Positional analysis

[Bertil]

In his book "Winning Lotto/Lottery for everyday players" Jones claims
that sorting drawings for 6/49 games in numerical order in a table
and then listing the frequency of of the most common number per
each of the six positions will indicate the most likely numbers to be
drawn next. His table in Fig. 6.5 is totally phony and based on bogus
numbers as made evident by the fact there are not the same total
for each position. It varies from 49 to 70 while the mean is 58.

Is this concept or method used be any player of 6/49 games?

Stig Holmquist

 

[johnph77]

6/49.Numeric.Position.Frequency.Chart

..........A........B........C........D........E........F......Total.

.1.....1712304..............................................1712304.
.2.....1533939...178365.....................................1712304.
.3.....1370754...326370....15180............................1712304.
.4.....1221759...446985....42570......990...................1712304.
.5.....1086008...543004....79464.....3784.......44..........1712304.
.6......962598...617050...123410.....9030......215........1.1712304.
.7......850668...671580...172200....17220......630........6.1712304.
.8......749398...708890...223860....28700.....1435.......21.1712304.
.9......658008...731120...276640....43680.....2800.......56.1712304.
10......575757...740259...329004....62244.....4914......126.1712304.
11......501942...738150...379620....84360.....7980......252.1712304.
12......435897...726495...427350...109890....12210......462.1712304.
13......376992...706860...471240...138600....17820......792.1712304.
14......324632...680680...510510...170170....25025.....1287.1712304.
15......278256...649264...544544...204204....34034.....2002.1712304.
16......237336...613800...572880...240240....45045.....3003.1712304.
17......201376...575360...595200...277760....58240.....4368.1712304.
18......169911...534905...611320...316200....73780.....6188.1712304.
19......142506...493290...621180...354960....91800.....8568.1712304.
20......118755...451269...624834...393414...112404....11628.1712304.
21.......98280...409500...622440...430920...135660....15504.1712304.
22.......80730...368550...614250...466830...161595....20349.1712304.
23.......65780...328900...600600...500500...190190....26334.1712304.
24.......53130...290950...581900...531300...221375....33649.1712304.
25.......42504...255024...558624...558624...255024....42504.1712304.
26.......33649...221375...531300...581900...290950....53130.1712304.
27.......26334...190190...500500...600600...328900....65780.1712304.
28.......20349...161595...466830...614250...368550....80730.1712304.
29.......15504...135660...430920...622440...409500....98280.1712304.
30.......11628...112404...393414...624834...451269...118755.1712304.
31........8568....91800...354960...621180...493290...142506.1712304.
32........6188....73780...316200...611320...534905...169911.1712304.
33........4368....58240...277760...595200...575360...201376.1712304.
34........3003....45045...240240...572880...613800...237336.1712304.
35........2002....34034...204204...544544...649264...278256.1712304.
36........1287....25025...170170...510510...680680...324632.1712304.
37.........792....17820...138600...471240...706860...376992.1712304.
38.........462....12210...109890...427350...726495...435897.1712304.
39.........252.....7980....84360...379620...738150...501942.1712304.
40.........126.....4914....62244...329004...740259...575757.1712304.
41..........56.....2800....43680...276640...731120...658008.1712304.
42..........21.....1435....28700...223860...708890...749398.1712304.
43...........6......630....17220...172200...671580...850668.1712304.
44...........1......215.....9030...123410...617050...962598.1712304.
45...................44.....3784....79464...543004..1086008.1712304.
46...........................990....42570...446985..1221759.1712304.
47..................................15180...326370..1370754.1712304.
48..........................................178365..1533939.1712304.
49..................................................1712304.1712304.

Total.13983816.13983816.13983816.13983816.13983816.13983816.

 

[Bertil]

6/49.Numeric.Position.Frequency.Chart

johnph77,
Thank you for the chart. Do you use position analysis for Powerball?
Would you be willing to list a chart for 5/55?

How many draws must one use to have a realistic chance to get three or more numbers correct? After 55 draws all numbers are likely to have been
drawn at least once. That seems too few draws for a statistical analysis.

Stig Holmquist

 

[johnph77]

5/55 Position Frequency Chart​

..........A.......B.......C.......D.......E....Total.

....1..316251.................................316251.
....2..292825...23426.........................316251.
....3..270725...44200....1326.................316251.
....4..249900...62475....3825......51.........316251.
....5..230300...78400....7350.....200.......1.316251.
....6..211876...92120...11760.....490.......5.316251.
....7..194580..103776...16920.....960......15.316251.
....8..178365..113505...22701....1645......35.316251.
....9..163185..121440...28980....2576......70.316251.
...10..148995..127710...35640....3780.....126.316251.
...11..135751..132440...42570....5280.....210.316251.
...12..123410..135751...49665....7095.....330.316251.
...13..111930..137760...56826....9240.....495.316251.
...14..101270..138580...63960...11726.....715.316251.
...15...91390..138320...70980...14560....1001.316251.
...16...82251..137085...77805...17745....1365.316251.
...17...73815..134976...84360...21280....1820.316251.
...18...66045..132090...90576...25160....2380.316251.
...19...58905..128520...96390...29376....3060.316251.
...20...52360..124355..101745...33915....3876.316251.
...21...46376..119680..106590...38760....4845.316251.
...22...40920..114576..110880...43890....5985.316251.
...23...35960..109120..114576...49280....7315.316251.
...24...31465..103385..117645...54901....8855.316251.
...25...27405...97440..120060...60720...10626.316251.
...26...23751...91350..121800...66700...12650.316251.
...27...20475...85176..122850...72800...14950.316251.
...28...17550...78975..123201...78975...17550.316251.
...29...14950...72800..122850...85176...20475.316251.
...30...12650...66700..121800...91350...23751.316251.
...31...10626...60720..120060...97440...27405.316251.
...32....8855...54901..117645..103385...31465.316251.
...33....7315...49280..114576..109120...35960.316251.
...34....5985...43890..110880..114576...40920.316251.
...35....4845...38760..106590..119680...46376.316251.
...36....3876...33915..101745..124355...52360.316251.
...37....3060...29376...96390..128520...58905.316251.
...38....2380...25160...90576..132090...66045.316251.
...39....1820...21280...84360..134976...73815.316251.
...40....1365...17745...77805..137085...82251.316251.
...41....1001...14560...70980..138320...91390.316251.
...42.....715...11726...63960..138580..101270.316251.
...43.....495....9240...56826..137760..111930.316251.
...44.....330....7095...49665..135751..123410.316251.
...45.....210....5280...42570..132440..135751.316251.
...46.....126....3780...35640..127710..148995.316251.
...47......70....2576...28980..121440..163185.316251.
...48......35....1645...22701..113505..178365.316251.
...49......15.....960...16920..103776..194580.316251.
...50.......5.....490...11760...92120..211876.316251.
...51.......1.....200....7350...78400..230300.316251.
...52..............51....3825...62475..249900.316251.
...53....................1326...44200..270725.316251.
...54...........................23426..292825.316251.
...55..................................316251.316251.

Total.3478761.3478761.3478761.3478761.3478761..

I haven't had a lot of time to devote to lottery projects in the last couple of years - other projects have taken priority - so I haven't done what I want to do regarding analysis, except on an individual request. I've done 90% position analyses, 90% sum analyses, combinations of the two, all of the trend types, (hot/hot, hot/cold, cold/hot and cold/cold) and haven't been able to come to any definite conclusions on any game I've worked with. And, in a lottery with over 1.7 million possibilities, 55 is far too small a statistical sample from which to draw any viable conclusions.

Incidentally, all of this information is available on my web site - numeric position charts, sum charts, payout percentages, and more.

http://www.johnph77.com/math/

I have nothing for sale - all information is available for viewing free of charge. All I ask is that you don't copy and post elsewhere as your own creation.

 

[Bertil]

Johnph77
I'm gratefull and pleased with the 5/55 data and it occurred to me that it would be very interesting and usefull to have all data recalculated as %.

Specifically, ball#2 has relative frequencies of 92.6 and 7.4%, ball #3 has
85.6, 14.0 and 0.6%, ball#4 has 79.0,19.75 and1.25% all based on 316251.
Given these percentages one can predict how many times any number is
likely to appear in any of the five positions providing one also calculates
the standard deviation for each percent.

I went to your website and tried to log onto "Individual lottery game
numeric positions... but was unable to gain access because I was asked
for username and password. I typed inwhat I use for this thread but was
denied. What am I doing wrong?

Stig Holmqist

 

[johnph77]

Nothing - that's the way that portion of the site is designed.

Originally, I had all sum and positional charts set up as individual game pages but the plagiarism became so rampant I reconstructed the pages to the way they are now. The information is in the large charts, just much harder to copy. I control the access to the individual game pages.

The percentages you request are easily done - I'd have to add those columns to the existing game chart. I should be able to post before the end of the week.

The 90% analysis I referred to is a vertically-oriented exercise - it would show the numbers that would fall into a particular column 90% of the time. I've worked it out for the 6/49 matrix but never the 5/55. Again, later this week.

 

[johnph77]

As requested:

[SIZE="1"]```````````````````````````````````5/55                                                  
````|`````A`````A%``|`````B`````B%``|````C`````C%``|````D`````D%``|````E`````E%``|``Total
```1|``316251`100.00|```````````````|``````````````|``````````````|``````````````|`316251
```2|``292825``92.59|```23426```7.41|``````````````|``````````````|``````````````|`316251
```3|``270725``85.60|```44200``13.98|```1326```0.42|``````````````|``````````````|`316251
```4|``249900``79.02|```62475``19.75|```3825```1.21|`````51```0.02|``````````````|`316251
```5|``230300``72.82|```78400``24.79|```7350```2.32|````200```0.06|``````1```0.00|`316251
```6|``211876``67.00|```92120``29.13|``11760```3.72|````490```0.15|``````5```0.00|`316251
```7|``194580``61.53|``103776``32.81|``16920```5.35|````960```0.30|`````15```0.00|`316251
```8|``178365``56.40|``113505``35.89|``22701```7.18|```1645```0.52|`````35```0.01|`316251
```9|``163185``51.60|``121440``38.40|``28980```9.16|```2576```0.81|`````70```0.02|`316251
``10|``148995``47.11|``127710``40.38|``35640``11.27|```3780```1.20|````126```0.04|`316251
``11|``135751``42.93|``132440``41.88|``42570``13.46|```5280```1.67|````210```0.07|`316251
``12|``123410``39.02|``135751``42.93|``49665``15.70|```7095```2.24|````330```0.10|`316251
``13|``111930``35.39|``137760``43.56|``56826``17.97|```9240```2.92|````495```0.16|`316251
``14|``101270``32.02|``138580``43.82|``63960``20.22|``11726```3.71|````715```0.23|`316251
``15|```91390``28.90|``138320``43.74|``70980``22.44|``14560```4.60|```1001```0.32|`316251
``16|```82251``26.01|``137085``43.35|``77805``24.60|``17745```5.61|```1365```0.43|`316251
``17|```73815``23.34|``134976``42.68|``84360``26.68|``21280```6.73|```1820```0.58|`316251
``18|```66045``20.88|``132090``41.77|``90576``28.64|``25160```7.96|```2380```0.75|`316251
``19|```58905``18.63|``128520``40.64|``96390``30.48|``29376```9.29|```3060```0.97|`316251
``20|```52360``16.56|``124355``39.32|`101745``32.17|``33915``10.72|```3876```1.23|`316251
``21|```46376``14.66|``119680``37.84|`106590``33.70|``38760``12.26|```4845```1.53|`316251
``22|```40920``12.94|``114576``36.23|`110880``35.06|``43890``13.88|```5985```1.89|`316251
``23|```35960``11.37|``109120``34.50|`114576``36.23|``49280``15.58|```7315```2.31|`316251
``24|```31465```9.95|``103385``32.69|`117645``37.20|``54901``17.36|```8855```2.80|`316251
``25|```27405```8.67|```97440``30.81|`120060``37.96|``60720``19.20|``10626```3.36|`316251
``26|```23751```7.51|```91350``28.89|`121800``38.51|``66700``21.09|``12650```4.00|`316251
``27|```20475```6.47|```85176``26.93|`122850``38.85|``72800``23.02|``14950```4.73|`316251
``28|```17550```5.55|```78975``24.97|`123201``38.96|``78975``24.97|``17550```5.55|`316251
``29|```14950```4.73|```72800``23.02|`122850``38.85|``85176``26.93|``20475```6.47|`316251
``30|```12650```4.00|```66700``21.09|`121800``38.51|``91350``28.89|``23751```7.51|`316251
``31|```10626```3.36|```60720``19.20|`120060``37.96|``97440``30.81|``27405```8.67|`316251
``32|````8855```2.80|```54901``17.36|`117645``37.20|`103385``32.69|``31465```9.95|`316251
``33|````7315```2.31|```49280``15.58|`114576``36.23|`109120``34.50|``35960``11.37|`316251
``34|````5985```1.89|```43890``13.88|`110880``35.06|`114576``36.23|``40920``12.94|`316251
``35|````4845```1.53|```38760``12.26|`106590``33.70|`119680``37.84|``46376``14.66|`316251
``36|````3876```1.23|```33915``10.72|`101745``32.17|`124355``39.32|``52360``16.56|`316251
``37|````3060```0.97|```29376```9.29|``96390``30.48|`128520``40.64|``58905``18.63|`316251
``38|````2380```0.75|```25160```7.96|``90576``28.64|`132090``41.77|``66045``20.88|`316251
``39|````1820```0.58|```21280```6.73|``84360``26.68|`134976``42.68|``73815``23.34|`316251
``40|````1365```0.43|```17745```5.61|``77805``24.60|`137085``43.35|``82251``26.01|`316251
``41|````1001```0.32|```14560```4.60|``70980``22.44|`138320``43.74|``91390``28.90|`316251
``42|`````715```0.23|```11726```3.71|``63960``20.22|`138580``43.82|`101270``32.02|`316251
``43|`````495```0.16|````9240```2.92|``56826``17.97|`137760``43.56|`111930``35.39|`316251
``44|`````330```0.10|````7095```2.24|``49665``15.70|`135751``42.93|`123410``39.02|`316251
``45|`````210```0.07|````5280```1.67|``42570``13.46|`132440``41.88|`135751``42.93|`316251
``46|`````126```0.04|````3780```1.20|``35640``11.27|`127710``40.38|`148995``47.11|`316251
``47|``````70```0.02|````2576```0.81|``28980```9.16|`121440``38.40|`163185``51.60|`316251
``48|``````35```0.01|````1645```0.52|``22701```7.18|`113505``35.89|`178365``56.40|`316251
``49|``````15```0.00|`````960```0.30|``16920```5.35|`103776``32.81|`194580``61.53|`316251
``50|```````5```0.00|`````490```0.15|``11760```3.72|``92120``29.13|`211876``67.00|`316251
``51|```````1```0.00|`````200```0.06|```7350```2.32|``78400``24.79|`230300``72.82|`316251
``52|```````````````|``````51```0.02|```3825```1.21|``62475``19.75|`249900``79.02|`316251
``53|```````````````|```````````````|```1326```0.42|``44200``13.98|`270725``85.60|`316251
``54|```````````````|```````````````|``````````````|``23426```7.41|`292825``92.59|`316251
``55|```````````````|```````````````|``````````````|``````````````|`316251`100.00|`316251
``TL|`3478761```````|`3478761```````|3478761```````|3478761```````|3478761```````|```````[/SIZE]

 

[johnph77]

5/55 90% Chart:

[SIZE="1"]`````````````````````5/55                                
````|`````A``|`````B``|`````C``|`````D``|`````E``|``Total
```1|``316251|````````|````````|````````|````````|`316251
```2|``292825|````````|````````|````````|````````|`316251
```3|``270725|````````|````````|````````|````````|`316251
```4|``249900|```62475|````````|````````|````````|`316251
```5|``230300|```78400|````````|````````|````````|`316251
```6|``211876|```92120|````````|````````|````````|`316251
```7|``194580|``103776|````````|````````|````````|`316251
```8|``178365|``113505|````````|````````|````````|`316251
```9|``163185|``121440|````````|````````|````````|`316251
``10|``148995|``127710|````````|````````|````````|`316251
``11|``135751|``132440|````````|````````|````````|`316251
``12|``123410|``135751|```49665|````````|````````|`316251
``13|``111930|``137760|```56826|````````|````````|`316251
``14|``101270|``138580|```63960|````````|````````|`316251
``15|```91390|``138320|```70980|````````|````````|`316251
``16|```82251|``137085|```77805|````````|````````|`316251
``17|```73815|``134976|```84360|````````|````````|`316251
``18|```66045|``132090|```90576|````````|````````|`316251
``19|```58905|``128520|```96390|````````|````````|`316251
``20|```52360|``124355|``101745|````````|````````|`316251
``21|````````|``119680|``106590|````````|````````|`316251
``22|````````|``114576|``110880|````````|````````|`316251
``23|````````|``109120|``114576|```49280|````````|`316251
``24|````````|``103385|``117645|```54901|````````|`316251
``25|````````|```97440|``120060|```60720|````````|`316251
``26|````````|```91350|``121800|```66700|````````|`316251
``27|````````|```85176|``122850|```72800|````````|`316251
``28|````````|```78975|``123201|```78975|````````|`316251
``29|````````|```72800|``122850|```85176|````````|`316251
``30|````````|```66700|``121800|```91350|````````|`316251
``31|````````|```60720|``120060|```97440|````````|`316251
``32|````````|```54901|``117645|``103385|````````|`316251
``33|````````|```49280|``114576|``109120|````````|`316251
``34|````````|````````|``110880|``114576|````````|`316251
``35|````````|````````|``106590|``119680|````````|`316251
``36|````````|````````|``101745|``124355|```52360|`316251
``37|````````|````````|```96390|``128520|```58905|`316251
``38|````````|````````|```90576|``132090|```66045|`316251
``39|````````|````````|```84360|``134976|```73815|`316251
``40|````````|````````|```77805|``137085|```82251|`316251
``41|````````|````````|```70980|``138320|```91390|`316251
``42|````````|````````|```63960|``138580|``101270|`316251
``43|````````|````````|```56826|``137760|``111930|`316251
``44|````````|````````|```49665|``135751|``123410|`316251
``45|````````|````````|````````|``132440|``135751|`316251
``46|````````|````````|````````|``127710|``148995|`316251
``47|````````|````````|````````|``121440|``163185|`316251
``48|````````|````````|````````|``113505|``178365|`316251
``49|````````|````````|````````|``103776|``194580|`316251
``50|````````|````````|````````|```92120|``211876|`316251
``51|````````|````````|````````|```78400|``230300|`316251
``52|````````|````````|````````|```62475|``249900|`316251
``53|````````|````````|````````|````````|``270725|`316251
``54|````````|````````|````````|````````|``292825|`316251
``55|````````|````````|````````|````````|``316251|`316251
``TL|`3478761|`3478761|`3478761|`3478761|`3478761|```````
````|````````|````````|````````|````````|````````|```````
````|`3154129|`3143406|`3136617|`3143406|`3154129|```````
````|``90.67`|``90.36`|``90.16`|``90.36`|``90.67`|`60.52`[/SIZE]

The numbers shown in the respective columns of the chart will appear in at least 90% of the draws. Using this criteria it woulld be expected that 60.52% of all draws would appear in all five columns, but, when programmed, 2,331,967 combinations, or 67.03%, will have all five numbers within these ranges.

 

[Bertil]

Johnph77,
Excellent work. Many thanks. Please tell me how I might log onto "Individual
Lottery games numeric positions...

Stig Holmquist

 

[johnph77]

Johnph77,
Excellent work. Many thanks. Please tell me how I might log onto "Individual
Lottery games numeric positions...

Stig Holmquist

Email me from the link on my site.

 

[GillesD]

Positional results for Lotto 6/49

After 2392 draws for Lotto 6/49,

For N1, 100% of the numbers drawn are between 1 and 38
and 91.4% of the numbers drawn are betrween 1 and 16

For N2, 100% of the numbers drawn are between 2 and 43
and 91.0% of the numbers drawn are betrween 3 and 26

For N3, 100% of the numbers drawn are between 3 and 44
and 90.8% of the numbers drawn are betrween 8 and 35

For N4, 100% of the numbers drawn are between 4 and 47
and 91.0% of the numbers drawn are betrween 16 and 42

For N5, 100% of the numbers drawn are between 11 and 48
and 90.1% of the numbers drawn are betrween 26 and 47

For N6, 100% of the numbers drawn are between 13 and 49
and 91.9% of the numbers drawn are betrween 35 and 49

where N1 to N6 are respective position 1 to 6

 

[johnph77]

A 6/49 90% Position Chart would look like so:

``````````A````````B`````````C```````D````````E````````F``````Total
```1```1712304``````````````````````````````````````````````1712304
```2```1533939``````````````````````````````````````````````1533939
```3```1370754```326370`````````````````````````````````````1697124
```4```1221759```446985`````````````````````````````````````1668744
```5```1086008```543004`````````````````````````````````````1629012
```6````962598```617050`````````````````````````````````````1579648
```7````850668```671580`````````````````````````````````````1522248
```8````749398```708890```223860````````````````````````````1682148
```9````658008```731120```276640````````````````````````````1665768
``10````575757```740259```329004````````````````````````````1645020
``11````501942```738150```379620````````````````````````````1619712
``12````435897```726495```427350````````````````````````````1589742
``13````376992```706860```471240````````````````````````````1555092
``14````324632```680680```510510````````````````````````````1515822
``15````278256```649264```544544````````````````````````````1472064
``16`````````````613800```572880```240240```````````````````1426920
``17`````````````575360```595200```277760```````````````````1448320
``18`````````````534905```611320```316200```````````````````1462425
``19`````````````493290```621180```354960```````````````````1469430
``20`````````````451269```624834```393414```````````````````1469517
``21`````````````409500```622440```430920```````````````````1462860
``22`````````````368550```614250```466830```````````````````1449630
``23`````````````328900```600600```500500```````````````````1430000
``24`````````````290950```581900```531300```````````````````1404150
``25`````````````255024```558624```558624```255024``````````1627296
``26``````````````````````531300```581900```290950``````````1404150
``27``````````````````````500500```600600```328900``````````1430000
``28``````````````````````466830```614250```368550``````````1449630
``29``````````````````````430920```622440```409500``````````1462860
``30``````````````````````393414```624834```451269``````````1469517
``31``````````````````````354960```621180```493290``````````1469430
``32``````````````````````316200```611320```534905``````````1462425
``33``````````````````````277760```595200```575360``````````1448320
``34``````````````````````240240```572880```613800``````````1426920
``35```````````````````````````````544544```649264```278256`1472064
``36```````````````````````````````510510```680680```324632`1515822
``37```````````````````````````````471240```706860```376992`1555092
``38```````````````````````````````427350```726495```435897`1589742
``39```````````````````````````````379620```738150```501942`1619712
``40```````````````````````````````329004```740259```575757`1645020
``41```````````````````````````````276640```731120```658008`1665768
``42```````````````````````````````223860```708890```749398`1682148
``43````````````````````````````````````````671580```850668`1522248
``44````````````````````````````````````````617050```962598`1579648
``45````````````````````````````````````````543004``1086008`1629012
``46````````````````````````````````````````446985``1221759`1668744
``47````````````````````````````````````````326370``1370754`1697124
``48````````````````````````````````````````````````1533939`1533939
``49````````````````````````````````````````````````1712304`1712304
Total`12638912`12608255`12678120`12678120`12608255`12638912````````
````````90.38%```90.16%```90.66%```90.66%```90.16%```90.38%``53.14%
Close to past results.....

 

[Bertil]

Johnph77,
Excellent work. Many thanks. Please tell me how I might log onto "Individual
Lottery games numeric positions...

Stig Holmquist

I decided to test the % values on the last 55 draws of Powerball.
There were 8 of ball #35 while the mean frequency for each would be 5.
But to my surprise one was in position 1, where the expected rate is1.5%.
Thus it occurred eight times more often than expected in position 1.
Is this calculation correct and if so, how do I account for it?

Stig Holmquist

 

[johnph77]

If one were to make use of the values shown in the chart, 35 should appear in the #1 spot approximately 14 times in every 10,000 draws ((4845/3478761)*(10000)). If an event were to occur on average once every 55 draws, it would be expected to occur 182 times in 10,000 draws.

This is 13 times more than usual, but, given the small sample, isn't regarded as an anomaly - after all, it has to appear sometime.

BTW, my Email address is located at the bottom of my main web page (dele the "math/" in the provided address) and is coded to prevent spam. In order for you to view the individual game charts I have to create a site account for you.

 

[johnph77]

Stig -

The previous chart with percentages indicated the positioning and percentage of each number in each column - when it appeared. Therefore the percentages in each row will total 100%. But from your last question it appears that what you wanted was the number of times and the percentage of each number in a particular column. In that chart, the percentages in each column, rather than row, should total 100%. See if this doesn't serve your purpose better.

````````````````````````````````````````5/55                                               
`````````A`````A%``|`````B`````B%``|`````C`````C%``|`````D`````D%``|`````E`````E%``|``Total
```1``316251`9.0909|```````````````|```````````````|```````````````|```````````````|`316251
```2``292825`8.4175|```23426`0.6734|```````````````|```````````````|```````````````|`316251
```3``270725`7.7822|```44200`1.2706|````1326`0.0381|```````````````|```````````````|`316251
```4``249900`7.1836|```62475`1.7959|````3825`0.1100|``````51`0.0015|```````````````|`316251
```5``230300`6.6202|```78400`2.2537|````7350`0.2113|`````200`0.0057|```````1`0.0000|`316251
```6``211876`6.0906|```92120`2.6481|```11760`0.3381|`````490`0.0141|```````5`0.0001|`316251
```7``194580`5.5934|``103776`2.9831|```16920`0.4864|`````960`0.0276|``````15`0.0004|`316251
```8``178365`5.1273|``113505`3.2628|```22701`0.6526|````1645`0.0473|``````35`0.0010|`316251
```9``163185`4.6909|``121440`3.4909|```28980`0.8331|````2576`0.0740|``````70`0.0020|`316251
``10``148995`4.2830|``127710`3.6711|```35640`1.0245|````3780`0.1087|`````126`0.0036|`316251
``11``135751`3.9023|``132440`3.8071|```42570`1.2237|````5280`0.1518|`````210`0.0060|`316251
``12``123410`3.5475|``135751`3.9023|```49665`1.4277|````7095`0.2040|`````330`0.0095|`316251
``13``111930`3.2175|``137760`3.9600|```56826`1.6335|````9240`0.2656|`````495`0.0142|`316251
``14``101270`2.9111|``138580`3.9836|```63960`1.8386|```11726`0.3371|`````715`0.0206|`316251
``15```91390`2.6271|``138320`3.9761|```70980`2.0404|```14560`0.4185|````1001`0.0288|`316251
``16```82251`2.3644|``137085`3.9406|```77805`2.2366|```17745`0.5101|````1365`0.0392|`316251
``17```73815`2.1219|``134976`3.8800|```84360`2.4250|```21280`0.6117|````1820`0.0523|`316251
``18```66045`1.8985|``132090`3.7970|```90576`2.6037|```25160`0.7232|````2380`0.0684|`316251
``19```58905`1.6933|``128520`3.6944|```96390`2.7708|```29376`0.8444|````3060`0.0880|`316251
``20```52360`1.5051|``124355`3.5747|``101745`2.9247|```33915`0.9749|````3876`0.1114|`316251
``21```46376`1.3331|``119680`3.4403|``106590`3.0640|```38760`1.1142|````4845`0.1393|`316251
``22```40920`1.1763|``114576`3.2936|``110880`3.1873|```43890`1.2617|````5985`0.1720|`316251
``23```35960`1.0337|``109120`3.1367|``114576`3.2936|```49280`1.4166|````7315`0.2103|`316251
``24```31465`0.9045|``103385`2.9719|``117645`3.3818|```54901`1.5782|````8855`0.2545|`316251
``25```27405`0.7878|```97440`2.8010|``120060`3.4512|```60720`1.7454|```10626`0.3055|`316251
``26```23751`0.6827|```91350`2.6259|``121800`3.5012|```66700`1.9173|```12650`0.3636|`316251
``27```20475`0.5886|```85176`2.4485|``122850`3.5314|```72800`2.0927|```14950`0.4298|`316251
``28```17550`0.5045|```78975`2.2702|``123201`3.5415|```78975`2.2702|```17550`0.5045|`316251
``29```14950`0.4298|```72800`2.0927|``122850`3.5314|```85176`2.4485|```20475`0.5886|`316251
``30```12650`0.3636|```66700`1.9173|``121800`3.5012|```91350`2.6259|```23751`0.6827|`316251
``31```10626`0.3055|```60720`1.7454|``120060`3.4512|```97440`2.8010|```27405`0.7878|`316251
``32````8855`0.2545|```54901`1.5782|``117645`3.3818|``103385`2.9719|```31465`0.9045|`316251
``33````7315`0.2103|```49280`1.4166|``114576`3.2936|``109120`3.1367|```35960`1.0337|`316251
``34````5985`0.1720|```43890`1.2617|``110880`3.1873|``114576`3.2936|```40920`1.1763|`316251
``35````4845`0.1393|```38760`1.1142|``106590`3.0640|``119680`3.4403|```46376`1.3331|`316251
``36````3876`0.1114|```33915`0.9749|``101745`2.9247|``124355`3.5747|```52360`1.5051|`316251
``37````3060`0.0880|```29376`0.8444|```96390`2.7708|``128520`3.6944|```58905`1.6933|`316251
``38````2380`0.0684|```25160`0.7232|```90576`2.6037|``132090`3.7970|```66045`1.8985|`316251
``39````1820`0.0523|```21280`0.6117|```84360`2.4250|``134976`3.8800|```73815`2.1219|`316251
``40````1365`0.0392|```17745`0.5101|```77805`2.2366|``137085`3.9406|```82251`2.3644|`316251
``41````1001`0.0288|```14560`0.4185|```70980`2.0404|``138320`3.9761|```91390`2.6271|`316251
``42`````715`0.0206|```11726`0.3371|```63960`1.8386|``138580`3.9836|``101270`2.9111|`316251
``43`````495`0.0142|````9240`0.2656|```56826`1.6335|``137760`3.9600|``111930`3.2175|`316251
``44`````330`0.0095|````7095`0.2040|```49665`1.4277|``135751`3.9023|``123410`3.5475|`316251
``45`````210`0.0060|````5280`0.1518|```42570`1.2237|``132440`3.8071|``135751`3.9023|`316251
``46`````126`0.0036|````3780`0.1087|```35640`1.0245|``127710`3.6711|``148995`4.2830|`316251
``47``````70`0.0020|````2576`0.0740|```28980`0.8331|``121440`3.4909|``163185`4.6909|`316251
``48``````35`0.0010|````1645`0.0473|```22701`0.6526|``113505`3.2628|``178365`5.1273|`316251
``49``````15`0.0004|`````960`0.0276|```16920`0.4864|``103776`2.9831|``194580`5.5934|`316251
``50```````5`0.0001|`````490`0.0141|```11760`0.3381|```92120`2.6481|``211876`6.0906|`316251
``51```````1`0.0000|`````200`0.0057|````7350`0.2113|```78400`2.2537|``230300`6.6202|`316251
``52```````````````|``````51`0.0015|````3825`0.1100|```62475`1.7959|``249900`7.1836|`316251
``53```````````````|```````````````|````1326`0.0381|```44200`1.2706|``270725`7.7822|`316251
``54```````````````|```````````````|```````````````|```23426`0.6734|``292825`8.4175|`316251
``55```````````````|```````````````|```````````````|```````````````|``316251`9.0909|`316251
``TL`3478761```````|`3478761```````|`3478761```````|`3478761```````|`3478761```````|```````

 

[Bertil]

Hi John,
By now you might have concluded that my skills and understanding of
statistics are at best elementary and come from selfstudy.

Your new set of % seem to be derived from dividing the first set by 55/5=11.
My problem now is how to apply them correctly.I suspect that maybe I should
not go backwards to examine the last 55 draws but rather start from the first
run of the new Powerball matrix 55/5 so that I should look at when the #35
was drawn. It was on the 126th draw. Should I now mutiply 126 by 0.139%
and get 0.175 or should I mutiply 0.139 by the mean expected frequency per
ball,viz. 126/11=11.45 to get 0.0159? Whichever I use I get a very low value
instead of 1. Does this mean that ball #35 is acting abnormally?

Also, I was unable to find any e-mail on your web site.

Stig Holmquist

 

[johnph77]

Stig -

Nothing wrong with your analytical capabilities, your observation is on the spot = and consistent with the 5/55 matrix.

With that, any of the 55 numbers would be statistically expected to appear once every 11 drawings. If #35 did not appear for 125 drawings that would be statistically abnormal. If needed, I'd have to work out a probability analysis to determine the odds of such an occurance but, off the top of my head it would seem about 1 in 2,000 or more. And, as part of that analysis, has #35 appeared more often than expected since then - i.e. more than once every 11 drawings?

My Email link appears at the bottom of my main page -

http://www.johnph77.com.

 

[Bertil]

Hi John,

Sorry to have to disagree with your comment that after 11 draws all 55 numbers would be expected to have appeared. Just take a look at the last
11 draws and you will find that 20 numbers are missing because of duplication
A simple probability calculation indicates 20 with a std.dev.of 4.It will take
on average 55 draws to be reasonable certain that all 55 have been drawn.
You can test this by looking at stats at USA Mega.Just look at the last 10
and add one more and you find 20 +/-4 missing and then look at the last 50
and there is one missing.

Stig Holmquist

 

[johnph77]

Hi John,

Sorry to have to disagree with your comment that after 11 draws all 55 numbers would be expected to have appeared. Just take a look at the last
11 draws and you will find that 20 numbers are missing because of duplication
A simple probability calculation indicates 20 with a std.dev.of 4.It will take
on average 55 draws to be reasonable certain that all 55 have been drawn.
You can test this by looking at stats at USA Mega.Just look at the last 10
and add one more and you find 20 +/-4 missing and then look at the last 50
and there is one missing.

Stig Holmquist

Which is why I said "any" in the first sentence of the quote. Perhaps "each" would be a better word in that instance. And, of course, "all" would be reckless, irresponsible and incorrect.

I did a quick spreadsheet calc on a number not appearing in consecutive draws. The odds of a given number not appearing in a given draw are (10::11)*100, or 90.9090.....%. The odds of that number not appearing in two given draws are ((10::11)^2)*100, or 82.6446.....%. Continuing with that process through 126 draws yields a formula of ((10::11)^126)*100, or 0.00060886592568732.....% - statistically, a rare occurance.

 

[Bertil]

Hi John,

Sorry to have to disagree with your comment that after 11 draws all 55 numbers would be expected to have appeared. Just take a look at the last
11 draws and you will find that 20 numbers are missing because of duplication
A simple probability calculation indicates 20 with a std.dev.of 4.It will take
on average 55 draws to be reasonable certain that all 55 have been drawn.
You can test this by looking at stats at USA Mega.Just look at the last 10
and add one more and you find 20 +/-4 missing and then look at the last 50
and there is one missing.

Stig Holmquist

There is a simple and interesting way of generating 11 lines with 5 numers
per line without duplications by not replacing any drawn ball untill the end.

Get hold of a set of Bingo balls and take out all numbers greater than 55.
Now draw one at a time five times and record the numbers as drawn ,not
in numerical order and do not replace any.Next repeat ten times till all 55
have been drawn and recorded.

Each set of eleven lines with five numbers can now serve as a source of
additional sets of five numbers by reading the top five in each column
and also the bottom five as well as reading diagonals two ways.

A new set of eleven lines with five can be generated from scratch ad infinatum because there maybe 1.7x10^50 diferent sets of eleven lines.

Next comes an intriguing idea. Calculate the sum for each line and while all
must have a mean of 140 each set will all have a different variance from 140.
Its value may range from 539 to 6875 but what kind of distribution will it be?

Stig Holmquist