'Start of file BBallQ.Bas ************************************************** DECLARE SUB ReadInt (Mess AS STRING, Min AS INTEGER, Max AS INTEGER, Nom AS INTEGER, I AS INTEGER) 'Read in an integer DECLARE SUB ReadReal (Mess AS STRING, Min AS DOUBLE, Max AS DOUBLE, Nom AS DOUBLE, R AS DOUBLE) 'Read in a Real number Name$ = "BBallQ - Baseball probability (if each game is a 50-50 chance)." Version$ = "QuickBASIC Version 2.03, last revised: 1993-09-27, 0600 hours" Author$ = "Copyright (c) 1981-1993 by author: Harry J. Smith," Address$ = "19628 Via Monte Dr., Saratoga CA 95070. All rights reserved." '*************************************************************************** 'Computes the probability that the 1st place team will beat the 2nd place 'team for the division title, assuming each has a 50-50 chance of winning 'any given future game. Uses a bivariate binomial distribution as a model 'Developed in Turbo Pascal 5.0, converted to QuickBASIC 4.5 'Global variables: ESC$ = CHR$(27) DIM TN1 AS STRING 'Team's name, 1st place team DIM TN2 AS STRING 'Team's name, 2nd place team DIM GL1 AS INTEGER 'Games Left to play, 1st place team DIM GL2 AS INTEGER 'Games Left to play, 2nd place team DIM GE AS INTEGER 'Games to play each other DIM GA AS DOUBLE 'Games 1st place team is ahead. 0, 0.5, ... DIM GA2 AS INTEGER 'Twice games ahead = 2 * GA, 0, 1, ... DIM MNT1 AS INTEGER 'Magic Number to tie for 1st place team DIM MNW1 AS INTEGER 'Magic Number to win for 1st place team DIM MNT2 AS INTEGER 'Magic Number to tie for 2nd place team DIM MNW2 AS INTEGER 'Magic Number to win for 2nd place team DIM P AS DOUBLE 'Probability that 1st place team beats 2nd place team DIM Q AS DOUBLE 'Probability that 2nd place team beats 1st place team DIM Ch$(1) 'Character DIM Debug AS INTEGER '<> 0 if debug turned on '-------------------------------------- 'Main program, BBallQ Debug = 0 DO GOSUB Init GOSUB GetCase GOSUB ExpandCase GOSUB ComputeProb GOSUB Init GOSUB DisplayCase GOSUB DisplayProb PRINT "Press any key to continue... (or ESC to exit)"; Ch$ = INPUT$(1) LOOP UNTIL Ch$ = ESC$ END 'End Main program, BBallQ '-------------------------------------- Init: 'Initialize program COLOR 14, 1 'Yellow on Blue CLS PRINT PRINT Name$ PRINT Version$ PRINT Author$ PRINT Address$ PRINT RETURN 'Init '-------------------------------------- GetCase: 'Get data for a case to compute DIM I AS INTEGER ' Giants, Braves 1993 TN1 = "Braves": TN2 = "Giants" GL1 = 6: GL2 = 7: GE = 0: GA = 1.5 '1993-09-27, 1 / Q = 4.7175 St$ = "Games Left to play, 1st place team (-2 => Exit, -1 => Test case)" CALL ReadInt(St$, -2, 162, -1, I) IF I = -2 THEN END IF I >= 0 THEN TN1 = " ": TN2 = " " GL1 = I CALL ReadInt("Games Left to play, 2nd place team", 0, 162, GL1, GL2) CALL ReadInt("Games to play each other", 0, 24, 0, GE) DO CALL ReadReal("Games ahead, 0, 0.5, ...", 0, 162#, 0, GA) LOOP UNTIL (INT(GA + GA) = GA + GA) END IF RETURN 'GetCase '-------------------------------------- ExpandCase: 'Compute related data GA2 = CINT(2 * GA) 'Round I = GL1 + GL2 - GA2 IF (I MOD 2 = 1) THEN 'if I is odd PRINT "Error in data" PRINT "Press any key to continue...": Ch$ = INPUT$(1) END IF MNT1 = INT(I / 2): MNW1 = MNT1 + 1 MNT2 = GL1 + GL2 - MNT1: MNW2 = MNT2 + 1 RETURN 'ExpandCase '-------------------------------------- DisplayCase: PRINT USING "########"; GL1; PRINT " = Games Left to play, 1st place team ("; TN1; ")" PRINT USING "########"; GL2; PRINT " = Games Left to play, 2nd place team ("; TN2; ")" PRINT USING "########"; GE; : PRINT " = Games to play each other" PRINT USING "######.#"; GA; : PRINT " = Games 1st place team is ahead. 0, 0.5, ..." PRINT USING "########"; MNT1; : PRINT " = Magic Number to tie for 1st place team" PRINT USING "########"; MNW1; : PRINT " = Magic Number to win for 1st place team" PRINT USING "########"; MNT2; : PRINT " = Magic Number to tie for 2nd place team" PRINT USING "########"; MNW2; : PRINT " = Magic Number to win for 2nd place team" PRINT RETURN 'DisplayCase '-------------------------------------- ComputeProb: 'Compute probability using a bivariate binomial 'distribution as a model ' DIM I AS INTEGER DIM J AS INTEGER DIM A AS DOUBLE DIM B AS DOUBLE DIM E(0 TO 24) AS DOUBLE 'Binomial coefficients, games to play each other DIM S(0 TO 24) AS DOUBLE 'Running sum of 2 * E[I] DIM F(0 TO 162) AS DOUBLE 'B. C., games not played with each other DIM G(0 TO 162) AS DOUBLE 'Sum of 2 * E[I] for 2nd place team win, E[I] for tie A = GL1 + GL2 - GE - GE 'A = not played with each other games B = 1 F(0) = 1 FOR I = 1 TO MNT1 'Compute binomial coefficients F(I) = F(I - 1) * A / B A = A - 1 B = B + 1 NEXT I A = GE B = 1 E(0) = 1 S(0) = 2 FOR I = 1 TO GE 'Compute binomial coefficients E(I) = E(I - 1) * A / B A = A - 1 B = B + 1 S(I) = S(I - 1) + 2 * E(I) NEXT I FOR I = 0 TO MNT1 'Compute G[I] J = INT((MNT1 - I) / 2) IF J <= GE THEN G(I) = S(J) IF (J + J) = (MNT1 - I) THEN G(I) = G(I) - E(J) ELSE 'Adjust for tie ELSE G(I) = S(GE) END IF NEXT I IF Debug THEN GOSUB DisplayCase FOR I = 0 TO MNT1 PRINT "F["; I; "] = "; F(I) NEXT I PRINT PRINT "Press any key to continue...": Ch$ = INPUT$(1) PRINT FOR I = 0 TO GE PRINT "E["; I; "] = "; E(I) NEXT I PRINT PRINT "Press any key to continue...": Ch$ = INPUT$(1) PRINT FOR I = 0 TO GE PRINT "S["; I; "] = "; S(I) NEXT I PRINT PRINT "Press any key to continue...": Ch$ = INPUT$(1) PRINT FOR I = 0 TO MNT1 PRINT "G["; I; "] = "; G(I) NEXT I PRINT PRINT "Press any key to continue...": Ch$ = INPUT$(1) PRINT END IF 'Debug Q = 0 FOR I = 0 TO MNT1 'Compute probability that 2nd place team beats 1st place team Q = Q + F(I) * G(I) NEXT I A = GL1 + GL2 - GE + 1 B = EXP(A * LOG(2#)) '2 ** Flips (natural log) Q = Q / B P = 1 - Q RETURN 'ComputeProb '-------------------------------------- DisplayProb: 'Display probability PRINT USING "#####.####"; P; PRINT " = P = Probability that 1st place team beats 2nd place team" PRINT USING "#####.####"; Q; PRINT " = Q = Probability that 2nd place team beats 1st place team" IF Q > 0 THEN PRINT USING "#####.####"; 1 / Q; PRINT " = 1 / Q, (Odds = "; PRINT USING "#.####"; P / Q; PRINT " : 1)" END IF PRINT RETURN 'DisplayProb '-------------------------------------- SUB ReadInt (Mess AS STRING, Min AS INTEGER, Max AS INTEGER, Nom AS INTEGER, I AS INTEGER) 'Read in an integer from keyboard DIM LI AS LONG DO PRINT Mess PRINT " ["; Min; ","; Max; "] (ENTER => "; Nom; INPUT "): ", St$ LI = VAL(St$) LOOP UNTIL ((LI >= Min) AND (LI <= Max)) OR (St$ = "") IF St$ = "" THEN LI = Nom I = LI PRINT "Input = "; I PRINT END SUB 'ReadInt '-------------------------------------- SUB ReadReal (Mess AS STRING, Min AS DOUBLE, Max AS DOUBLE, Nom AS DOUBLE, R AS DOUBLE) 'Read in a Real from keyboard DO PRINT Mess PRINT " ["; : PRINT USING "#.#"; Min; : PRINT ", "; PRINT USING "###.#"; Max; : PRINT "] (ENTER => "; PRINT USING "#.#"; Nom; INPUT "): ", St$ R = VAL(St$) LOOP UNTIL ((R >= Min) AND (R <= Max)) OR (St$ = "") IF St$ = "" THEN R = Nom PRINT "Input = "; : PRINT USING "###.#"; R PRINT END SUB 'ReadReal 'End of file BBallQ.Bas *************************************

Return to Harry's Home Page

This page accessed times since October 20, 2004.

Page created by: hjsmithh@sbcglobal.net

Changes last made on Saturday, 14-May-05 12:42:47 PDT