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Probability of a MegaMillions rollover.

Topic closed. 352 replies. Last post 10 years ago by Prob988.

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Posted: February 4, 2006, 5:44 am - IP Logged

After 315 (Closer to 310) it would probably jump to 390 on the next roll like powerball would have except for the cap rule. How does higher sales impact these predictions? Like if it went from 302 to 375 to 475?

I really can't say, since we haven't gone beyond there.  This is a mathematical model that uses curve fitting techniques to generate model sales figures from which I generate the jackpots.  It doesn't make "educated guesses."  It's pure math.  The curve is determined by inputs of sales from previous drawings.  Each point is generated by a running average.  The $315 jackpot only has one data point input so far, whereas the current jackpots have 5 different jackpots that have reached this area.

The model is inaccurate for the first several drawings (because of the minimum jackpot sizes), but in the jackpot region in which we are now, it seems to be accurate within 1 to 2%.  We can see that it predicted the new 51.8 M cash/$88M annuity jackpot pretty well.

I suspect it will prove less accurate out beyond a $300M jackpot.

Mathematical models are better in areas where history has several repeats.  When conditions change they are not so good.    For instance weather forecasters had no idea what was going on with the hurricanes this summer because the climate is rapidly changing.  They were continually surprised by the power of the hurricanes because their old models didn't work very well, because heat flows have changed with the atmosphere.  This is why I don't have a program like this for powerball.  The matrix changed too recently.  There really isn't enough data. 

 

 

 

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    Posted: February 4, 2006, 10:11 am - IP Logged

    The MM has rolled over.  The cash value is now $51.9M and the annuity value is $88.  A running average of 9th draw sales since the matrix change suggests that the sales will be around 24.6M.  If this many tickets are ultimately sold, the probability of various numbers of winners is given in the following table:

    086.94%
    112.17%
    20.85%
    30.04%

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      Posted: February 5, 2006, 9:52 pm - IP Logged

      Here is the long term probability spreadsheet updated with the latest data.

       

       $513,994,723.76$306,060,49551.46%0.92%
       $451,651,912.87$268,938,18455.40%1.79%
       $396,232,427.14$235,938,40059.16%3.23%
       $346,967,413.99$206,603,32462.71%5.46%
      $315 $303,173,403.84$180,525,98166.04%8.71%
      $262 $264,242,828.12$157,344,59369.16%13.19%
      $225 $229,635,590.25$136,737,55672.05%19.07%
      $192 $198,871,572.76$118,418,98274.72%26.47%
      $165 $171,523,976.40$102,134,73177.18%35.42%
      $147 $147,213,399.05$87,658,88879.43%45.90%
      $128 $125,602,572.15$74,790,62381.49%57.78%
      $108 $106,391,681.67$63,351,41083.36%70.91%
      $90 $89,314,208.65$53,182,55285.06%85.06%

       

      As before, the first column is the historical values in the run that went to $315M last year in this matrix.  The second column is a calculated value of the annuity generally advertised.  The third column is the cash values obtained as discussed below, the 4th column is the probability that each particular roll will rollover and the last column is the probability that a particular roll plus all other rolls between here and there will rollover.  Thus we see we have a better than even chance of having a $147M annuity jackpot in this run and a slightly less than even chance that we will have a $170M annuity.

      The actual advertised cash value right now is $51.9M and the actual annuity advertised value is $88M.  The annuity value reached in the last jackpot was $44.5, about 0.5M from what the model predicted before update.  (Updated with the new data, the program would have predicted $44.1 for that run.)

      The data is the average of sales as listed on the lottoreport website for each drawing in a sequence until the jackpot is won.  The data applied to generate the equation  now generates the following equation for predicting sales, from which the jackpots are calculated:


      S = $9,853,856*exp(0.112*N)

      where exp() refers to the exponential function and N is the drawing in the sequence of starting (N=1) jackpots and rollover jackpots.    The cash jackpot is calculated by summing all the predicted sales in the run and multiplying this sum by 0.318.

      I am very happy with the way the model is performing right now.  It seems fairly accurate.

      For those with an interest in mathematics, the least squares model equations can be found here:

      http://mathworld.wolfram.com/LeastSquaresFittingExponential.html

       

       

       

       

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        Posted: February 8, 2006, 8:04 am - IP Logged

        The MM has rolled over.  The cash value is now $60.7M and the annuity value is $102M.  A running average of 10th draw sales (2 data points) since the matrix change suggests that the sales will be around 29.9M.  If this many tickets are ultimately sold, the probability of various numbers of winners is given in the following table:

        084.37%
        114.34%
        21.22%
        30.07%

        The mathematical model for predicting jackpots was off by 4.3% on the cash value.  I'm not sure how accurate it will prove since from here on in we have just 2 data points for sales figures dating to the matrix change.

         

        For what it's worth, here is the long term table of jackpot probabilities according to the model.

         

         

         $584,283,588.32$347,914,31847.38%0.51%
        $514,188,051.06$306,175,61251.47%1.08%
        $451,869,021.66$269,067,46355.41%2.10%
        $396,463,762.26$236,076,14959.16%3.79%
        $347,205,248.47$206,744,94362.71%6.41%
        $315 $303,411,550.76$180,667,78766.04%10.23%
        $262 $264,476,393.96$157,483,67169.15%15.49%
        $225 $229,860,763.98$136,871,63772.04%22.40%
        $192 $199,085,445.79$118,546,33474.71%31.09%
        $165 $171,724,389.25$102,254,06877.16%41.61%
        $147 $147,398,810.85$87,769,29279.42%53.93%
        $128 $125,771,949.93$74,891,47981.47%67.90%
        $108 $106,544,406.58$63,442,35183.35%83.35%

         

        We'll see how accurate the model will prove later in the run, if it continues.

         

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          Posted: February 11, 2006, 8:09 am - IP Logged

          The MM has rolled over.  The cash value is now $71.5M and the annuity value is $120M.  A running average of 11th draw sales (2 data points) since the matrix change suggests that the sales will be around $31.0M.  If this many tickets are ultimately sold, the probability of various numbers of winners is given in the following table:

          083.83%
          114.79%
          21.30%
          30.08%

          The mathematical model for predicting jackpots was off by 4.4% on the cash value when compared with the advertised jackpot.  I'm not sure how accurate it will prove since from here on in we have just 2 data points for sales figures dating to the matrix change.

          The model looks off based on the advertised sales, but the actual cash jackpot, despite prediction of a $60.7M cash jackpot, reached $62.7M last time out, based on sales, while the model predicted $63.4M in sales.    This was within 1.1%.  Thus the model used here predicted that actual last jackpot better than the lottery advertising did for cash value.  It is important to make the distinction between what is advertised and what is delivered.  Here the lottery is under advertising itself.

          For what it's worth, here is the long term table of jackpot probabilities according to the model:

           

           $585,220,376.56$348,693,80847.38%0.61%
           $515,176,000.86$306,959,03451.46%1.29%
           $452,879,138.14$269,840,48655.39%2.50%
           $397,472,846.53$236,827,57159.13%4.52%
           $348,194,969.35$207,466,16962.67%7.65%
          $315 $304,367,651.02$181,352,39265.99%12.20%
          $262 $265,388,012.67$158,127,02469.10%18.49%
          $225 $230,719,859.01$137,470,58371.98%26.76%
          $192 $199,886,302.59$119,098,92274.65%37.17%
          $165 $172,463,203.84$102,759,32677.10%49.80%
          $147 $148,073,336.68$88,227,03079.35%64.59%
          $128 $126,381,199.50$75,302,13181.41%81.41%

           

          As before, the first column is the historical values in the run that went to $315M last year in this matrix.  The second column is a calculated value of the annuity generally advertised.  The third column is the cash values obtained as discussed below, the 4th column is the probability that each particular roll will rollover and the last column is the probability that a particular roll plus all other rolls between here and there will rollover.


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            Posted: February 11, 2006, 12:53 pm - IP Logged

            Prob988, CA SLP Jackpot hit 84 million after 20 rolls and then it finally won on January 21st. How did these sales of MM have fared since then? Also, Mega Millions only had one jackpot winner when it rolled only once in 2006. I think it's very rare to see jackpot winners at the starting point.

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              Posted: February 11, 2006, 9:01 pm - IP Logged

              Prob988, CA SLP Jackpot hit 84 million after 20 rolls and then it finally won on January 21st. How did these sales of MM have fared since then? Also, Mega Millions only had one jackpot winner when it rolled only once in 2006. I think it's very rare to see jackpot winners at the starting point.

              Qualatively, without too much analysis, sales for MM seemed relatively unaffected by the large CA jackpot.  CA often exceeds NY sales, but NY seems to have contributed the most to MM sales in general.  There doesn't seem to have been much of a change, which is somewhat surprising.

               

              According to my records there have been more than one winner only twice in the since switching from the Big Game to Megamillions.  On 11/11/03 there were 3 winners of a $70M annuity jackpot and 2 winners of a $35M annuity jackpot on 11/29/05.

              There has only been one occasion where back to back jackpots (no rollovers) occurred.  This was 7/23/04 and 7/27/04.   

              This is a measure of how long the odds are against winning the lottery.  However the odds against winning the lottery are much smaller than the odds of being born.  Everyone who exists has already won the lottery in that sense. 

               

               

               

               

               

                dvdiva's avatar - 8ball

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                Posted: February 13, 2006, 1:36 am - IP Logged

                Unless they are a test tube baby.

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                  Posted: February 13, 2006, 8:13 am - IP Logged

                  Unless they are a test tube baby.

                  No, the same odds apply to test tube babies.

                  Test tube babies are even more unlikely that normally conceived babies.

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                    Posted: February 15, 2006, 8:49 pm - IP Logged

                    The MM has rolled over.  The cash value is now $85.4 and the annuity value is $145M.  A running average of 12th draw sales (2 data points) since the matrix change suggests that the sales will be around $36.1M.  If this many tickets are ultimately sold, the probability of various numbers of winners is given in the following table:

                     

                    081.43%
                    116.73%
                    21.72%
                    30.12%
                    40.01%

                    The actual jackpot reached, according to sales, a $73.8M cash value.  The modeling program I use was therefore off by about 2%, which is not too bad compared to my expectation.

                     

                    The updated long term model gives the following values:

                     

                     $587,107,275.18$349,595,69647.32%0.74%
                    $516,897,359.09$307,788,88251.40%1.57%
                    $454,444,670.30$270,601,14555.32%3.05%
                    $398,892,142.19$237,522,13959.06%5.51%
                    $349,477,402.18$208,097,90862.60%9.33%
                    $315 $305,522,309.34$181,924,64865.92%14.91%
                    $262 $266,423,647.98$158,643,17269.03%22.62%
                    $225 $231,644,849.39$137,933,97971.92%32.76%
                    $192 $200,708,628.34$119,512,86574.58%45.56%
                    $165 $173,190,432.99$103,127,03177.04%61.09%
                    $147 $148,712,618.67$88,551,60579.29%79.29%

                     

                    If this model continues to be reasonably accurate, we have a slightly less than even chance of seeing a jackpot around $230M annuity.

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                      Posted: February 18, 2006, 1:13 am - IP Logged

                      The Megamillions has rolled again, with an annuity jackpot of $170M.

                      I will update the probability thread sometime this weekend to reflect the new numbers 

                       

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                        Posted: February 18, 2006, 7:45 am - IP Logged

                        The MM has rolled over.  The cash value is now $101.3 and the annuity value is $170M.  A running average of 13th draw sales (2 data points) since the matrix change suggests that the sales will be around $36.6M.  If this many tickets are ultimately sold, the probability of various numbers of winners is given in the following table:

                        081.20%
                        116.91%
                        21.76%
                        30.12%
                        40.01%

                        LotteryReport has not yet posted the sales for the last drawing.  I use these to update the long range projection model.  I will post the updated long range projection model later.

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                          Posted: February 18, 2006, 9:53 am - IP Logged

                          The actual cash jackpot reached, according to sales, a $89.9M on the last drawing.  The model predicted $88.6M and was off by 1.5%, which is not too bad for this sort of thing.

                           

                          The updated long term model gives the following values:

                           

                           $601,373,813.49$358,090,77146.34%0.83%
                           $529,187,846.70$315,107,30950.47%1.79%
                           $465,016,040.33$276,895,91554.45%3.54%
                           $407,968,654.03$242,926,78958.25%6.51%
                           $357,254,727.35$212,728,95161.85%11.17%
                          $315 $312,171,113.06$185,883,70865.24%18.07%
                          $262 $272,092,728.09$162,018,85268.41%27.69%
                          $225 $236,463,886.72$140,803,49671.35%40.48%
                          $192 $204,790,596.04$121,943,49174.08%56.73%
                          $165 $176,633,706.72$105,177,34476.59%76.59%

                           

                          I expect that the model will be less accurate has the drawings get larger.

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                            Posted: February 22, 2006, 3:43 am - IP Logged

                            The MM has rolled over.  The cash value is now $120.8 and the annuity value is $203M.  A running average of 14th draw sales (2 data points) since the matrix change suggests that the sales will be around $48.8M.  If this many tickets are ultimately sold, the probability of various numbers of winners is given in the following table: 

                            076.10%
                            120.79%
                            22.84%
                            30.26%
                            40.02%

                            The actual cash jackpot for this last drawing reached, based on the provisional sales figures, from www.lotteryreport.com, $105.8M.  This is within 0.6% of figure predicted by the model, posted in my last post, a very good fit.  The model is performing well in this region.  (With the existing data on performance, significant deviations begin to occur only on the 16th draw, so the model may be very close for two drawings - and it remains a decent approximation through all known data going up to the $315 annuity jackpot last year.)

                            Here is what the model now looks like after incorporation of the latest data point:

                             $690,593,143.29$411,216,82641.49%0.42%
                             $608,030,975.32$362,054,80845.77%1.02%
                             $534,692,086.03$318,384,83349.95%2.22%
                             $469,546,114.04$279,593,36853.97%4.45%
                             $411,677,802.86$245,135,41957.82%8.25%
                             $360,274,142.20$214,526,87661.47%14.27%
                            $315 $314,612,945.66$187,337,70964.91%23.22%
                            $262 $274,052,704.57$163,185,92968.12%35.77%
                            $225 $238,023,575.20$141,732,22071.10%52.52%
                            $192 $206,019,372.85$122,675,17273.86%73.86%

                             

                             

                             

                             

                             

                             

                             


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                              Posted: February 22, 2006, 2:25 pm - IP Logged

                              Prob988, if MM Jackpot rolls, I hope it reaches 240 million in next draw. MM raised from 170 million to 175 million in last draw because of CA impact.

                                 
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