0.20 0.20 2 0.47 0.93 0.20 0.40 0.10 0.20 0.33 0.67 3 0.17 0.50 0.20 0.60 0.10 0.30 0.10 0.30 4 0.03 0.13 0.03 0.13 0.07 0.28 0.07 0.27 5 0.03 0.17 0.07 0.33 0.07 0.33 0.03 0.17 6 0.03 0.20 0.00 0.00 0.00 0.00 0.03 0.20 2.00 1.73 1.51 1.80 16

What the Students Do Volume 1, Issue 8 Data Analysis 2nd General Lyceum of Kamatero Average number of goals each team scored per season Pas Giannina Kerkyra Panetolikos Asteras Tripolis n p(n) n∙p(n) p(n) n∙p(n) p(n) n∙p(n) p(n) n∙p(n) 0 0.30 0.00 0.50 0.00 0.40 0.00 0.30 0.00 1 0.53 0.53 0.33 0.33 0.33 0.33 0.43 0.43 2 0.07 0.13 0.13 0.27 0.20 0.40 0.13 0.27 3 0.07 0.20 0.00 0.00 0.03 0.10 0.07 0.20 4 0.03 0.13 0.03 0.13 0.03 0.13 0.07 0.27 5 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 6 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.00 0.73 0.97 1.17 Average number of goals each team scored per season Larissa Levadiakos Iraklis Veria n p(n) n∙p(n) p(n) n∙p(n) p(n) n∙p(n) p(n) n∙p(n) 0 0.40 0.00 0.47 0.00 0.37 0.00 0.60 0.00 1 0.47 0.47 0.27 0.27 0.37 0.37 0.23 0.23 2 0.13 0.27 0.17 0.33 0.23 0.47 0.07 0.13 3 0.00 0.00 0.10 0.30 0.03 0.10 0.03 0.10 4 0.00 0.00 0.00 0.00 0.00 0.00 0.07 0.27 5 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 6 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.73 0.90 0.93 0.73 Answer: The information we get is the average number of goals each team scored per season. 17

What the Students Do Volume 1, Issue 8 Data Analysis 2nd General Lyceum of Kamatero 5. Use of the average number of goals to calculate so-called coincidence in the outcome of the games. Coincidence is a relatively effective deviation and according to the Poisson distribution, it equals The outcome of each game is more difficult to predict as the coincidence value increases. This is only a rough estimation; however, it can be argued that football is based on coincidence. Coincidence in real gaming can often be as high as 100 %. At the same time, coincidence is higher when the football team is lower in the table. 18

What the Students Do Volume 1, Issue 8 Data Analysis 2nd General Lyceum of Kamatero Coincidence Olympiakos PAOK Panathinaikos AEK n 2 1.73 1.51 1.80 1/n 0.5 2.00 0.66 0.56 1/2 (1/n) 0.71 1.41 1.51 1.80 Coincidence Panionios Xanthi Platanias Atromitos n 1.17 1.13 1.13 0.97 1/n 0.86 0.88 0.88 1.03 (1/n) 1/2 0.93 0.94 0.94 1.02 19

What the Students Do Volume 1, Issue 8 Data Analysis 2nd General Lyceum of Kamatero Coincidence Pas Giannina Kerkyra Panetolikos Asteras Tripolis n 1.00 0.73 0.97 1.17 1/n 1 1.36 1.03 0.86 (1/n) 1/2 1 1.17 1.02 0.93 Coincidence Larissa Levadiakos Iraklis Veria n 0.73 0.90 0.93 0.73 1/n 1.36 1.11 1.07 1.36 (1/n) 1/2 1.17 1.05 1.04 1.17 20

What the Students Do Volume 1, Issue 8 Probability 2nd General Lyceum of Kamatero 6. Students already calculated the average number of goals that each single team scored per match. Let r1 be the average number of goals that the first team scores per match and r2 the average number of goals that the second team scores per match. We define R as the quotient: R = r1 / r2 . The probability that the first team will score the next goal is calculated using and the probability that the second team will score the next goal is calculated using The students calculate probabilities p1 and p2 for each team using the data obtained in 29 rounds so as to compare the theoretical calculations with the actual football results in the 30th round of the Superleague. 21

What the Students Do Volume 1, Issue 8 Probability 2nd General Lyceum of Kamatero Calculation of probabilities p1 and p2 for each team 1η Αγωνιστική r1 r2 R=r1/r2 p1 p2 1st round 1 Olympiakos Asteras Tripolis 2 1.17 1.71 0.63 0.37 2 AEK Panetolikos 1.8 0.97 1.86 0.65 0.35 3 Platanias Panathinaikos 1.13 1.51 0.75 0.43 0.57 4 Iraklis Xanthi 0.93 1.13 0.82 0.45 0.55 5 Larissa Veria 0.73 0.73 1.00 0.50 0.50 6 Panionios Pas Giannina 1.17 1 1.17 0.54 0.46 7 Kerkyra Atromitos 0.73 0.97 0.75 0.43 0.57 8 Levadiakos PAOK 0.9 1.73 0.52 0.34 0.66 2η Αγωνιστική R=r1/r2 p1 p2 r2 r1 2nd round 1 Panathinaikos Kerkyra 1.51 0.73 2.07 0.67 0.33 2 Platanias Larissa 1.13 0.73 1.55 0.61 0.39 3 Veria Iraklis 0.73 0.93 0.78 0.44 0.56 4 Xanthi Olympiakos 1.13 2 0.57 0.36 0.64 5 Atromitos Levadiakos 0.97 0.9 1.08 0.52 0.48 AEK 1.17 1.8 0.65 0.39 0.61 6 Asteras Tripolis 7 PAOK Pas Giannina 1.73 1 1.73 0.63 0.37 8 Panetolikos Panionios 0.97 1.17 0.83 0.45 0.55 22

What the Students Do Volume 1, Issue 8 Probability 2nd General Lyceum of Kamatero Calculation of probabilities p1 and p2 for each team 3η Αγωνιστική r2 R=r1/r2 p1 p2 r1 3rd round 1 Larissa Iraklis 0.73 0.93 0.78 0.44 0.56 2 Kerkyra Platanias 0.73 1.13 0.65 0.39 0.61 3 Olympiakos Veria 2 0.73 2.74 0.73 0.27 4 Levadiakos Panathinaikos 0.9 1.51 0.60 0.37 0.63 5 PAOK Panetolikos 1.73 0.97 1.78 0.64 0.36 6 AEK Xanthi 1.8 1.13 1.59 0.61 0.39 7 Pas Giannina Atromitos 1 0.97 1.03 0.51 0.49 8 Panionios Asteras Tripolis 1.17 1.17 1.00 0.50 0.50 4η Αγωνιστική 4th round r1 r2 R=r1/r2 p1 p2 1 Kerkyra Larissa 0.73 0.73 1.00 0.50 0.50 2 Iraklis Olympiakos 0.93 2 0.47 0.32 0.68 3 Platanias Levadiakos 1.13 0.9 1.26 0.56 0.44 4 Panathinaikos Pas Giannina 1.51 1 1.51 0.60 0.40 AEK 0.73 1.8 0.41 0.29 0.71 5 Veria 6 Xanthi Panionios 1.13 1.17 0.97 0.49 0.51 7 Atromitos Panetolikos 0.97 0.97 1.00 0.50 0.50 8 Asteras Tripolis PAOK 1.17 1.73 0.68 0.40 0.60 23

What the Students Do Volume 1, Issue 8 Probability 2nd General Lyceum of Kamatero Calculation of probabilities p1 and p2 for each team 5η Αγωνιστική 5th round r1 r2 R=r1/r2 p1 p2 1 Larissa Olympiakos 0.73 2 0.37 0.27 0.73 2 Levadiakos Kerkyra 0.9 0.73 1.23 0.55 0.45 3 AEK Iraklis 1.8 0.93 1.94 0.66 0.34 4 Pas Giannina Platanias 1 1.13 0.88 0.47 0.53 5 Panionios Veria 1.17 0.73 1.60 0.62 0.38 6 Panetolikos Panathinaikos 0.97 1.51 0.64 0.39 0.61 7 PAOK Xanthi 1.73 1.13 1.53 0.60 0.40 8 Atromitos Asteras Tripolis 0.97 1.17 0.83 0.45 0.55 6η Αγωνιστική R=r1/r2 p1 p2 r2 r1 6th round 1 Olympiakos AEK 2 1.8 1.11 0.53 0.47 2 Veria PAOK 0.73 1.73 0.42 0.30 0.70 3 Panathinaikos Asteras Tripolis 1.51 1.17 1.29 0.56 0.44 4 Levadiakos Larissa 0.9 0.73 1.23 0.55 0.45 5 Kerkyra Pas Giannina 0.73 1 0.73 0.42 0.58 6 Iraklis Panionios 0.93 1.17 0.79 0.44 0.56 7 Platanias Panetolikos 1.13 0.97 1.16 0.54 0.46 8 Xanthi Atromitos 1.13 0.97 1.16 0.54 0.46 24

What the Students Do Volume 1, Issue 8 Probability 2nd General Lyceum of Kamatero Calculation of probabilities p1 and p2 for each team 7η Αγωνιστική 7th round r1 r2 R=r1/r2 p1 p2 1 Larissa AEK 0.73 1.8 0.41 0.29 0.71 2 Pas Giannina Levadiakos 1 0.9 1.11 0.53 0.47 3 Panionios Olympiakos 1.17 2 0.59 0.37 0.63 4 Panetolikos Kerkyra 0.97 0.73 1.33 0.57 0.43 5 PAOK Iraklis 1.73 0.93 1.86 0.65 0.35 6 Asteras Tripolis Platanias 1.17 1.13 1.04 0.51 0.49 7 Atromitos Veria 0.97 0.73 1.33 0.57 0.43 8 Panathinaikos Xanthi 1.51 1.13 1.34 0.57 0.43 8η Αγωνιστική R=r1/r2 p1 p2 r2 r1 8th round 1 Pas Giannina Larissa 1 0.73 1.37 0.58 0.42 2 AEK Panionios 1.8 1.17 1.54 0.61 0.39 3 Levadiakos Panetolikos 0.9 0.97 0.93 0.48 0.52 4 Olympiakos PAOK 2 1.73 1.16 0.54 0.46 5 Kerkyra Asteras Tripolis 0.73 1.17 0.62 0.38 0.62 6 Iraklis Atromitos 0.93 0.97 0.96 0.49 0.51 7 Platanias Xanthi 1.13 1.13 1.00 0.50 0.50 8 Veria Panathinaikos 0.73 1.51 0.48 0.33 0.67 25

What the Students Do Volume 1, Issue 8 Probability 2nd General Lyceum of Kamatero Calculation of probabilities p1 and p2 for each team 9η Αγωνιστική R=r1/r2 p1 p2 r1 r2 9th round 1 PAOK AEK 1.73 1.8 0.96 0.49 0.51 2 Larissa Panionios 0.73 1.17 0.62 0.38 0.62 3 Panetolikos Pas Giannina 0.97 1 0.97 0.49 0.51 4 Asteras Tripolis Levadiakos 1.17 0.9 1.30 0.57 0.43 5 Atromitos Olympiakos 0.97 2 0.49 0.33 0.67 6 Xanthi Kerkyra 1.13 0.73 1.55 0.61 0.39 7 Panathinaikos Iraklis 1.51 0.93 1.62 0.62 0.38 8 Veria Platanias 0.73 1.13 0.65 0.39 0.61 10η Αγωνιστική R=r1/r2 p1 p2 r2 r1 10th round 1 Olympiakos Panathinaikos 2 1.51 1.32 0.57 0.43 2 Panetolikos Larissa 0.97 0.73 1.33 0.57 0.43 3 Panionios PAOK 1.17 1.73 0.68 0.40 0.60 4 Pas Giannina Asteras Tripolis 1 1.17 0.85 0.46 0.54 5 AEK Atromitos 1.8 0.97 1.86 0.65 0.35 6 Levadiakos Xanthi 0.9 1.13 0.80 0.44 0.56 7 Kerkyra Veria 0.73 0.73 1.00 0.50 0.50 8 Iraklis Platanias 0.93 1.13 0.82 0.45 0.55 26

What the Students Do Volume 1, Issue 8 Probability 2nd General Lyceum of Kamatero Calculation of probabilities p1 and p2 for each team 11η Αγωνιστική R=r1/r2 p1 p2 r2 r1 11th round 1 Panathinaikos AEK 1.51 1.8 0.84 0.46 0.54 2 Larissa PAOK 0.73 1.73 0.42 0.30 0.70 3 Asteras Tripolis Panetolikos 1.17 0.97 1.21 0.55 0.45 4 Atromitos Panionios 0.97 1.17 0.83 0.45 0.55 5 Xanthi Pas Giannina 1.13 1 1.13 0.53 0.47 6 Veria Levadiakos 0.73 0.9 0.81 0.45 0.55 7 Platanias Olympiakos 1.13 2 0.57 0.36 0.64 8 Iraklis Kerkyra 0.93 0.73 1.27 0.56 0.44 12η Αγωνιστική R=r1/r2 p1 p2 r2 r1 12th round 1 Panathinaikos AEK 1.51 1.8 0.84 0.46 0.54 2 Larissa PAOK 0.73 1.73 0.42 0.30 0.70 3 Asteras Tripolis Panetolikos 1.17 0.97 1.21 0.55 0.45 4 Atromitos Panionios 0.97 1.17 0.83 0.45 0.55 5 Xanthi Pas Giannina 1.13 1 1.13 0.53 0.47 6 Veria Levadiakos 0.73 0.9 0.81 0.45 0.55 7 Platanias Olympiakos 1.13 2 0.57 0.36 0.64 8 Iraklis Kerkyra 0.93 0.73 1.27 0.56 0.44 27

What the Students Do Volume 1, Issue 8 Probability 2nd General Lyceum of Kamatero Calculation of probabilities p1 and p2 for each team 13η Αγωνιστική R=r1/r2 p1 p2 r2 r1 13th round 1 Panathinaikos PAOK 1.51 1.73 0.87 0.47 0.53 2 Larissa Atromitos 0.73 0.97 0.75 0.43 0.57 3 Xanthi Asteras Tripolis 1.13 1.17 0.97 0.49 0.51 4 Veria Panetolikos 0.73 0.97 0.75 0.43 0.57 5 Platanias Panionios 1.13 1.17 0.97 0.49 0.51 6 Iraklis Pas Giannina 0.93 1 0.93 0.48 0.52 7 Kerkyra AEK 0.73 1.8 0.41 0.29 0.71 8 Olympiakos Levadiakos 2 0.9 2.22 0.69 0.31 14η Αγωνιστική R=r1/r2 p1 p2 r2 r1 14th round 1 Xanthi Larissa 1.13 0.73 1.55 0.61 0.39 2 Atromitos Panathinaikos 0.97 1.51 0.64 0.39 0.61 3 Asteras Tripolis Veria 1.17 0.73 1.60 0.62 0.38 4 PAOK Platanias 1.73 1.13 1.53 0.60 0.40 5 Panetolikos Iraklis 0.97 0.93 1.04 0.51 0.49 6 Panionios Kerkyra 1.17 0.73 1.60 0.62 0.38 7 Pas Giannina Olympiakos 1 2 0.50 0.33 0.67 8 AEK Levadiakos 1.8 0.9 2.00 0.67 0.33 28

What the Students Do Volume 1, Issue 8 Probability 2nd General Lyceum of Kamatero Calculation of probabilities p1 and p2 for each team 15η Αγωνιστική R=r1/r2 p1 p2 r1 r2 15th round 1 Larissa Panathinaikos 0.73 1.51 0.48 0.33 0.67 2 Veria Xanthi 0.73 1.13 0.65 0.39 0.61 3 Platanias Atromitos 1.13 0.97 1.16 0.54 0.46 4 Iraklis Asteras Tripolis 0.93 1.17 0.79 0.44 0.56 5 Kerkyra PAOK 0.73 1.73 0.42 0.30 0.70 6 Olympiakos Panetolikos 2 0.97 2.06 0.67 0.33 7 Levadiakos Panionios 0.9 1.17 0.77 0.43 0.57 8 AEK Pas Giannina 1.8 1 1.80 0.64 0.36 16η Αγωνιστική r2 R=r1/r2 p1 p2 r1 16 th round 1 Asteras Tripolis Olympiakos 1.17 2 0.59 0.37 0.65 2 Panetolikos AEK 0.97 1.8 0.54 0.35 0.43 3 Panathinaikos Platanias 1.51 1.13 1.34 0.57 0.45 4 Xanthi Iraklis 1.13 0.93 1.22 0.55 0.50 5 Veria Larissa 0.73 0.73 1.00 0.50 0.54 6 Pas Giannina Panionios 1 1.17 0.85 0.46 0.43 7 Atromitos Kerkyra 0.97 0.73 1.33 0.57 0.34 8 PAOK Levadiakos 1.73 0.9 1.92 0.66 1.00 29

What the Students Do Volume 1, Issue 8 Probability 2nd General Lyceum of Kamatero Calculation of probabilities p1 and p2 for each team 17η Αγωνιστική 17th round r1 r2 R=r1/r2 p1 p2 1 Kerkyra Panathinaikos 0.73 1.51 0.48 0.33 0.67 2 Larissa Platanias 0.73 1.13 0.65 0.39 0.61 3 Iraklis Veria 0.93 0.73 1.27 0.56 0.44 4 Olympiakos Xanthi 2 1.13 1.77 0.64 0.36 5 Levadiakos Atromitos 0.9 0.97 0.93 0.48 0.52 6 AEK Asteras Tripolis 1.8 1.17 1.54 0.61 0.39 7 Pas Giannina PAOK 1 1.73 0.58 0.37 0.63 8 Panionios Panetolikos 1.17 0.97 1.21 0.55 0.45 18η Αγωνιστική 18th round r1 r2 R=r1/r2 p1 p2 1 Iraklis Larissa 0.93 0.73 1.27 0.56 0.44 2 Platanias Kerkyra 1.13 0.73 1.55 0.61 0.39 3 Veria Olympiakos 0.73 2 0.37 0.27 0.73 4 Panathinaikos Levadiakos 1.51 0.9 1.68 0.63 0.37 5 Panetolikos PAOK 0.97 1.73 0.56 0.36 0.64 6 Xanthi AEK 1.13 1.8 0.63 0.39 0.61 7 Atromitos Pas Giannina 0.97 1 0.97 0.49 0.51 8 Asteras Tripolis Panionios 1.17 1.17 1.00 0.50 0.50 30

What the Students Do Volume 1, Issue 8 Probability 2nd General Lyceum of Kamatero Calculation of probabilities p1 and p2 for each team 19η Αγωνιστική 19th round r1 r2 R=r1/r2 p1 p2 1 Larissa Kerkyra 0.73 0.73 1.00 0.50 0.50 2 Olympiakos Iraklis 2 0.93 2.15 0.68 0.32 3 Levadiakos Platanias 0.9 1.13 0.80 0.44 0.56 4 Pas Giannina Panathinaikos 1 1.51 0.66 0.40 0.60 5 AEK Veria 1.8 0.73 2.47 0.71 0.29 6 Panionios Xanthi 1.17 1.13 1.04 0.51 0.49 7 Panetolikos Atromitos 0.97 0.97 1.00 0.50 0.50 8 PAOK Asteras Tripolis 1.73 1.17 1.48 0.60 0.40 20η Αγωνιστική r1 r2 R=r1/r2 p1 p2 20th round 1 Olympiakos Larissa 2 0.73 2.74 0.73 0.27 2 Kerkyra Levadiakos 0.73 0.9 0.81 0.45 0.55 3 Iraklis AEK 0.93 1.8 0.52 0.34 0.66 4 Platanias Pas Giannina 1.13 1 1.13 0.53 0.47 5 Veria Panionios 0.73 1.17 0.62 0.38 0.62 6 Panathinaikos Panetolikos 1.51 0.97 1.56 0.61 0.39 7 Xanthi PAOK 1.13 1.73 0.65 0.40 0.60 8 Asteras Tripolis Atromitos 1.17 0.97 1.21 0.55 0.45 31

What the Students Do Volume 1, Issue 8 Probability 2nd General Lyceum of Kamatero Calculation of probabilities p1 and p2 for each team 21η Αγωνιστική r1 r2 R=r1/r2 p1 p2 21st round 1 AEK Olympiakos 1.8 2 0.90 0.47 0.53 2 PAOK Veria 1.73 0.73 2.37 0.70 0.30 3 Asteras Tripolis Panathinaikos 1.17 1.51 0.77 0.44 0.56 4 Larissa Levadiakos 0.73 0.9 0.81 0.45 0.55 5 Pas Giannina Kerkyra 1 0.73 1.37 0.58 0.42 6 Panionios Iraklis 1.17 0.93 1.26 0.56 0.44 7 Panetolikos Platanias 0.97 1.13 0.86 0.46 0.54 8 Atromitos Xanthi 0.97 1.13 0.86 0.46 0.54 22η Αγωνιστική r2 R=r1/r2 p1 p2 r1 22nd round 1 AEK Larissa 1.8 0.73 2.47 0.71 0.29 2 Levadiakos Pas Giannina 0.9 1 0.90 0.47 0.53 3 Olympiakos Panionios 2 1.17 1.71 0.63 0.37 4 Kerkyra Panetolikos 0.73 0.97 0.75 0.43 0.57 5 Iraklis PAOK 0.93 1.73 0.54 0.35 0.65 6 Platanias Asteras Tripolis 1.13 1.17 0.97 0.49 0.51 7 Veria Atromitos 0.73 0.97 0.75 0.43 0.57 8 Xanthi Panathinaikos 1.13 1.51 0.75 0.43 0.57 32

What the Students Do Volume 1, Issue 8 Probability 2nd General Lyceum of Kamatero Calculation of probabilities p1 and p2 for each team 23η Αγωνιστική r1 r2 R=r1/r2 p1 p2 23rd round 1 Larissa Pas Giannina 0.73 1 0.73 0.42 0.58 2 Panionios AEK 1.17 1.8 0.65 0.39 0.61 3 Panetolikos Levadiakos 0.97 0.9 1.08 0.52 0.48 4 PAOK Olympiakos 1.73 2 0.87 0.46 0.54 5 Asteras Tripolis Kerkyra 1.17 0.73 1.60 0.62 0.38 6 Atromitos Iraklis 0.97 0.93 1.04 0.51 0.49 7 Xanthi Platanias 1.13 1.13 1.00 0.50 0.50 8 Panathinaikos Veria 1.51 0.73 2.07 0.67 0.33 24η Αγωνιστική 24th round r1 r2 R=r1/r2 p1 p2 1 AEK PAOK 1.8 1.73 1.04 0.51 0.49 2 Panionios Larissa 1.17 0.73 1.60 0.62 0.38 3 Pas Giannina Panetolikos 1 0.97 1.03 0.51 0.49 4 Levadiakos Asteras Tripolis 0.9 1.17 0.77 0.43 0.57 5 Olympiakos Atromitos 2 0.97 2.06 0.67 0.33 6 Kerkyra Xanthi 0.73 1.13 0.65 0.39 0.61 7 Iraklis Panathinaikos 0.93 1.51 0.62 0.38 0.62 8 Platanias Veria 1.13 0.73 1.55 0.61 0.39 33

What the Students Do Volume 1, Issue 8 Probability 2nd General Lyceum of Kamatero Calculation of probabilities p1 and p2 for each team 25η Αγωνιστική r1 r2 R=r1/r2 p1 p2 25th round 1 Panathinaikos Olympiakos 1.51 2 0.76 0.43 0.57 2 Larissa Panetolikos 0.73 0.97 0.75 0.43 0.57 3 PAOK Panionios 1.73 1.17 1.48 0.60 0.40 4 Asteras Tripolis Pas Giannina 1.17 1 1.17 0.54 0.46 5 Atromitos AEK 0.97 1.8 0.54 0.35 0.65 6 Xanthi Levadiakos 1.13 0.9 1.26 0.56 0.44 7 Veria Kerkyra 0.73 0.73 1.00 0.50 0.50 8 Platanias Iraklis 1.13 0.93 1.22 0.55 0.45 26η Αγωνιστική r1 r2 R=r1/r2 p1 p2 26th round 1 AEK Panathinaikos 1.8 1.51 1.19 0.54 0.46 2 PAOK Larissa 1.73 0.73 2.37 0.70 0.30 3 Panetolikos Asteras Tripolis 0.97 1.17 0.83 0.45 0.55 4 Panionios Atromitos 1.17 0.97 1.21 0.55 0.45 5 Pas Giannina Xanthi 1 1.13 0.88 0.47 0.53 6 Levadiakos Veria 0.9 0.73 1.23 0.55 0.45 7 Olympiakos Platanias 2 1.13 1.77 0.64 0.36 8 Kerkyra Iraklis 0.73 0.93 0.78 0.44 0.56 34

What the Students Do Volume 1, Issue 8 Probability 2nd General Lyceum of Kamatero Calculation of probabilities p1 and p2 for each team 27η Αγωνιστική 27th round r1 r2 R=r1/r2 p1 p2 1 AEK Panathinaikos 1.8 1.51 1.19 0.54 0.46 2 PAOK Larissa 1.73 0.73 2.37 0.70 0.30 3 Panetolikos Asteras Tripolis 0.97 1.17 0.83 0.45 0.55 4 Panionios Atromitos 1.17 0.97 1.21 0.55 0.45 5 Pas Giannina Xanthi 1 1.13 0.88 0.47 0.53 6 Levadiakos Veria 0.9 0.73 1.23 0.55 0.45 7 Olympiakos Platanias 2 1.13 1.77 0.64 0.36 8 Kerkyra Iraklis 0.73 0.93 0.78 0.44 0.56 28η Αγωνιστική 28th round r1 r2 R=r1/r2 p1 p2 1 PAOK Panathinaikos 1.73 1.51 1.15 0.53 0.47 2 Atromitos Larissa 0.97 0.73 1.33 0.57 0.43 3 Asteras Tripolis Xanthi 1.17 1.13 1.04 0.51 0.49 4 Panetolikos Veria 0.97 0.73 1.33 0.57 0.43 5 Panionios Platanias 1.17 1.13 1.04 0.51 0.49 6 Pas Giannina Iraklis 1 0.93 1.08 0.52 0.48 7 AEK Kerkyra 1.8 0.73 2.47 0.71 0.29 8 Levadiakos Olympiakos 0.9 2 0.45 0.31 0.69 35

What the Students Do Volume 1, Issue 8 Probability 2nd General Lyceum of Kamatero Calculation of probabilities p1 and p2 for each team 29η Αγωνιστική 29th round r1 r2 R=r1/r2 p1 p2 1 Larissa Xanthi 0.73 1.13 0.65 0.39 0.61 2 Panathinaikos Atromitos 1.51 0.97 1.56 0.61 0.39 3 Veria Asteras Tripolis 0.73 1.17 0.62 0.38 0.62 4 Platanias PAOK 1.13 1.73 0.65 0.40 0.60 5 Iraklis Panetolikos 0.93 0.97 0.96 0.49 0.51 6 Kerkyra Panionios 0.73 1.17 0.62 0.38 0.62 7 Olympiakos Pas Giannina 2 1 2.00 0.67 0.33 8 Levadiakos AEK 0.9 1.8 0.50 0.33 0.67 30η Αγωνιστική 30th round r1 r2 R=r1/r2 p1 p2 1 Panathinaikos Larissa 1.51 0.73 2.07 0.67 0.33 2 Xanthi Veria 1.13 0.73 1.55 0.61 0.39 3 Atromitos Platanias 0.97 1.13 0.86 0.46 0.54 4 Asteras Tripolis Iraklis 1.17 0.93 1.26 0.56 0.44 5 PAOK Kerkyra 1.73 0.73 2.37 0.70 0.30 6 Panetolikos Olympiakos 0.97 2 0.49 0.33 0.67 7 Panionios Levadiakos 1.17 0.9 1.30 0.57 0.43 8 Pas Giannina AEK 1 1.8 0.56 0.36 0.64 36

What the Students Do Volume 1, Issue 8 Probability 2nd General Lyceum of Kamatero 7. If, at a particular moment in the match, both teams have together scored n goals, the probability that all of the goals have been scored by the first team is, and the probability that all of the goals have been scored by the second team is . The probability that the first team has scored k of n goals is Students calculate this probability for the eight matches of the 30th round for the Superleague Greece, season 2016-17. The results are displayed on the following tables. Students compare these probabilities with the real score of these eight matches. 37

What the Students Do Volume 1, Issue 8 Probability 2nd General Lyceum of Kamatero probability probability probability probability probability that all of that all of 30η Αγωνιστική total first team first team first team the goals the goals number number has scored has scored has scored p1 p2 have been have been of match of goals, 30nth round n k=1 k= 2 k=3 scored by scored by of n=3 of n=3 of n=3 the first the second team team 1 Panathinaikos Larissa 3 0.1 0.31 0.31 0.67 0.33 0.31 0.03 probabil- probabil- probabil- probabil- ity that all ity that all total ity first ity first probability of the of the number team has team has first team has number 30η Αγωνιστική p1 p2 goals have goals have of match of scored scored scored k=3 been been 30nth round goals, n k=1 k=2 of n=3 scored by scored by of n=3 of n=3 the first the sec- team ond team 2 Xanthi Veria 3 0.1 0.26 0.22 0.61 0.39 0.22 0.06 proba- proba- bility bility proba- proba- proba- proba- proba- that all that all bility bility bility bility bility of the of the num- total first first first first first goals goals number team ber of 30η Αγωνιστική team team team team p1 p2 have have match 30nth round of goals, has has has has has been been n scored scored scored scored scored scored scored k=1 k=2 k=3 k=4 k=5 of n=5 of n=5 of n=5 of n=5 of n=5 by the by the first team second team 3 Atromitos Platanias 5 0.0085 0.032 0.058 0.054 0.02 0.46 0.54 0.02 0.05 38

What the Students Do Volume 1, Issue 8 Probability 2nd General Lyceum of Kamatero proba- probabil- probabil- probabil- probabil- probabil- bility ity that all ity that all total ity first ity first ity first first of the of the num- 30η Αγωνιστική number team has team has team has team goals goals have ber of p1 p2 match 30nth round of goals, scored scored scored has have been been n k=1 k=2 k=3 scored scored by scored by of n=4 of n=4 of n=4 k=4 the first the sec- of n=4 team ond team 4 Asteras Tripolis Iraklis 4 0.034 0.12 0.18 0.1 0.56 0.44 0.1 0.04 proba- bility probabil- proba- proba- proba- proba- that all ity that all bility probabil- probabil- bility bility bility total first ity first ity first first first first of the of the numb 30η Αγωνιστική num- team team has team has team team team goals goals er of ber of has scored scored has has has p1 p2 have have match 30nth round goals, scored k=2 k=3 scored scored scored been been n scored scored by k=1 of n=5 of n=5 k=4 k=5 k=6 of n=5 of n=5 of n=5 of n=5 by the the sec- first ond team team 5 PAOK Kerkyra 6 0.00175 0.015 0.065 0.16 0.22 0.12 0.70 0.30 0.12 0.00068 39

What the Students Do Volume 1, Issue 8 2nd General Lyceum of Kamatero Probability probabil- ity that all of the probability probability probability that all of total goals number first team first team have the goals 30η Αγωνιστική has scored has scored p1 p2 have been of goals, k=1 k=2 been scored by n scored of n=2 of n=2 the second by the team first team 6 Panetolikos Olympiakos 2 0.15 0.11 0.33 0.67 0.11 0.45 probabil- probabil- proba- probabil- probabil- probabil- bility ity that ity that total ity first ity first ity first first all of the all of the num- goals goals 30η Αγωνιστική ber of team has team has team has team p1 p2 have have scored has scored scored goals, been been n k=1 k=2 k=3 scored scored by scored by of n=4 of n=4 of n=4 k=4 of n=4 the first the sec- team ond team 7 Panionios Levadiakos 4 0.03 0.11 0.17 0.1 0.57 0.43 0.10 0.04 probabil- probability ity that all probability that all of total probability of the number first team first team has goals the goals 30η Αγωνιστική has scored p1 p2 have been of goals, k=1 scored k=2 have been scored by n of n scored by of n the second the first team team 8 Pas Giannina AEK 2 0.17 0.13 0.36 0.64 0.13 0.41 40

Sport Science Stories Volume 1, Issue 8 2nd General Lyceum http://lolanaenaallo.blogspot.gr/2013/06/blog-post_17.html of Kamatero Το πρώτο δελτίο ΠΡΟ-ΠΟ, η ακμή και η παρακμή του πιο λαϊκού παιχνιδιού στην Ελλάδα! The e-Twinning Group: Sport Science Stories 2017-18 41

Sport Science Stories Volume 1, Issue 8 2nd General Lyceum http://lolanaenaallo.blogspot.gr/2013/06/blog-post_17.html of Kamatero Το πρώτο δελτίο ΠΡΟ-ΠΟ, η ακμή και η παρακμή του πιο λαϊκού παιχνιδιού στην Ελλάδα! Στα τέλη της δεκαετίας του ’50, σε όλες σχεδόν τις ευ- ρωπαϊκές χώ- ρες είχαν δη- μιουργηθεί φορείς που ασχολούνταν με την πρό- γνωση επί των αποτελε- σμάτων πο- δοσφαίρου. The e-Twinning Group: Sport Science Stories 2017-18 42

Sport Science Stories Volume 1, Issue 8 2nd General Lyceum http://lolanaenaallo.blogspot.gr/2013/06/blog-post_17.html of Kamatero Το πρώτο δελτίο ΠΡΟ-ΠΟ, η ακμή και η παρακμή του πιο λαϊκού παιχνιδιού στην Ελλάδα! Έτσι τον Δεκέμβριο του 1958 ιδρύθηκε και στη χώρα μας αντίστοιχος φορέας με την ονομασία Οργανισμός Προγνωστικών Αγώνων Ποδοσφαίρου (Ο.Π.Α.Π.) με σκοπό την οργάνωση και την λειτουργία του Δελτίου Προγνωστικών Ποδοσφαιρικών Αγώ- νων (ΠΡΟ-ΠΟ), προκειμένου να εξευρεθούν πόροι για την στήριξη του Ελληνικού Α- θλητισμού. Το όνομα του παιχνι- διού ΠΡΟ-ΠΟ προέ- κυψε έπειτα από δια- γωνισμό με έπαθλο ένα χρηματικό βρα- βείο. Συμπτωματικά η συγκεκριμένη ονο- μασία είχε προταθεί από τρεις διαφορετι- κούς συμμετέχοντες στον διαγωνισμό, στους οποίους και μοιράσθηκε εξίσου το χρηματικό βραβεί- ο. Το ΠΡΟ-ΠΟ θε- σπίστηκε με Βασιλικό Διάταγ- μα στις 20 Δεκεμβρί- ου 1958. 43

Sport Science Stories Volume 1, Issue 8 2nd General Lyceum http://lolanaenaallo.blogspot.gr/2013/06/blog-post_17.html of Kamatero Το πρώτο δελτίο ΠΡΟ-ΠΟ, η ακμή και η παρακμή του πιο λαϊκού παιχνιδιού στην Ελλάδα! Την Κυριακή 1η Μαρτίου 1959 έγινε ο πρώτος διαγωνισμός του ΠΡΟ-ΠΟ, που έμελλε να καταξιωθεί στη συνείδηση των Ελλήνων σαν ένα λαϊκό παιγνίδι πρό- βλεψης και τύχης που γέμιζε με ελπίδα τους παίκτες και πρόσφερε πολλά χρή- ματα και νέα ζωή στους τυχερούς νικητές του. 44

Sport Science Stories Volume 1, Issue 8 2nd General Lyceum http://lolanaenaallo.blogspot.gr/2013/06/blog-post_17.html of Kamatero Το πρώτο δελτίο ΠΡΟ-ΠΟ, η ακμή και η παρακμή του πιο λαϊκού παιχνιδιού στην Ελλάδα! Το πρώτο δελτίο ΠΡΟ-ΠΟ περιελάμβανε 12 αγώνες και 2 αναπληρωμα- τικούς και ήταν δίστηλο, ενώ είχε δύο κατηγορίες νικητών (12άρηδες και 11άρηδες) που μοιράζονταν το 45% των εσόδων κάθε διαγωνισμού. 45

Sports betting Volume 1, Issue 8 Alexandros Markoulakis Supervising teachers: 2nd General Lyceum Eugenia Potiriadou of Kamatero The e-Twinning Group: Sport Science Stories 2017-18 46