Regression towards the mean / Gambler's Fallacy

**Pokerjoe** · 09-02-09, 04:26 AM

This is actually a huge philosophical question, and important not just for following other cappers.

If you think the cappers are coin-flipping, then it doesn't matter which you follow.

If you think they have skills, the question breaks down like this:

There are basically two kinds of regression: causal, and dilutive.

Causal is like this: take a deck of cards. Turn them over, one at a time. If you start out with a lot of red cards, you will "regress" back to 50% by the end of the deck. The overabundance of red cards early "causes" the regression.

But dilutive regression is like this: take a coin, and flip it. If you get an overabundance of heads early, but keep flipping, and get 50/50 results thereafter, your percentage of heads will drop, but only because the initial overabundance of heads has been diluted as the sample size expanded. The overabundance doesn't cause the percentage to drop; the sample increase merely dilutes the initial overabundance's impact of the percentage.

So, which is it, with your handicappers?

**the shadow** · 09-02-09, 04:30 AM

Bet them both!!!!!!!!!!!!!
You just said they will hit 60% ats

**Pancho sanza** · 09-02-09, 09:11 AM

60 % ATS? Not happening.

**juuso** · 09-02-09, 09:14 AM

Yep, expecting a +EV capper to do well after a 20 game downswing falls in the domain of gamblers fallacy. 20 games are miniscule sample size and wild streaks are expected to happen.

If both cappers are +EV and roughly as good, there is no difference. Sports games are independent events. They are both just as likely to be positive for the next 20 picks. Just pick either, or preferably, tail both of them.

**Dark Horse** · 09-02-09, 09:46 AM

The question isn't about isolated events or coin flips, but about streaks. There is a cyclical element to this that is often overlooked, or ridiculed, by linear minds. Think about regression towards the mean as gradually 'coming full circle'. So if you know for a fact that a capper is going to pick 60% long term and is only hitting 54%, he obviously has some catching up to do. The opposite is true for a capper who is picking much higher than his long term percentage. We're not talking about the very next event, but long term.

But in this case there isn't enough clarity. First of all, we don't know the person, nor his motivations. The reason why he's picking much below his average isn't clear. He may simply be experimenting with a new approach. And the question of winning percentages itself is somewhat nebulous. Many people throw all sports on one big pile, but percentages should be applied on a league by league basis, because it can't be assumed that a player has the same level of expertise in all sports. In addition, regardless of expertise, ML sports as hockey and baseball may result in a very different percentage than ATS sports as football and basketball. So if the choice was to follow or fade I would pass, because there's not enough information.

**u21c3f6** · 09-02-09, 10:16 AM

As you have stated the question, yes, I agree with you that you should wager on A's selections.

This is based on your assertation that both cappers will have selected exactly 60% wins at some point in the future. Of course, this assertation is probably impossible to know for a fact.

Joe.

**Peep** · 09-02-09, 10:20 AM

Neither. You don't know if one is any better than the other.

I have a question for the philosophers though.

Let's say that both were indeedy flipping coins. Which one should you play now?

I would say either. If you are +10 after twenty flips of the coin and going to 1000, I would bet +105 either way that you finished over +10 or under +10.

**ICE-BLOOD** · 09-02-09, 12:01 PM

tough call

reminds me of going 1-4 on an nfl sunday with a remaining upcoming play on monday night deciding whether to wager more

**roasthawg** · 09-02-09, 12:39 PM

You have a 60% chance of winning with either one. No amount of winning or losing streaks is going to change that going forward if they are still 60% cappers. Regression to the mean is a descriptive term, not a predictive tool.

**the shadow** · 09-02-09, 02:27 PM

this is a test!!!
roasthawg is correct

**Pokerjoe** · 09-02-09, 02:36 PM

Except, roasthawg, in the case where results can "cause" the regression, as in the deck of cards example I gave.

In sports, it can work like this: suppose you have a system that's profitable.
It picks Team A early, which thereafter goes 3-0 ATS. If a team goes 3-0 ATS, it's going to get backed more often, the advantage will decrease, and thus you could fairly say that the ATS success will "cause" the later regression.
But if the system goes 0-3, the opposite will be true.

You could say the old MNF home dog system was like this. It's success caused its demise. So a bettor who didn't have ratings with which to anchor the MNF home dog advantage would have been better off saying "wow, this thing is in all the capping mags, it's been really successful, so, "I'd better get off it."

IOW, the OP's capper's approach is part of the answer, and he didn't mention their approach, so we can't really say. But if they're using un-anchored systems (that is, systems which aren't projecting a score, like the old MNF home dog system), then the results might logically be subject to regression.

**reno cool** · 09-03-09, 03:49 AM

If you know they both have an expected % of 60 there is no difference. However, I dont know how you'd ever know this for sure.
Certainly don't see any reason to prefer the one going 6-14. Regression would only imply that he's more likely to do better than 6-14 in his next 20, but we already knew that.

**the shadow** · 09-03-09, 02:41 PM

Pokerjoe, how do we know that mnf results weren't a matter of luck?
Were all mnf games off 3 points,or is like flipping a coin where heads came up more than tails over 150 games+-?
I believe it's a combination of both!!
good thread!!

**Pokerjoe** · 09-03-09, 04:50 PM

Originally posted by the shadow

Pokerjoe, how do we know that mnf results weren't a matter of luck?
Were all mnf games off 3 points,or is like flipping a coin where heads came up more than tails over 150 games+-?
I believe it's a combination of both!!
good thread!!

Well they could have been luck, sure. But it's at least possible that linemakers underestimated the novelty (at the time) of appearing on MNF, and thus a resulting special incentive to home dogs. It really did used to be a big thing. Not so much now, although still maybe worth an extra, say, 1/2 point in HFA.

But the point isn't about any given system or capper, it's about the impact of method on the question of expected regression.

IF the expected results don't change with past results (as in a capper with a system whereby he knows X points difference from his rating and the spread will equal Y advantage), then results merely reflect variance and thus have no expect future regression, and thus shouldn't empact EV.

But if past results have causal impact (as with the possible examples I've noted previously), then yeah, those results will impact future returns, conversely.

**PowerMovePicks** · 09-03-09, 10:53 PM

Not enough information is given. Some cappers get too loose when they are up big (18-2) and some get too tight when they are down big (6-14) and some stay cool calm and collected. Your best bet is still and always will be to put in the time yourself and cap the games yourself.

**rk9** · 09-04-09, 09:20 AM

If the cappers were 100% sure that they would hit 60% for the season then the card analogy works because the season makes it a finite set. IE the capper has to hit 14 out of 20 the last week to hit 60% of the year. However since no one is positive they will hit 60% this is completely hypothetical.

Instead this should be thought of as infinite. So they each have a 60% chance and same chance of winning. Think of a coin that you flip 100 times. it hits heads 90 times out of 100. the odds that the next flip, 10 flips, 100 flips that you hit tails is still 50%.

**Dark Horse** · 09-04-09, 11:50 AM

Originally posted by rk9

If the cappers were 100% sure that they would hit 60% for the season then the card analogy works because the season makes it a finite set. IE the capper has to hit 14 out of 20 the last week to hit 60% of the year. However since no one is positive they will hit 60% this is completely hypothetical.

Instead this should be thought of as infinite. So they each have a 60% chance and same chance of winning. Think of a coin that you flip 100 times. it hits heads 90 times out of 100. the odds that the next flip, 10 flips, 100 flips that you hit tails is still 50%.

To say it is 'infinite' is a perfectly safe bet. But it doesn't translate very well into every day life. Along that same line of reasoning, one could not determine a (ATS) winning percentage until at the very end of the bettor's life. And that will still not approach an infinite number of bets.

In reality it only takes a few hundred bets to determine a winning percentage with a high rate of 'stability' (determined by Z-factor). Let's place the number high, at 1000 bets.

Let's say somebody picks 57% ATS over a 1000 bets. With nothing else changing, will he pick that same percentage over the next 1000 bets? And, if not, what variance could be expected?

I do agree with the infinite outlook, but in a cyclical, rather than linear picture. A person will tend to come full circle to the point where he started out from (at least to within a few 'degrees'). A familiar time cycle is a year, so we may as well start out with that.

We also have to deal with fluctuations in skill level, luck, and betting environment, so it is important to determine how far a person can stray from his average during one cycle.

In the end the picture may be as personal as a fingerprint. And the answer may turn out to be that some bettors have a much greater stability, in (closely) meeting their winning percentage year after year, than others.

Luck plays an important part on a seasonal scale. Contests are a good example of this. More often than not, one bettor gets hot and wins, only to find himself back in the pack the next year. By the same token bad luck factors in. I would suggest that experienced cappers can keep bad luck under control, by avoiding conditions that invite it; but good luck is not so easily charmed.

**Pokerjoe** · 09-04-09, 01:46 PM

Of course the infinite set is the normal way of looking at it (meaning that seeming regression is reflective of the dilution effect of increasing sample size).

But it is possible for past results to influence future results. With a roulette wheel or a coin flip, no. But sportsbetting takes place in a market, and past results can influence future odds.

Coin flip results don't influence future coin flips. But ATS results do influence future spreads.

If you handicap that Team A will be grossly underrated this year, and decide to bet on them every game, if after 5 games Team A is 5-0 against the spread, that fact will definitely influence your future expectation on betting on Team A. This is so true, you might want to stop betting on Team A BECAUSE you're already 5-0 on them.

So if you're following two handicappers who's approach is to identify under and over rated teams at a season's start--and let's hypothesize that they've proven themselves good at that approach--then you might very well want to back the handicapper who starts off poorly, and drop the capper who starts off hot.

Unlike coin flips, sportsbetting results are not always independent.

And I say this is a big issue in this biz because most of us agree with the idea of betting a % of our BRs. Our BRs increase with winning, and decrease with losing.

So if our past results are negatively correlated with future results, we're using a counterproductive money management system.

**rk9** · 09-04-09, 08:03 PM

dark horse- I agree with you. I guess what I was trying to say is even if we know the bettor will win 57% of the time, that losing 10 in a row does not mean he has a greater chance of winning his next bet.

Poker Joe- I understand the dependency if you are betting one team because adjustments will be made to a team who keeps beating the spread. However if you were betting different teams each week strictly depending on your leans (from rankings or whatever), would a bettors previous ATS results influence the future results? I guess I look at as independent, what do you think?

**the shadow** · 09-04-09, 09:27 PM

darkhorse makes a good point!! if the speed of light is the fastest known to man,how come it can't escape the black hole?

perhaps darkness is faster!!

just keep on plugging away,and hope for the best!!!!!!

**Wrecktangle** · 09-06-09, 02:23 PM

Rev Thomas Bayes says Handicapper B. You do NOT absolutely know each is performing at the 60% level in the "real world."

**Pokerjoe** · 09-06-09, 04:39 PM

Originally posted by rk9

dark horse- I agree with you. I guess what I was trying to say is even if we know the bettor will win 57% of the time, that losing 10 in a row does not mean he has a greater chance of winning his next bet.

Poker Joe- I understand the dependency if you are betting one team because adjustments will be made to a team who keeps beating the spread. However if you were betting different teams each week strictly depending on your leans (from rankings or whatever), would a bettors previous ATS results influence the future results? I guess I look at as independent, what do you think?

Gut-capping is probably independent. But I would also say that I can see how it might not be, depending on the capper's personality. Some people might cap better if they've been winning; confidence and all that; being in the zone. Others might get cocky and inattentive. Others might subconsciously (that is, in their gut) be favoring certain teams or situations (maybe a preference for home dogs or something) that can have causal regression.

If any well-known segment of bet types (like home dogs) goes on a long enough streak, the line will begin to change to reflect it. Thus it could become -EV solely because it's been winning.