**'GOAT' Points**- The points assigned to players for various tennis achievements, like winning or going deep into tournaments, ATP and Elo rankings, Grand Slam (career and calendar year), big wins, head-to-head ratios, title, streak, performance and statistics records.**Elo Rating System**- The Elo rating is a method for calculating the relative skill levels of players in competitor-versus-competitor games such as chess or tennis. It is named after its creator Arpad Elo, a Hungarian-born American physics professor.**Court Speed**- Court Speed Index (1 - 100): 80 * cube-root(Ace % * (Service Points Won % - 50%) * (Service Games Won % - 50%)) - 56, where statistics figures are adjusted with server's and returner's relative figure difference averaged by season and surface**Surface Specialization**- Surface Specialization rating quantifies how much a player is specialized in his favorite surface. A rating of 50% means that player performance on the favorite surface is at least twice as good as on the worst surface. A theoretical rating of 100% is used when a player wins all matches on the favorite surface and loses all matches on the least favorite surface. The relative difference between the two winning percentages is calculated as the arithmetic mean of the relative difference between winning percentages and the relative difference between corresponding losing percentages. Examples: difference between 50% and 60% is 18%, between 60% and 80% is 37%, between 80% and 90% is 31%. Winning and losing percentages are best-of-adjusted, to address that some surfaces are more often played as BO5 compared to other surfaces.**Adjusted H2H**- Adjusted H2H takes into account surface and importance skew in H2H matches and normalizes it (average of Surface Adjusted H2H and Importance Adjusted H2H)**Surface Adjusted H2H**- Surface adjusted H2H takes into account how much two players have played against each other on different surfaces and then weights their surface H2Hs with how much each of them played on the particular surface**Importance Adjusted H2H**- Importance adjusted H2H weights H2H matches by match importance by tournament level and round as in Big Wins and then normalizes H2H to the actual number of H2H matches played**Tournament Participation**- Participation percentage measures how much the best players participate in the draw (100% if all top players participate in the draw). Formula: sum(ParticipationWeight(rank)) / sum(ParticipationWeight(1..PlayerCount)): i.e. the sum of participation weights of all players in the draw compared to maximal participation weight if all top players would have participated, where participation weight depend on ranking (see Participation Weights in the Glossary page).**Tournament Strength**- Tournament strength measures the strength of the participating players based on weighted Elo ratings of the participating players. Formula: sum(ParticipationWeight(EloSeeding) * (Elo - 1500) / 400) * BestOfFactor, i.e. weighted sum of participating players strengths based on Elo Rating multiplied by best-of factor: 1.25 for Grand Slam, 1 for other tournaments (better player has ~25% more chance to win in best-of-5 compared to best-of-3), where weight depends on Elo-based seeding (see Participation Weights in the Glossary page).**Tournament Elo Rating**- Average Elo rating measures the average strength of the participating players. Formula: sum(ParticipationWeight(EloSeeding) * EloRating) / sum(ParticipationWeight(1..PlayerCount)), i.e. weighted average of participating players Elo ratings at the beginning of the tournament, where weight depend on Elo-based seeding (see Participation Weights in the Glossary page).**Participation Weights**- Participation weights: Weights of players participating in the tournament based on their ranking or seeding (depends on context): [1: 100, 2: 85, 3: 75, 4: 67, 5: 60, 6: 55, 7-8: 50, 9-10: 45, 11-13: 40, 14-16: 35, 17-20: 30, 21-25: 25, 26-30: 20, 31-35: 16, 36-40: 13, 41-45: 10, 46-50: 8, 51-60: 6, 61-70: 5, 71-80: 4, 81-100: 3, 101-150: 2, 151-200: 1]**Title Difficulty**- A factor of difficulty to win the title compared to a difficulty for an average title winner to win an average tournament event of the same tournament level (calculation steps: first, probabilities to win the matches on the path to a title for an average title winner of the same tournament level are calculated based on average Elo Ratings of the title winners as well as Elo Ratings of the opponents the actual winner has faced (P = 1 / (1 + 10 ^ ((AvgWinnerElo - ActualOpponentElo) / 400)); second, difficulty to win the title is calculated as 1 - the product of winning probabilities from the first step (difficulty = 1 - title winning probability); third, title difficulty is normalized so that the average difficulty of the same tournament level is 1). Example: Difficulty factor of 1.125 means that a title was 12.5% harder to win compared to an average title of the same tournament level.**Rivalry Score**- Rivalry score: sum(1 + match GOAT points), where match GOAT points are: [GS F: 8, GS SF: 4, GS QF: 2, GS R16: 1, TF F: 6, TF SF: 3, TF RR: 1, M F: 4, M SF: 2...] as in Big Wins match factor in GOAT Points legend**Match Greatness Score**- Match Greatness Score is proportional to match factor (depending on tournament level and round as in Big Wins), player rankings factor (as in Big Wins), player career-high rankings factor (as in Big Wins), player Elo Ratings (((WinnerElo - 1500) / 400 + (LoserElo - 1500) / 400) / 2) and match length (sqrt(sets * (games + 2 * tie-breaks)))**Mental Toughness Rating**- Mental Toughness Rating compares players in pressure situations: Mental Toughness Rating = Mental Points won / Mental Points lost**Mental Point**- Mental Points are weighted pressure situations: Mental Point = 2 * Best-of-3 Deciding Set + 4 * Best-of-5 Deciding Set + 2 * Final Match + Non-Deciding Set Tie-Break + 2 * Deciding Set Tie Break**Draw Bonus**- Draw Bonus represents how much a player has benefited or penalized with the actual draw. It is calculated as a relative difference in the title-winning percentage of the actual draw compared to the average draw without seeding and with random byes. Thus Draw Bonus incorporates both draw luck and draw seeding factors.

**First Serve Effectiveness**- First Serve Effectiveness: 1st serve points won % divided by 2nd serve points won %**Service In-play Points Won %**- Service in-play points won % (excluding aces and double faults)**Serve Rating**- Ace % - Double Faults % + 1st Serve % + 1st Serve Points Won % + 2nd Serve Points Won % + Break Points Saved % + Service Games Won %**1st / 2nd Serve Speed Ratio**^{}- First serve average speed divided by second serve average speed**Serve Maximum / Average Speed Ratio**^{}- Serve maximum speed divided by serve average speed**Return In-play Points Won %**- Return in-play points won % (excluding aces and double faults against)**Return Rating**- 1st Serve Return Points Won % + 2nd Serve Return Points Won % + Break Points Converted % + Return Games Won %**Total 2nd Serve In-play Points Won %**- Total (serve + return) 2nd serve in-play points won %**Return to Service Points Ratio**- Return points played divided by service points played**Points Dominance Ratio**- Points Dominance Ratio: % of return points won divided by % of service points lost**In-play Points Dominance Ratio**- In-play Points Dominance Ratio: % of return in-play points won divided by % of service in-play points lost (excluding aces and double faults)**2nd Serve In-play Points Dominance Ratio**- 2-nd Serve In-play Points Dominance Ratio: % of 2-nd serve return in-play points won divided by % of 2-nd serve service in-play points lost (excluding double faults)**Winner %**^{}- Number of sinners divided by total points won**Unforced Error %**^{}- Number of unforced errors divided by total points lost**Forced Error %**^{}- Number of forced errors divided by total points lost**Winners to Unforced Errors Ratio**^{}- Number of winners divided by number of unforced errors**Winner Against %**^{}- Number of winners against the player divided by total points lost**Unforced Error Against %**^{}- Number of unforced errors against the player divided by total points won**Forced Error Against %**^{}- Number of forced errors against the player divided by total points won**Winners to Forced Errors Against Ratio**^{}- Number of winners divided by number of forced errors against the player**Net Points %**^{}- Number of net points played divided by total points played**Points Won at Net %**^{}- Number of net points won divided by total points won**Net Effectiveness**^{}- % of net points won divided by % of total points won**Games Dominance Ratio**- Games Dominance Ratio: % of return games won divided by % of service games lost**Break Points Ratio**- Break Points Ratio: % of break points converted divided by % of faced break points lost**Over-Performing Ratio**- Points to Matches Over-Performing Ratio: % of matches won divided by % of total points won**Points to Sets Over-Performing Ratio**- Points to Sets Over-Performing Ratio: % of sets won divided by % of total points won**Points to Games Over-Performing Ratio**- Points to Games Over-Performing Ratio: % of games won divided by % of total points won**Service Points to Service Games Over-Performing Ratio**- Service Points to Service Games Over-Performing Ratio: % of service games won divided by % of service points won**Return Points to Return Games Over-Performing Ratio**- Return Points to Return Games Over-Performing Ratio: % of return games won divided by % of return points won**Points to Tie-Breaks Over-Performing Ratio**- Points to Tie-Breaks Over-Performing Ratio: % of tie-breaks won divided by % of total points won**Games to Matches Over-Performing Ratio**- Games to Matches Over-Performing Ratio: % of matches won divided by % of games won**Games to Sets Over-Performing Ratio**- Games to Sets Over-Performing Ratio: % of sets won divided by % of games won**Sets to Matches Over-Performing Ratio**- Sets to Matches Over-Performing Ratio: % of matches won divided by % of sets won**Break Points Over-Performing Ratio**- Break Points Over-Performing Ratio: % of break points won (saved + converted) divided by % of total points won**Break Points Saved Over-Performing Ratio**- Break Points Saved Over-Performing Ratio: % of break points saved divided by % of service points won**Break Points Converted Over-Performing Ratio**- Break Points Converted Over-Performing Ratio: % of break points converted divided by % of return points won**Opponent Rank**- Average opponent rank (geometric mean)**Opponent Elo Rating**- Average opponent Elo rating (arithmetic mean)**Upsets scored**- Matches won over higher-ranked players (according to ATP ranking)**Upsets scored %**- % of Matches won over higher-ranked players (according to ATP ranking)**Upsets against**- Matches lost from lower-ranked players (according to ATP ranking)**Upsets against %**- % of Matches lost from lower-ranked players (according to ATP ranking)**Upsets**- Matches won over higher-ranked players + Matches lost from lower-ranked players (according to ATP ranking)**Upsets %**- % Matches won over higher-ranked players + Matches lost from lower-ranked players (according to ATP ranking)