Season Win Totals Math

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  • jayule
    SBR Rookie
    • 04-20-12
    • 16

    #1
    Season Win Totals Math
    Quick math question on season win totals.

    Let's say the Atlanta Falcons have a season win total 8.5, with -140 on the over and 120 on the under. The no-vig % for that are 56.2% chance of over and 43.8% of under. How do I take those percentages apply them to the 8.5. I assume it will give me some number like 8.7 but I'm not sure how to apply the % chance of happening to the base # of 8.5. I read somewhere that 50 cents of juice equals a half game but I'm not sure how to calculate that. Any help would be appreciated.

    Jayule
  • mathdotcom
    SBR Posting Legend
    • 03-24-08
    • 11689

    #2
    When a point/run/goal/win is worth a lot, there's no such thing as a perfect number that you can always offer -110/-110 on each side because of the unfortunate reason that 8.5 -140/120 is the same as 8.7 -140/120

    In this case if you offered 8 -110/-110 you would love the over and if you offered 9 -110/-110 I presume you would have to like the under. (Surely a win is worth at least 30cents)

    If you want to put a fair price on a total of 8 or 9 you will have to know what a half-win is worth
    Comment
    • Justin7
      SBR Hall of Famer
      • 07-31-06
      • 8577

      #3
      Originally posted by jayule
      Quick math question on season win totals.

      Let's say the Atlanta Falcons have a season win total 8.5, with -140 on the over and 120 on the under. The no-vig % for that are 56.2% chance of over and 43.8% of under. How do I take those percentages apply them to the 8.5. I assume it will give me some number like 8.7 but I'm not sure how to apply the % chance of happening to the base # of 8.5. I read somewhere that 50 cents of juice equals a half game but I'm not sure how to calculate that. Any help would be appreciated.

      Jayule
      Half-games are worth a ton in the NFL. For 8.5, first figure out the no-juice line. That gives you a baseline for winning 9+ games. With that, you can use a binomial distribution to figure out the implied odds of winning a single game. And with that, you can price any over/under.
      Comment
      • MonkeyF0cker
        SBR Posting Legend
        • 06-12-07
        • 12144

        #4
        Originally posted by Justin7
        Half-games are worth a ton in the NFL. For 8.5, first figure out the no-juice line. That gives you a baseline for winning 9+ games. With that, you can use a binomial distribution to figure out the implied odds of winning a single game. And with that, you can price any over/under.
        Eh? You're going to treat every game with equal probability?

        Interesting approach.
        Comment
        • mark49
          SBR Rookie
          • 03-03-08
          • 42

          #5
          This is probably not the way to approach it but I used power ratings to make a line (and from that a percentage chance of winning) for each game on the Falcons schedule and used them in a monte carlo sim to work out the probability for each win total.

          The cumulative for 0 to 8 wins came out at 45% (55% for 9+)
          Exactly eight wins came out at 18.9% and exactly nine wins 20%

          Not sure if that has any use though?

          I would guess a lot of those win totals will be tweaked to reflect public opinion etc
          Comment
          • Justin7
            SBR Hall of Famer
            • 07-31-06
            • 8577

            #6
            Originally posted by MonkeyF0cker
            Eh? You're going to treat every game with equal probability?

            Interesting approach.
            It gets you close. You can use two binomials on the old win percentage (adding 0.1, and subtracting 0.1 from the win percentages) to get closer. You guys are tough on your grading of 3-sentence solutions.
            Comment
            • Emily_Haines
              SBR Posting Legend
              • 04-14-09
              • 15917

              #7
              Screw the math............this works better

              NFL win totals research: Over last decade, blindly betting the 'over' on totals of 6 or less hits 65% (28-15-1)
              Comment
              • Waterstpub87
                SBR MVP
                • 09-09-09
                • 4102

                #8
                Originally posted by Emily_Haines
                Screw the math............this works better

                NFL win totals research: Over last decade, blindly betting the 'over' on totals of 6 or less hits 65% (28-15-1)
                It makes sense because the public overestimates the magnitude of skill. I wonder if that would make the inverse true, betting the under on 12 or 11 would hit that much.
                Comment
                • MonkeyF0cker
                  SBR Posting Legend
                  • 06-12-07
                  • 12144

                  #9
                  Originally posted by Justin7
                  It gets you close. You can use two binomials on the old win percentage (adding 0.1, and subtracting 0.1 from the win percentages) to get closer. You guys are tough on your grading of 3-sentence solutions.
                  How close? What's the point of a three sentence solution if it's wrong?

                  And how does using "two binomials" get you closer? That's just as arbitrary as using equivalent probabilities.
                  Comment
                  • Justin7
                    SBR Hall of Famer
                    • 07-31-06
                    • 8577

                    #10
                    Originally posted by MonkeyF0cker
                    How close? What's the point of a three sentence solution if it's wrong?

                    And how does using "two binomials" get you closer? That's just as arbitrary as using equivalent probabilities.
                    In a 16 game season, you take the sum of two distributions. 8 games, p+0.1, added to 8 games, p-0.1.
                    Comment
                    • mathdotcom
                      SBR Posting Legend
                      • 03-24-08
                      • 11689

                      #11
                      Originally posted by Justin7
                      In a 16 game season, you take the sum of two distributions. 8 games, p+0.1, added to 8 games, p-0.1.
                      Comment
                      • MonkeyF0cker
                        SBR Posting Legend
                        • 06-12-07
                        • 12144

                        #12
                        Originally posted by Justin7
                        In a 16 game season, you take the sum of two distributions. 8 games, p+0.1, added to 8 games, p-0.1.
                        Uhh. What?

                        It's a combinatorics problem. There is no universal push frequency and what(ever) you're doing is just throwing darts.
                        Comment
                        • Justin7
                          SBR Hall of Famer
                          • 07-31-06
                          • 8577

                          #13
                          Originally posted by MonkeyF0cker
                          Uhh. What?

                          It's a combinatorics problem. There is no universal push frequency and what(ever) you're doing is just throwing darts.
                          Do you assign a p(t1,t2)? So 16 game season, odds of each game, and do a distribution? This has only a very marginal gain over a much simpler approach.

                          Limits are only 500, so this is sort of a waste of time. That said, if you are up to a friendly challenge, I'll do my season wins numbers, list plays. You do the same. Whomever is closer to closing prices wins.
                          Comment
                          • MonkeyF0cker
                            SBR Posting Legend
                            • 06-12-07
                            • 12144

                            #14
                            Originally posted by Justin7
                            Do you assign a p(t1,t2)? So 16 game season, odds of each game, and do a distribution? This has only a very marginal gain over a much simpler approach.

                            Limits are only 500, so this is sort of a waste of time. That said, if you are up to a friendly challenge, I'll do my season wins numbers, list plays. You do the same. Whomever is closer to closing prices wins.
                            WTF are you talking about? Marginal gain? The gain implicitly depends on your projected ML's. It has nothing to do with adding arbitrary percentages to random probabilities.

                            Closer to closing price doesn't mean anything to me in a futures market anyway. People like you are in the market. I don't model NFL and I don't waste my time or especially my capital on season-long futures. But, yeah, a sample of a possible 32 win totals would prove a whole lot either way anyway.
                            Comment
                            • Justin7
                              SBR Hall of Famer
                              • 07-31-06
                              • 8577

                              #15
                              Originally posted by MonkeyF0cker
                              WTF are you talking about? Marginal gain? The gain implicitly depends on your projected ML's. It has nothing to do with adding arbitrary percentages to random probabilities.

                              Closer to closing price doesn't mean anything to me in a futures market anyway. People like you are in the market. I don't model NFL and I don't waste my time or especially my capital on season-long futures. But, yeah, a sample of a possible 32 win totals would prove a whole lot either way anyway.
                              I'm talking about assigning a power ranking to each team. Give each team a ranking of 0 to 1, which is the probability of it beating an "average" team on a neutral field. The .1 adjustment (perhaps 0.09 is more accurate) is for HFA.

                              An average team with an average schedule have a distribution of Binom(8,0.6) + Binom(8,0.4). A good team (expected to win 12 games) would be Binom(8,0.85) + Binom(8,.65).
                              Comment
                              • MonkeyF0cker
                                SBR Posting Legend
                                • 06-12-07
                                • 12144

                                #16
                                Originally posted by Justin7
                                I'm talking about assigning a power ranking to each team. Give each team a ranking of 0 to 1, which is the probability of it beating an "average" team on a neutral field. The .1 adjustment (perhaps 0.09 is more accurate) is for HFA.

                                An average team with an average schedule have a distribution of Binom(8,0.6) + Binom(8,0.4). A good team (expected to win 12 games) would be Binom(8,0.85) + Binom(8,.65).
                                So, you go through all the trouble of creating accurate power rankings for teams, but then can't take the time to calculate a simple C(n, k) based on their actual schedule?

                                Uhh. Ok. Makes sense.

                                Comment
                                • Justin7
                                  SBR Hall of Famer
                                  • 07-31-06
                                  • 8577

                                  #17
                                  What is the gain from entering 32 16-game schedules? (or a 16x16 grid)? Is it worth the time? Probably not in a small market.
                                  Comment
                                  • MonkeyF0cker
                                    SBR Posting Legend
                                    • 06-12-07
                                    • 12144

                                    #18
                                    How long do you think it takes?
                                    Comment
                                    • AlwaysDrawing
                                      SBR Wise Guy
                                      • 11-20-09
                                      • 657

                                      #19
                                      You two...

                                      Each of you should just post the plays so the rest of the forum can win some maney.
                                      Comment
                                      • Justin7
                                        SBR Hall of Famer
                                        • 07-31-06
                                        • 8577

                                        #20
                                        40 minutes?

                                        If I get 6 $500 bets with a 6% EV, I have $180 in equity (on credit, obviously). Assume your improved method raises it to 7%. Would you sell 40 minutes of time for $30 in equity? I wouldn't.
                                        Comment
                                        • MonkeyF0cker
                                          SBR Posting Legend
                                          • 06-12-07
                                          • 12144

                                          #21
                                          Right. I'm sure you're making quite a bit more than $45/hr as a mod here. Why would you sell your time for that?

                                          But in a 16 game set, if you're only off by 1% in win percentage each game, it doesn't make much of a difference. Only a few insignificant percentage points of edge. Oh, wait, you're only getting a 6% edge? Well, I guess I'll take that back then.
                                          Comment
                                          • mathdotcom
                                            SBR Posting Legend
                                            • 03-24-08
                                            • 11689

                                            #22
                                            Originally posted by AlwaysDrawing
                                            You two...

                                            Each of you should just post the plays so the rest of the forum can win some maney.
                                            Maney maney maney maney
                                            Comment
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