Statistics question re: sample size

[JTrain]

For anyone with a stats background:

If I have multiple results of a two-possibility event, how can I calculate the probability that the event was not a random 50-50 event (such as a coin toss).

For example, if there were four trials with possibilities A and B, and there were 3 A and 1 B, there's a good chance you are describing a coin flip, since it would not be very unusual to see 3 heads and 1 tail in four flips. But if there were 20 trials with 15 A and 5 B, despite being the same percentage A (75%), it's less likely that the event in question was a coin flip, although not incredibly unlikely. If there were 1000 trials and the results were 750 A, 250 B, it would be extremely unlikely that the event was a coin flip.

I'm looking to put a value on just how unlikely it is that the events are random in situations like these. Obviously this relates to betting in regards to knowing when a trend is probably revealing some causal link versus just statistical variance.

[shadymcgrady]

U are using a linear method to measure or quantify a nonlinear object in the variable being sports

[Buffalo Nickle]

Not a stats guy but I learned this from Pinnacle:

Take the square root of the number of bets made and add it to half the number of bets. That is roughly the number of bets needed to win to be statistically significant.

So with 500 bets, the square root is roughly 22. Add 22 to 250 for 272 over 500 bets. You need to hit 272 (54.4%) to beat a coin flip substantially enough to consider that you might have skill.

[Waterstpub87]

First find standard deviation, sqrt(.5*.5*1000) = 15.8

So 1 standard devation is from 484 to 516.

95 confidence would be roughly 532 or so

99 confidence would be 538 or so

1 in 1000 chance would be 550 or so.

Might be small errors, writing on phone

[Bostongambler]

Deviation x=75% of 100 for 500 at bats as you say. SR 22-23.98888, to 75 a/d = sum total of 75. Plus or minus the divination.

[JTrain]

I think I may have figured it out. You have to use binomial probabilities and a calculator like this one:

http://vassarstats.net/binomialX.html

Let's say your record was 33-27. That's 60 bets. You want to know what the odds that a coin flip could achieve those results. The less likely a coin flip could achieve it, the more likely that you are a skilled bettor.

Enter:

n = total bets
k = losses
p = 0.5

Then hit Calculate.

Look at the P: k or fewer out of n number. In this example, it's 0.259479001595

Multiply by 2 (you want both ends of the spectrum): 0.259479 x 2 = 0.518958

Therefore, there is a 51.89% chance that a coin flipper could have achieved that result or better. So there isn't good evidence that you are a skilled bettor at 33-27. It's just as likely to be chance.

Another example, record of 36-24

P = 0.077500952002
P x 2 = 0.155001904

Therefore, there is a 15.5% chance that a coin flipper could have achieved that result or better. So it's very likely that your record is due in part to skill.

[Waterstpub87]

I think I may have figured it out. You have to use binomial probabilities and a calculator like this one:

http://vassarstats.net/binomialX.html

Let's say your record was 33-27. That's 60 bets. You want to know what the odds that a coin flip could achieve those results. The less likely a coin flip could achieve it, the more likely that you are a skilled bettor.

Enter:

n = total bets
k = losses
p = 0.5

Then hit Calculate.

Look at the P: k or fewer out of n number. In this example, it's 0.259479001595

Multiply by 2 (you want both ends of the spectrum): 0.259479 x 2 = 0.518958

Therefore, there is a 51.89% chance that a coin flipper could have achieved that result or better. So there isn't good evidence that you are a skilled bettor at 33-27. It's just as likely to be chance.

Another example, record of 36-24

P = 0.077500952002
P x 2 = 0.155001904

Therefore, there is a 15.5% chance that a coin flipper could have achieved that result or better. So it's very likely that your record is due in part to skill.

15.5% does not indicate that it is likely your record is due to skill. Less than 1% chance would indicate that maybe your record is partly due to skill, and that would be generous.

You cannot tell anything after 60 plays. Get to 10,000 and then check.

[JayRow]

JTrain, you may want to review the "conditions" for binomials. It works when all events have the same, independent probability of success.

So, it works for coinflips.

It does not work for a record in which sports games and bets have different probabilities/moneylines. MAYBE you could use it for an ATS record but that would probably be a violation too.

[JTrain]

15.5% does not indicate that it is likely your record is due to skill. Less than 1% chance would indicate that maybe your record is partly due to skill, and that would be generous.

You cannot tell anything after 60 plays. Get to 10,000 and then check.

15.5% shows that it is quite unlikely to occur in a pure chance scenario.

You contradict yourself by saying A) less than 1% chance could indicate skill and B) 60 plays cannot tell anything. If you are 45-15 after 60 plays, the chance of a coin flip being that far from 50-50 after 60 flips is less than two-tenths of one percent. So that would even meet your standard of skill detection.

It seems to me anything less than 25% would at least indicate it likely that it was not due to pure chance (closer to 0 than 50), with the lower you go obviously being more likely. Of course, there is no guarantee, just probabilities. Even someone with a record of 100-0 could theoretically just be astronomically lucky.

JTrain, you may want to review the "conditions" for binomials. It works when all events have the same, independent probability of success.

So, it works for coinflips.

It does not work for a record in which sports games and bets have different probabilities/moneylines. MAYBE you could use it for an ATS record but that would probably be a violation too.

Yeah, coin flip is the comparison. So you can only use it for plays where there are two equal sides, like spreads and totals. Won't work when betting money lines like you do.

[Waterstpub87]

15.5% shows that it is quite unlikely to occur in a pure chance scenario.

You contradict yourself by saying A) less than 1% chance could indicate skill and B) 60 plays cannot tell anything. If you are 45-15 after 60 plays, the chance of a coin flip being that far from 50-50 after 60 flips is less than two-tenths of one percent. So that would even meet your standard of skill detection.

It seems to me anything less than 25% would at least indicate it likely that it was not due to pure chance (closer to 0 than 50), with the lower you go obviously being more likely. Of course, there is no guarantee, just probabilities. Even someone with a record of 100-0 could theoretically just be astronomically lucky.




Yeah, coin flip is the comparison. So you can only use it for plays where there are two equal sides, like spreads and totals. Won't work when betting money lines like you do.

If you put 100 people in a room, and had them flip coins, would the 15 that went 36 and 24 or better have skill at flipping coins?

The skill % is dependent on sample size. I would not trust anything less than 1000 at all, much less 60. No one in the real world, science or quantitive finance, would lend any significance to anything in the top % 15 with 60 datapoints. 15% seems small, but it is very large when dealing with confidence levels.

Understand, not evidence of does not mean definatly not there. You cannot know, it is not a negative.

If it makes you feel better, believe it. Just don't mortgage your house to bet it.

If you want to be more confident measure your beating of the closing line.

[JayRow]

There is much debate in the statistics community if a p-value of .05 is appropriate. Times are a-changing.

[JTrain]

If you put 100 people in a room, and had them flip coins, would the 15 that went 36 and 24 or better have skill at flipping coins?

The skill % is dependent on sample size. I would not trust anything less than 1000 at all, much less 60. No one in the real world, science or quantitive finance, would lend any significance to anything in the top % 15 with 60 datapoints. 15% seems small, but it is very large when dealing with confidence levels.

Understand, not evidence of does not mean definatly not there. You cannot know, it is not a negative.

If it makes you feel better, believe it. Just don't mortgage your house to bet it.

If you want to be more confident measure your beating of the closing line.

If we agree the calculations are correct in showing the likelihood of a series of coin flips hitting that far from 50-50, that's good with me. That's what I was looking for.

Sample size is built into the calculation. People can decide what percentage they need to satisfy their conditions for confidence.

I do take your point on confidence levels. However, when deciding to tail someone, we generally don't have the luxury of waiting for them to have 1000 recorded plays under their belt. If a bettor is 40-20 and I calculate the odds of a random 50-50 event (coin flip) achieving that to be 1.4%, and the person seems to have an intelligent approach, then I'm going to conclude it likely that they weren't just very lucky.

[Waterstpub87]

If we agree the calculations are correct in showing the likelihood of a series of coin flips hitting that far from 50-50, that's good with me. That's what I was looking for.

Sample size is built into the calculation. People can decide what percentage they need to satisfy their conditions for confidence.

I do take your point on confidence levels. However, when deciding to tail someone, we generally don't have the luxury of waiting for them to have 1000 recorded plays under their belt. If a bettor is 40-20 and I calculate the odds of a random 50-50 event (coin flip) achieving that to be 1.4%, and the person seems to have an intelligent approach, then I'm going to conclude it likely that they weren't just very lucky.

If you know the answer that you want ahead of time, why bother with the statistics.

Glad that you found what you were looking for. Good luck with your tailing.

[JTrain]

Not sure what you mean by knowing the answer ahead of time. I'm just trying to use the statistics to understand the probabilities of certain events.

I appreciate your caution and would be glad to hear some of the math behind confidence levels. You say "Less than 1% chance would indicate that maybe your record is partly due to skill, and that would be generous." Can you show the math to be more specific?

For example, if someone had a record of 350-25, how would you calculate the percentage chance that they were skilled vs. pure luck?

[RudyRuetigger]

jtrain you are way fukkin off here

[jjgold]

Stats do not matter on sports
It's why everyone loses

All
In the line

[Waterstpub87]

Not sure what you mean by knowing the answer ahead of time. I'm just trying to use the statistics to understand the probabilities of certain events.

I appreciate your caution and would be glad to hear some of the math behind confidence levels. You say "Less than 1% chance would indicate that maybe your record is partly due to skill, and that would be generous." Can you show the math to be more specific?

For example, if someone had a record of 350-25, how would you calculate the percentage chance that they were skilled vs. pure luck?

Compute z score and find p values. Most confidence values are either less than 5 or 1 %. I am on a phone, so I am not able to find the score of 350 and 25, but you would accept that as non normal.

It is the intuition behind the math that you do not realize is the problem. Imaging that you broke down a life time of betting into 60 bet series. Some of these series would go 30 and 30, some 40 and 20 and some 50 and 10. Your 50 and 10 would be very significant, but that in itself does not mean that you are a winning gambler. You just had a good run. It is harder to get lucky over a larger number of bets, therefore if you want to establish skill, you would be more confident with a larger number of bet.

Unfortunately, statistics is not geometry. Things are never definate, only likely or unlikely.