Another sample size system...

[Pot luck]

OK I see. Lets call them approximately independent .

In relation to OP's problem and Dark Horses response, the issue is that he may have been particularly successful betting games during an unusual period of time, catching an edge on a short term trend ('draw season' in Italy for a poignant example) in which case a longer window is needed to establish whether he can successfully bet games all season long.

OP stated however, that he is betting on games in many leagues at different stages in their seasons and therefore a short term trend is probably not the issue.

[hutennis]

I guess I should've pointed it out, but I did not mean to get involved with OP at all.
Too many things there look strange and are needed to be taken at face value. For my taste at least. So I pass.

I just wanted to make a comments on something that is more general in nature and is being misused imho pretty often. Like sample size, probability etc.
I'm still waiting for any thoughts on my size/probability/z score argument from "sample size not large enough" crowd.
I guess I gotta be patient.

[donjuan]

There are a couple of interesting points here I'd like to have explained please.

1. Sample size big enough...

Since we all know what is "big enough" we should have pretty good feel of what is not "big enough", right?

I see it here all the time.
"LOL at your 120 games sample size" or "Stop crying about 40 games sample size" etc.
So the idea of what is not "big enough" is certainly there.

Well, I have a question then... Let's see.

After a 1000 coin flips the results are 545 heads, 455 tails.
Now we can safely say that coin is not fair. Heads have an edge.
Probability that they don't is 0.24% with corresponding z score of 2.82.

Now, lets reduce our sample size to just 10 coin flips.

Wow, this is not even funny, right? For sure it's well pass LOL as far as sample size. It has to be at least LMAO or maybe even ROFL.
Yeh, maybe. But the thing is that in those 10 flips there was not a single tail.
Do I need another 990 tries to conclude that coin is not fair and heads have an edge?
Or probability of 0 for 10 being 0.000977 with z score 3.09 should be enough?

And if it is enough then once again it's not the size that matters, but probability (z score) of observed results.
So instead of LOL at 40 games sample size we should ROFL at 1.93 z score.

Am I missing anything?

2. Test period. Wider window, at least a year.

What the hell are you talking about????

How would independent event (coin flip, draw of the card, result of football game, horse race or tennis match) even know about time period??? Why would it care????
Independent events are not humans. Not only they don't have memory, they have no idea what the calendar is either!!!!

Do you imply that results drawn from 10000 data points collected over a year are more valid then results of 1000000 Monte Carlo simulations done in 1.3 seconds?

Welcome to the pseudo-scientific world of Dark Horse.

[Dark Horse]

lol. The weather must be driving you crazy.

[evo34]

There is a reason a sample spread out over time is generally more predictive than the same sample size over a very short time frame. Transient variables tend to even out over time (weather, injuries, refereeing style shifts, etc.). These variables will not necessarily even out with a huge sample over a compressed time period (as they tend to affect games in groups, not entirely independent of each other). And most betting models will have biases (often unintentional) that are helped/hurt by such variables. By contrast, a theoretical coin flip is not going to have transient variables affecting it. So 10 flips in 10 seconds is worth exactly the same as 10 flips over 10 years.

It's the same in stock trading. You would never want to draw conclusions on six weeks of test data, no matter how large the sample. The reason is that you may be sampling a very unusual market (massive bull run, major political unrest, etc.) that is not likely to represent conditions going forward.

There are a couple of interesting points here I'd like to have explained please. 1. Sample size big enough... Since we all know what is "big enough" we should have pretty good feel of what is not "big enough", right? I see it here all the time. "LOL at your 120 games sample size" or "Stop crying about 40 games sample size" etc. So the idea of what is not "big enough" is certainly there. Well, I have a question then... Let's see. After a 1000 coin flips the results are 545 heads, 455 tails. Now we can safely say that coin is not fair. Heads have an edge. Probability that they don't is 0.24% with corresponding z score of 2.82. Now, lets reduce our sample size to just 10 coin flips. Wow, this is not even funny, right? For sure it's well pass LOL as far as sample size. It has to be at least LMAO or maybe even ROFL. Yeh, maybe. But the thing is that in those 10 flips there was not a single tail. Do I need another 990 tries to conclude that coin is not fair and heads have an edge? Or probability of 0 for 10 being 0.000977 with z score 3.09 should be enough? And if it is enough then once again it's not the size that matters, but probability (z score) of observed results. So instead of LOL at 40 games sample size we should ROFL at 1.93 z score. Am I missing anything? 2. Test period. Wider window, at least a year. What the hell are you talking about???? How would independent event (coin flip, draw of the card, result of football game, horse race or tennis match) even know about time period??? Why would it care???? Independent events are not humans. Not only they don't have memory, they have no idea what the calendar is either!!!! Do you imply that results drawn from 10000 data points collected over a year are more valid then results of 1000000 Monte Carlo simulations done in 1.3 seconds?

[Bao Jingyan]

There is a reason a sample spread out over time is generally more predictive than the same sample size over a very short time frame. Transient variables tend to even out over time (weather, injuries, refereeing style shifts, etc.). These variables will not necessarily even out with a huge sample over a compressed time period (as they tend to affect games in groups, not entirely independent of each other). And most betting models will have biases (often unintentional) that are helped/hurt by such variables. By contrast, a theoretical coin flip is not going to have transient variables affecting it. So 10 flips in 10 seconds is worth exactly the same as 10 flips over 10 years. It's the same in stock trading. You would never want to draw conclusions on six weeks of test data, no matter how large the sample. The reason is that you may be sampling a very unusual market (massive bull run, major political unrest, etc.) that is not likely to represent conditions going forward.

Back to OP, I think the idea of a distortion in results is counterbalanced by the range of matches bet (everything from amateur to top level professional, with games across five continents). I think if anything a 1000 game sample over a month in these conditions would be less susceptible to the trends you mention (weather, injuries, refereeing style shifts, etc.) than a full season in a single league.

[Bao Jingyan]

It's the same in stock trading. You would never want to draw conclusions on six weeks of test data, no matter how large the sample. The reason is that you may be sampling a very unusual market (massive bull run, major political unrest, etc.) that is not likely to represent conditions going forward.

IMO this is not a fair comparison. Markets are linked by nature, and it is likely that the affects of something like major political unrest will be felt across the board. With the exception of long term shifts in strategy or overarching rule changes, I don't see how a trend towards, say, more draws in the Ukrainian 2nd division affects a top level match in Brazil.

[Wrecktangle]

You need to think about causality a bit. Leagues change because rules change (NFL is a fine example of this) and then so win results change especially if you are using a simulation. Within a league within the year the situation changes: MLB has inter-league play, play in NBA changes after the trade deadline, play in CFB changes in bowl games, etc.

As another extreme example: one year, the league wide HFA in the NBA dropped to zero for approx. one month and then returned; totally screwed up the return.

Hardly anything is constant in sports and it will affect your win rate over time.