2. BASIC MODEL FORMULAS
• EVERY TEAM STARTED WITH A RATING OF 1500
• W = 30
• DIFFERENCE (HOME TEAM)=HOME TEAM CURRENT RATING - AWAY TEAM CURRENT RATING + HOME ADVANTAGE
• DIFFERENCE (AWAY TEAM)= AWAY TEAM CURRENT RATING - HOME TEAM CURRENT RATING - HOME ADVANTAGE
• EXPECTED WINNING PROBABILITY=1/(1+10^(-DIFFERENCE/400)
• OBSERVED PROBABILITY EQUALS 1 IF WIN, 0.5 IF DRAW AND 0 IF LOSE
• ERROR=OBSERVED PROBABILITY-EXPECTED PROBABILITY
• NEW RATING = PREVIOUS RATING + W * F * ERROR

3. F VALUE
• 𝑭 = |𝑮𝒐𝒂𝒍 𝑫𝒊𝒇𝒇𝒆𝒓𝒆𝒏𝒄𝒆|
• A TEAM THAT WINS BY MORE THAN 1 GOAL IS REWARDED

4. HOME ADVANTAGE CALCULATION
• BUNDESLIGA POINT SYSTEM AFTER 1995: 3 POINTS FOR WIN, 1 POINT FOR DRAW, 0 FOR LOSE
• SINCE 1995, 5814 GAMES PLAYED (2709 HOME WINS, 1485 DRAWS, 1620AWAY WINS)
• APPROXIMATELY 47% OF GAMES ENDED IN HOME WIN, 26% IN A DRAW, 27%IN AWAY WIN
• POINTS PER GAME = 3 * (0.47+0.27) + 2 * 0.26 = 2.75
• PPG (HOME TEAM) = 3 * 0.47 + 0.26 = 1.65 PPG (AWAY TEAM) = 3 * 0.27 + 0.26 = 1.09
• EXP(HT) = PPG(HT)/PPG = 0.60 EXP(AT) = PPG(AT)/PPG = 0.40
• 60% OF THE POINTS GO TO HOME TEAM AND 40% TO AWAY TEAM
• BASIC EXP FORMULA USED IN REVERSE, SOLVED FOR –(RA-RB)
• RA-RB=72

5. SEASON CARRYOVER RATING
• ALL TEAMS STARTED AT 1500 RATING POINTS FOR 2010/2011
• FORMULA NEEDED TO CALCULATE STARTING RATING POINTS FOR THE NEXTSEASONS
• NEW SEASON RATING = 1500 + ((PREVIOUS SEASON FINAL RATING– 1500)/2)
• FOR PROMOTED TEAMS:
STARTING RATING = 1500 + ((AVERAGE PREVIOUS SEASON FINAL RATINGOF RELEGATED TEAMS-1500)/2)

6. THE “DRAW” PROBLEM
• DRAW NEEDS EXACTLY 50% EXPECTED WINNING PROBABILITY
• TWO PATHS: RANGE OR DRAW NO BET
• DRAW NO BET (OR ASIAN HANDICAP 0) IS A SPECIAL BET THAT RETURNSTHE MONEY IF GAME ENDS IN A
DRAW
• WHEN DRAW, BET IS VOID AND NOT INCLUDED IN PERFORMANCE PERCENTAGE CALCULATION