Variance
August 4th, 2012 at 2:24:46 PM
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Is there any way to lower variance besides the following?
1. Lower bet size
2. Less bets
3. Less juice
4. Better winning %
1. Lower bet size
2. Less bets
3. Less juice
4. Better winning %
August 4th, 2012 at 2:30:30 PM
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Some people think using more than one handicapper
lowers the variance. That way your variance isn't
tied to that of just one guy. All handicappers have
winning streaks, finding one and then finding
another after that can work wonders.
lowers the variance. That way your variance isn't
tied to that of just one guy. All handicappers have
winning streaks, finding one and then finding
another after that can work wonders.
"It's not called gambling if the math is on your side."
August 4th, 2012 at 2:37:44 PM
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For instance, here's the guy I follow for baseball..
He's got a 61% hit rate going this summer, though
he's starting to falter. The same thing happened to
him last year at this time.
He's got a 61% hit rate going this summer, though
he's starting to falter. The same thing happened to
him last year at this time.
"It's not called gambling if the math is on your side."
August 4th, 2012 at 2:48:43 PM
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#2 is not correct IF you do have an edge, you want as many bets as you can possibly make, with the largest possible bankroll to RoR.Quote: bigpete88Is there any way to lower variance besides the following?
1. Lower bet size
2. Less bets
3. Less juice
4. Better winning %
That way EV (positive in your case) will quickly swamp variance as the number of bets INCREASE, not decrease.
Even the Wizard has said this.
I do not have a link at the moment.
"The longer you play, the ratio of money lost to money bet will get closer to the expectation for that game."
So IF you have an edge "the ratio of money won to money bet will get closer to the expectation for that game"
So lots of bets and lots of money bet (they go hand in hand) is what the +EV player should strive for.
winsome johnny (not Win some johnny)
August 4th, 2012 at 3:27:22 PM
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Quote: 7craps#2 is not correct IF you do have an edge, you want as many bets as you can possibly make
[...]
"The longer you play, the ratio of money lost to money bet will get closer to the expectation for that game."
You need to distinguish between "total variance" and the "ratio of your net wins (or losses) with your net stakes".
Your expected wins (or losses) increase linear with the number of bets when playing with positive (or negative) EV.
Whereas the total variance always *increases* - but much slower. It increases with the square root of the number of bets (all for constant betsize and EV).
Hence the contradictory discussion whether variance increases or decreases.
However there is no contradiction: the total variance always *increases*, while the ratio always *decreases*, since the variance growths slower than your expected wins (or losses).
Short example:
If your very first bet is $100 win or lose bet on even odds, then the total variance is roughly $100 around whatever your EV is. Say if you lose, since nothing will ever bring back your initial $100, your lifetime total variance must always be larger than those lost $100 - around any EV. In fact a second $100 bet will increase the total variance to about $144 around EV.
Once you get over the point where your EV is larger than your total variance, you are getting into the "closer to expectation" zone. The number of bets needed is called N0. If you make those N0 bets, you have a ~67% chance of being ahead (if EV is positive).
August 4th, 2012 at 3:31:59 PM
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Using your 2500 bets example at 2% edge
https://wizardofvegas.com/forum/gambling/sports/10840-another-math-question/#post169697
This is using the normal distribution.
(When I have more time I can put more math and the formulas)
EV = 0.02*2500*110 = $5500
SD = $5237.6426 ( formula can be found here. I am lazy tody
https://wizardofvegas.com/forum/gambling/tables/1213-variance-in-craps/)
EV and SD about the same
1,2,3 SD
10737.64
15975.29
21212.93
-1,-2,-3SD
262.36
-4975.29
-10212.93
You have the same chance of being UP 15975.29 as you do being DOWN -4975.29
Now 12,500 bets
EV: $27499.99925
SD: $11711.72489
1,2,3 SD
39211.72414
50923.44904
62635.17393
-1,-2,-3SD
15788.27436
4076.54946
-7635.175434
You have the same chance of being UP 50923 as you do being UP 4076.
The 3SD value can still kill.
Cant make 12,500 bets with a 2% edge???
Very possible.
So cappers bet more when their edge is higher.
Just as Kelly says to do, IF you believe in Kelly betting in Sports.
More bets with a hgher average bet.
Solves the problem to a certain degree but the variance does go up when the bet increases.
The win rate must also.
But I already spelled that out.
25,000 bets
Hey look, No negative values for the -3SD.
EV: $54999.9985
SD: $16562.88018 way LESS than the EV.
1,2,3 SD
71562.87868
88125.75887
104688.6391
-1,-2,-3SD
38437.11832
21874.23813
5311.357945
Casinos can easily book 25,000 bets in one day.
Can one player?
So one player needs many days and many bets to over come the variance.
(and the proper bankroll to ride out the downswings)
https://wizardofvegas.com/forum/gambling/sports/10840-another-math-question/#post169697
This is using the normal distribution.
(When I have more time I can put more math and the formulas)
EV = 0.02*2500*110 = $5500
SD = $5237.6426 ( formula can be found here. I am lazy tody
https://wizardofvegas.com/forum/gambling/tables/1213-variance-in-craps/)
EV and SD about the same
1,2,3 SD
10737.64
15975.29
21212.93
-1,-2,-3SD
262.36
-4975.29
-10212.93
You have the same chance of being UP 15975.29 as you do being DOWN -4975.29
Now 12,500 bets
EV: $27499.99925
SD: $11711.72489
1,2,3 SD
39211.72414
50923.44904
62635.17393
-1,-2,-3SD
15788.27436
4076.54946
-7635.175434
You have the same chance of being UP 50923 as you do being UP 4076.
The 3SD value can still kill.
Cant make 12,500 bets with a 2% edge???
Very possible.
So cappers bet more when their edge is higher.
Just as Kelly says to do, IF you believe in Kelly betting in Sports.
More bets with a hgher average bet.
Solves the problem to a certain degree but the variance does go up when the bet increases.
The win rate must also.
But I already spelled that out.
25,000 bets
Hey look, No negative values for the -3SD.
EV: $54999.9985
SD: $16562.88018 way LESS than the EV.
1,2,3 SD
71562.87868
88125.75887
104688.6391
-1,-2,-3SD
38437.11832
21874.23813
5311.357945
Casinos can easily book 25,000 bets in one day.
Can one player?
So one player needs many days and many bets to over come the variance.
(and the proper bankroll to ride out the downswings)
winsome johnny (not Win some johnny)
August 4th, 2012 at 4:30:22 PM
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Thanks for your data. For a 2% advantage even bet one would calculate N0 to sqrt(N0) = 2% * N0, or N0 = 2500 - which agrees perfectly with your numbers (EV=$5500 and SD=$5238 for 2500 bets).
August 5th, 2012 at 11:55:57 AM
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7craps,
Thanks for correcting my number 2. I fully understand.
Thanks for correcting my number 2. I fully understand.
September 16th, 2012 at 2:43:22 PM
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Can anyone answer the following?
What is the variance difference of 3% ROI vs 9% ROI in sports betting. I am guesssing that it is a huge difference.
Also, using a 2% bet size of bankroll if that matters.
Thanks MustangSally and 7Craps!!! Thanks again!!!
What is the variance difference of 3% ROI vs 9% ROI in sports betting. I am guesssing that it is a huge difference.
Also, using a 2% bet size of bankroll if that matters.
Thanks MustangSally and 7Craps!!! Thanks again!!!
September 16th, 2012 at 2:54:20 PM
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Could you be more clear, variance of your bet ? variance of your bankroll ? ROI at what odds ?
September 16th, 2012 at 3:06:24 PM
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Thanks MangoJ for correcting me in the first place that more bets at +EV is better.
I am not asking about variance of bet size if that was your question. I am guessing that the standard deviation will be less at 9% ROI than 3% as 7Craps had spelled out.
Odds at -110 to win 100 just for this example.
I am not asking about variance of bet size if that was your question. I am guessing that the standard deviation will be less at 9% ROI than 3% as 7Craps had spelled out.
Odds at -110 to win 100 just for this example.
September 17th, 2012 at 7:51:49 AM
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For 54% win rate one can have a 3.09% ROIQuote: bigpete88I am guessing that the standard deviation will be less at 9% ROI than 3% as 7Craps had spelled out.
Odds at -110 to win 100 just for this example.
for 1 trial and $1 bet
ev: 0.0309
sd: 0.9515
for 400 trials and $110 bets
ev: 1,360.0000
sd: 2,093.2692
ROI% SD: 4.75743% (SD / handle)
Probability of being in the hole after 400 wagers: 25.794255% (about 1 in 4)
For 57% win rate one can have a 8.82% ROI
for 1 trial and $1 bet
ev: 0.0882
sd: 0.9451
for 400 trials and $110 bets
ev: 3,880.0000
sd: 2,079.3182
ROI% SD: 4.7257231% (SD / handle)
Probability of being in the hole after 400 wagers: 3.1020941% (about 1 in 32)
I would be more concerned that my 2% bet size is not over-betting my advantage since the win rate in sports betting is a variable.
This has been already talked to death by many experts.
Edward Thorp comes to mind in his "The Kelly Criterion in Blackjack, Sports Betting and the Stock Market" paper
ROI is still a very weak number to rely on. Variance works on that also for small number of trials.
reminds me of
Just like the cry-baby "tax the rich even MORE" goofballs with the billionaire pays less tax rate than the secretary bulls**t.
Let us see,
12% of $28,000,000 = $3,360,000 in taxes paid
The secretary pays a whopping 17% (41.7% MORE than the rich guy - this IS a fuc*ing crime!),
and the cry-babies- are still crying about that one...
17% of $60,000 = $10,200 in taxes paid
Now, Who over-payed, in actual $$$s, for the same government services???
The rich guy paying the f***ing low tax rate??
The cry-babies say so.
A**holes, all of them
winsome johnny (not Win some johnny)
March 15th, 2017 at 6:01:08 AM
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I can't figure another way to lower the variance but I'm sure you will find something in (link removed by mod) you want you can check it out. It worked fine for me.
(Mod comment: pretty sure this was spam but could have been an offer to help. So stopping with a warning to BettingNation for now.)
(Mod comment: pretty sure this was spam but could have been an offer to help. So stopping with a warning to BettingNation for now.)
Last edited by: beachbumbabs on Mar 15, 2017
April 12th, 2017 at 11:59:21 PM
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For those who are good at betting math? What's the odds that someone who is a $500 sports bettor (-110) is up $5000 after only 150 bets places?
What's the odds this is chance (assume 50/50 odds for each bet) vs skill (bettor has an edge somehow)?
Thank you
What's the odds this is chance (assume 50/50 odds for each bet) vs skill (bettor has an edge somehow)?
Thank you
April 13th, 2017 at 12:15:37 AM
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You're talking a record of 86-64 or so, with the vig making it not come out quite right. So a 57.33% win rate. That doesn't seem extraordinary to me, as we have an NFL contest each year here, and out of 20 or 30 playing each year, 6 or more will be above that rate at 150 games (see the various NFL picks threads here).
I could be wrong. Certainly with the bets so large, it's a nice chunk of change, but I would think it's run good rather than great picking.
I could be wrong. Certainly with the bets so large, it's a nice chunk of change, but I would think it's run good rather than great picking.
If the House lost every hand, they wouldn't deal the game.
April 13th, 2017 at 12:44:18 AM
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What if it took 1500 bets instead of the 150 would that imply skill (albeit very slight) since one is only getting 10 units of profit after 1500 bets? Or would a good run last this long?
At some point things head to 50/50 and the vig crushes you but when can we see if it's skill vs luck.
At some point things head to 50/50 and the vig crushes you but when can we see if it's skill vs luck.
April 14th, 2017 at 3:07:31 PM
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Near 60% win rates do quite well in the NFL Super Contest. You'd place and make 25K or more just by making the top 25. I suspect that having many 57% winners in the picks contest here has something to do with stale lines and sharp players.
I would like someone mathematical inclined to show how may picks that'd require before concluding 57% is skill vs luck; would 300 picks suffice? 1000?
I would like someone mathematical inclined to show how may picks that'd require before concluding 57% is skill vs luck; would 300 picks suffice? 1000?
April 14th, 2017 at 6:48:05 PM
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Quote: bazooookaFor those who are good at betting math? What's the odds that someone who is a $500 sports bettor (-110) is up $5000 after only 150 bets places?
What's the odds this is chance (assume 50/50 odds for each bet) vs skill (bettor has an edge somehow)?
Thank you
I believe 1 SD is $7072.
After that many bets (150) and betting $550 a game ($550*150 = $82,500), your EV is -$3,750.
Being up $5,000 would mean you're up $8,750 from EV. That's about 1.23 SD's. Putting the odds of this being chance around 10% or so.
That's assuming I did my math right.
April 14th, 2017 at 6:53:58 PM
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Thank you. Sounds about right to me. How many bets (roughly) till one would concludes that "chance" is down to near 1% assuming the same win percentage?
April 15th, 2017 at 9:06:43 AM
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good question, imoQuote: bazooookaWhat if it took 1500 bets instead of the 150 would that imply skill (albeit very slight) since one is only getting 10 units of profit after 1500 bets? Or would a good run last this long?
I say 1500 is a small sample sizeQuote: bazooookaAt some point things head to 50/50 and the vig crushes you but when can we see if it's skill vs luck.
I get, using Excel,
at 1500 bets
1 in 30 would still be showing a profit of at least $272.73
ands
1 in 55 would still be showing a profit of at least $5,045.45
some by just luck (I am lucky) would be winning even more
thinking it was more than luck, of course.
Sally
I Heart Vi Hart
April 15th, 2017 at 9:22:33 AM
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still using ExcelQuote: bazooookaThank you. Sounds about right to me.
(binomial probability distribution)
0.2838877
is the probability of showing at least a profit after 150 bets.
at least 10 unit profit is about
0.0824535
or about 1 in 12
good questionQuote: bazooookaHow many bets (roughly) till one would concludes that "chance" is down to near 1% assuming the same win percentage?
I just plugged in a few numbers instead of calculating (using ev and sd)
I get about 2400 bets for 1 in 105
of showing a profit
but remember
1 in100 is still a large value to some
and some R luckier than others
Sally
I Heart Vi Hart
April 16th, 2017 at 4:43:26 PM
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Sally,
I agree that luck can never be ruled out. I for one would back someone with a 1000+ picks at 57% percent. That kind of luck seems worthy of bet tailing.
I agree that luck can never be ruled out. I for one would back someone with a 1000+ picks at 57% percent. That kind of luck seems worthy of bet tailing.
April 16th, 2017 at 4:47:18 PM
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1 in 55 works for me? I hope my luck continues. The fact that only 1 in 30 will barely have any kind of profit left shows how hard it is to beat the vig since most are just flipping coins with their picks or worse.
May 8th, 2017 at 5:22:49 PM
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Sally,
I'm 500 bets in and still hitting at 55%; if this holds until 1000 or even 2000 bets what's odds of "luck" if one can hit 55% ATS that long?
I'm 500 bets in and still hitting at 55%; if this holds until 1000 or even 2000 bets what's odds of "luck" if one can hit 55% ATS that long?
May 8th, 2017 at 6:18:00 PM
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Quote: bazooookaSally,
I'm 500 bets in and still hitting at 55%; if this holds until 1000 or even 2000 bets what's odds of "luck" if one can hit 55% ATS that long?
What you are really asking is: given a record of 55% over "n" trials what is the "statistical confidence" that I am at least a 51% player -or a 53% player -or a 55% player?
I would encourage the respondents to quote the statistical confidence level.
For some reason, everyone in this dang forum talks about 3-sigma or 5-sigma -as if you don't have considerable confidence in something when you are only at 1.5 sigma. Frankly, if you have a statistical confidence of, say, 80%, then you are probably more confident of that fact that most things in your life.
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
May 8th, 2017 at 6:47:21 PM
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Gordon,
I agree. I assume 50/50 is baseline so I'd like to see how often someone can stay above that for 1000+ picks? And also assuming an edge how rare would it be to be below 50% after 1000+ picks. I imagine 1000+ picks would weed out skill vs luck especially if one was still at a 55% clip. But maybe not?
I agree. I assume 50/50 is baseline so I'd like to see how often someone can stay above that for 1000+ picks? And also assuming an edge how rare would it be to be below 50% after 1000+ picks. I imagine 1000+ picks would weed out skill vs luck especially if one was still at a 55% clip. But maybe not?
May 10th, 2017 at 5:03:57 AM
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Quote: bazooookaSally,
I'm 500 bets in and still hitting at 55%; if this holds until 1000 or even 2000 bets what's odds of "luck" if one can hit 55% ATS that long?
If you are beating closing lines and the take-back the majority of the time I would think we could take "luck" out of the equation in only 500 trials. If you are not, then we should still be looking for a larger sample size, unless there is some other reason to believe the 55% is a true reflection. What happened in the past is virtually meaningless compared to what you expect will happen going forward.
May 10th, 2017 at 6:40:34 AM
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I think the idea would be interesting betting $100, then $200, then $300, $100 up at a time until you get to $1000, betting whether you win or lose. $5500 total bets. Naturally you would rather win the last 4 over the first four, not lose them all. I can see doing this sequence but months between bets if not a year or more just waiting for a bet you think is right.
I am a robot.
May 10th, 2017 at 9:48:21 PM
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Bet Bouncing can ruin even good systems. I'm mainly a flat unit guys. Guys who are up but pick under 50% are just lucky. We all have those friends who goes big in playoffs etc to make up for a bad season. It works till it doesn't. Also guys that can beat the spread over 1000s of picks can still bust if they bet too big and then have a bad run of 11 out of 15 losers etc. It happens =(
