Middling-when is it mathematically worth it?

[Data]

You were the one who wanted to use full Kelly:

No, I was just saying that there's no reason to buy back even a 5% position @ 57% -110 (to maximize the full-kelly utility function) with a coinflip -110.

Then, later you say that making full Kelly bets is insane:

Betting >5% on an NFL total is insane unless you're a top .1% (or maybe even better) handicapper. If you think your edge is bigger than that at the time you bet it, and it isn't because you beat a book to a huge information-based steam move (or find a horribly stale line, in which case there's no way I could even get 2% down on it, lucky to even get .5%, much less a full 5%), you're almost certainly wrong.

Your initial generalized statement not to buy back was wrong. Now you are trying to come up with certain scenarios when not buying back is mathematically correct. The problem is, it does defend your initial incorrect generalized statement and you introduce more errors along the way.

You may be confused but it seems that you just want to defend your position at all costs. In case of the latter I give up, resistance is futile.

[tomcowley]

For god's sake, you can have an estimated 57% edge a bazillion different ways than capping an edge at 57% at the time you bet it. Why are you even arguing with me? Nothing I've said applies solely to pregame staking. My two specific statements- not to buy back a 1u bet at more than -1c disadvantage (vs. -110) and not to buy back a 5% bet at coinflip -110 (to maximize EG) are both 100% correct. The first statement of mine that you attacked was the buyback on a 5% bet, and you just made up kelly-multiplier numbers out of thin air to "refute that". Your only pseudo-legitimate objection is that I stated "sane" instead of "5% or less".

Your first statement- that -EV middling/buying back *IS* higher EG is flat out wrong. It takes quite specific circumstances that are not applicable to the vast majority of bets that could be middled/bought back in some form. People -EV middle way too much and it's giving away money and growth. I'm trying to show that and all you can do is bring up irrelevant crap about how you should have bet 10% pregame, or related stuff. Assuming perfect information, we can both derive optimal pregame staking strategies until the cows come home, but none of them apply to the question that comes up way more often. I have x% on this line, I currently estimate the fair line to be Y, and I can buy back on Z. What should I do? I repeat: What should I *DO*? Not: What should I *HAVE DONE*? (if that question is even possibly relevant, which for futures/series/halftimes/4qs, it isn't).

[Data]

Sir, you repeated a number of your previous erroneous statements that I already commented on, I have nothing to add.

However, the question below is rather important.

I have x% on this line, I currently estimate the fair line to be Y, and I can buy back on Z. What should I do? I repeat: What should I *DO*?

if you are:

1. a Kelly bettor who wants to maximize EU
2. know your Kelly multiplier
3. computer literate to the extent you can use Excel and can manage to install Excel Solver

then you can find the answer using Ganchrow's spreadsheet at http://forum.sbrforum.com/handicappe...readsheet.html.

[tomcowley]

Quote which statements in post #32 are erroneous.

[cinpls081]

I had Giants +3.5 and Stealers +2.5. It was all set up with the way the score was 14-12 fopr sure 15-14 or 17-15 was going to be the final then the middle was dashed by none other then a back up CENTER....I ended up winning 85 dollars but would have cashed a nice 2500 dollar ticket had the game ended in the above range. I had another one on Monday night Tenn +2.5 Colts + 3.5.... That game was also ALL SET UP and then bang I won 114 dollar vs. 2100 Love in game hedging there is no other way to bet.

[dwaechte]

You're obviously ignoring supernovas in saltwater lakes and their correlation to NHL 1st Period totals. That's the problem with assuming an efficient market and finding derivative bets that are off. Supernovas. Saltwater lakes. Super saltwater lakes. Hockey. 1st periods only. Superwater. Pseudoscience.

Normally I hate putting people down just for the sake of it, but that was pretty funny.

[Patrick McIrish]

Until you guys figure out the hot zones you're just pissing in the wind.

[Dark Horse]

Thanks for sharing cinpls. Reminds me of a NBA game a few years back, when Suns bench player James Jones ran back to block a pointless layup in the final second, with the game already won. You know, the kind of points no player in his right mind cares about. I guess he was trying to prove he should be a starter.

Donjuan, your easy references to pseudo-science simply reflect an unwillingness to think outside of the box. Good scientists are never afraid to explore the unknown. Which would make you not a scientist, but a data cruncher; someone who works with results discovered by others. To each his own. I, for one, have never met a successful sports bettor who, in the quest for new angles, wasn't willing to go beyond the information accessible to all.

[Dark Horse]

Until you guys figure out the hot zones you're just pissing in the wind.

Good to know that the 'think tank' has not been entirely run over by mathematicians with little understanding of sports betting. One of these gentlemen didn't even know what an overlay is. And how does he ask? "What on earth is that?" and "What the hell is that?"

I know RickySteve knows his business, but he's just a vitriolic character. Fine by me. I know he's a good gambler. But for some of these others to sing that tune is nothing short of hilarious.

For the record, I'm not saying this to be negative. To me a think tank is a place where ideas are exchanged and new angles explored, in a spirit of sharing and creative thought. Instead this place has turned into a number crunching factory, with little room for anything else. A missed chance at something more interesting.

[reno cool]

Good to know that the 'think tank' has not been entirely run over by mathematicians with little understanding of sports betting. One of these gentlemen didn't even know what an overlay is. And how does he ask? "What on earth is that?" and "What the hell is that?"

I know RickySteve knows his business, but he's just a vitriolic character. Fine by me. I know he's a good gambler. But for some of these others to sing that tune is nothing short of hilarious.

For the record, I'm not saying this to be negative. To me a think tank is a place where ideas are exchanged and new angles explored, in a spirit of sharing and creative thought. Instead this place has turned into a number crunching factory, with little room for anything else. A missed chance at something more interesting.

this is good

[donjuan]

Donjuan, your easy references to pseudo-science simply reflect an unwillingness to think outside of the box. Good scientists are never afraid to explore the unknown. Which would make you not a scientist, but a data cruncher; someone who works with results discovered by others. To each his own. I, for one, have never met a successful sports bettor who, in the quest for new angles, wasn't willing to go beyond the information accessible to all.

pseudoscience [(sooh-doh-seye-uhns)]

A system of theories or assertions about the natural world that claim or appear to be scientific but that, in fact, are not. For example, astronomy is a science, but astrology is generally viewed as a pseudoscience.

Your stuff on hot zones is almost as amusing as your stuff on streaks. Of course you refuse to back it up with the slightest hint of evidence but you expect people to believe you because you use some math/science terminology in your "explanation". Most of us see it for what it is: pseudoscience.

[tomcowley]

Good to know that the 'think tank' has not been entirely run over by mathematicians with little understanding of sports betting. One of these gentlemen didn't even know what an overlay is. And how does he ask? "What on earth is that?" and "What the hell is that?"

Some of us just call it "edge", since, using your terms, a 2-pt overlay from 38.5 to 40.5 isn't worth nearly the same amount as one from 46.5 to 48.5, so speaking about "a 2-pt overlay" out of context is meaningless, and speaking about one in context requires a mental conversion using the value of points to know how good it really is, or, in simple terms, you have to convert to edge/added win%. Sorry, I'll stick to "edge" and "win %" instead of a term I can't find a single good use for.

I'm still curious what a hot zone is.

[BigCap]

It really doesn't matter if you projected the total at 45, 47.5, or 50- that makes a minimal difference in the odds that it will land on 47-48 and therefore a minimal difference in the EV of the middle. If you played o46.5 -110, and the market is now 48.5 -110/-110 , then you DO have a +EV middle because you'll win about 7% of the time on a combination that pays 20:1. However, if you've bet o46.5 for a sane amount, and you consider the market to be fair at 48.5 -110/-110, you should just let o46.5 ride. It's higher EV and EG. You generally shouldn't middle a sane bet unless you think the second bet is 0EV or better on its own.

Let's walk thru this scenario with a bit more granularity to see if a middle is the right play or not.

Assume that a bettor perceives he has a small advantage betting over 46.5 -110, enough to bet a full kelly stake of 1%, which I believe by your definition would constitute a "sane" bet. This would then mean the bettor estimates the over 46.5 probability at 52.858%. So the bettor plops down 1% of his bankroll on over 46.5.

Now, the bettor sees under 48.5 -110 at another book. What does the bettor perceive the chances of under 48.5 hitting? If we assume the middle (47 & 48) frequency at 7%, it would be 1 - .52858 + .07 = 54.142%. So without even thinking the bettor will make this bet because it is +EV, and if he maximizes his EG he will bet 4.57% of his original bankroll on under 48.5. This assumes that over 46.5 is no longer available. Does this hold on smaller middle frequencies? In this specific case, the bettor would only begin hedging if the middle frequency was greater than about 4.85%, or about 52% probability hitting under 48.5. The majority of NFL two point middles are > 4.85%, so in most cases a kelly bettor betting at a "sane" edge will indeed bet the middle to increase growth.

Now, you indicate that the bettor should not middle over 46.5 -110 bet with under 48.5 -110, if the bettor thinks 48.5 is the true line. You are now estimating probability on over 46.5 hitting at 57% (using same middle frequency of 7%), which yields a kelly bet 9.7% of your bankroll, and EG of .43%. If the bettor plays under 48.5 -110 with 3.5% of original bankroll, he increases his EG to .49%.

So in either case, you are incorrect. When making SANE bets (i.e. 1% of bankroll), a typical NFL two point middle will increase EG. If you are making big kelly bets because of a perceived big edge, a typical NFL two point middle will also increase EG.

[tomcowley]

FFS, please read the thread. Objection 1: I never said you shouldn't 0EV/+EV middle. Ever. Derf. Objection 2: I've already stated that I should have just said 5% instead of sane, dead horse, meet stick. Anything else?

[Dark Horse]

you have mail

[BigCap]

Ok,

You generally shouldn't middle a sane bet unless you think the second bet is 0EV or better on its own.

If this is your advice as I am reading it again like you suggested, then I refuted it with my point that 2 point NFL total middles GENERALLY SHOULD be middled with a SANE kelly bet of 1%, even if the second bet is -EV. I'm sure you would agree that a kelly bet of 1% is a sane bet.

Then this,

Your first statement- that -EV middling/buying back *IS* higher EG is flat out wrong.

I showed you that you should middle a 52% chance bet laying -110, which indeed is a -EV bet.

And this,

The first statement of mine that you attacked was the buyback on a 5% bet, and you just made up kelly-multiplier numbers out of thin air to "refute that". Your only pseudo-legitimate objection is that I stated "sane" instead of "5% or less".

However, a full kelly bettor would NOT bet 5% of his bankroll on a 57/43 edge -110, they would bet 9.7%. Which by your "definition" is a large bet, > 5%. This is the point Data was trying to get across to you, that is somebody betting 5% of his bankroll on a 57/43 edge would be betting about half kelly.

So, to sum this up:

Point 1. Sane (1% kelly) bets on NFL totals GENERALLY SHOULD BE MIDDLED if you can get two points on a subsequent bet, even if the subsequent bet alone is -EV.

Point 2. Large bets on NFL totals betting @ kelly (roughly about 6.5% of bankroll, which equates to an edge of 55.5/44.5 at -110) GENERALLY SHOULD BE MIDDLED even if the subsequent bet is a coin flip, and the odds (-110) on the subsequent bet reduces it to -EV.

I have stated this as concisely as possible. I have read your posts and your advice appears to contradict each point. If you are not (or no longer) contradicting my above points then I am done with this.

[tomcowley]

First, you're quoting completely out of context, and the part you left out- that you consider the market to be currently fair at 48.5 -110/-110, the price offered, is rather important.

If this is your advice as I am reading it again like you suggested, then I refuted it with my point that 2 point NFL total middles GENERALLY SHOULD be middled with a SANE kelly bet of 1%, even if the second bet is -EV. I'm sure you would agree that a kelly bet of 1% is a sane bet.

Wrong. To maximize EG (I'm only saying this here once, but everything is with that intent), a +EV 1% bet shouldn't be middled, however big the middle is, unless the buyback bet is better than -2c disadvantage.

I showed you that you should middle a 52% chance bet laying -110, which indeed is a -EV bet.

Really, no shiite, you middle a 5% bet with a 52% bet on the other side? Wow. I learned something. Oh, wait, you're ignoring the quoted parts where the buyback on the 5% is a coinflip, not a 52% bet, and where I said you shouldn't buyback a 1% bet at -2c or worse, and 52% is not -2c or worse. So which of my statements were you referring to again?

However, a full kelly bettor would NOT bet 5% of his bankroll on a 57/43 edge -110, they would bet 9.7%. Which by your "definition" is a large bet, > 5%. This is the point Data was trying to get across to you, that is somebody betting 5% of his bankroll on a 57/43 edge would be betting about half kelly.

Which is only a tangentially relevant point in certain situations (not the least of which is getting that much down on the line), and not if your estimation of the fair line changes after you've bet it, for numerous reasons (information, halftime, 4th quarter, games played, etc).

Point 1. Sane (1% kelly) bets on NFL totals GENERALLY SHOULD BE MIDDLED if you can get two points on a subsequent bet, even if the subsequent bet alone is -EV.

Completely wrong, for a 1% bet, if the buyback bet is -EV by 2c or worse. If you want the exact decimal in between -1c and -2c, I'll work it out, but: -1c: middle. -2c: don't middle.

Point 2. Large bets on NFL totals betting @ kelly (roughly about 6.5% of bankroll, which equates to an edge of 55.5/44.5 at -110) GENERALLY SHOULD BE MIDDLED even if the subsequent bet is a coin flip, and the odds (-110) on the subsequent bet reduces it to -EV.

Correct. It's also irrelevant to any position you could accuse me of having at the time you first posted, oh, wait, except for the fact that I'd already said/agreed that you should middle sufficiently large bets with a coinflip (5% is not sufficiently large). Thanks for repeating that- maybe the next person who comes along will see it before posting, now that it has been repeated 4 times.

[BigCap]

Wow.

Here is your original post, before you went off on a tangent:

It really doesn't matter if you projected the total at 45, 47.5, or 50- that makes a minimal difference in the odds that it will land on 47-48 and therefore a minimal difference in the EV of the middle. If you played o46.5 -110, and the market is now 48.5 -110/-110 , then you DO have a +EV middle because you'll win about 7% of the time on a combination that pays 20:1. However, if you've bet o46.5 for a sane amount, and you consider the market to be fair at 48.5 -110/-110, you should just let o46.5 ride. It's higher EV and EG. You generally shouldn't middle a sane bet unless you think the second bet is 0EV or better on its own.

To which I replied:

Assume that a bettor perceives he has a small advantage betting over 46.5 -110, enough to bet a full kelly stake of 1%, which I believe by your definition would constitute a "sane" bet. This would then mean the bettor estimates the over 46.5 probability at 52.858%. So the bettor plops down 1% of his bankroll on over 46.5.

Now, the bettor sees under 48.5 -110 at another book. What does the bettor perceive the chances of under 48.5 hitting? If we assume the middle (47 & 48) frequency at 7%, it would be 1 - .52858 + .07 = 54.142%. So without even thinking the bettor will make this bet because it is +EV, and if he maximizes his EG he will bet 4.57% of his original bankroll on under 48.5. This assumes that over 46.5 is no longer available. Does this hold on smaller middle frequencies? In this specific case, the bettor would only begin hedging if the middle frequency was greater than about 4.85%, or about 52% probability hitting under 48.5. The majority of NFL two point middles are > 4.85%*, so in most cases a kelly bettor betting at a "sane" edge will indeed bet the middle to increase growth.

* - actually this is 4.81%.

Now, what is wrong here? In the context of NFL totals (which was the thread you were responding to), 2 point middle frequencies exceed 4.81% over 76% of the time. If you are in doubt about 4.81% being the threshold, I can show you the calculation. This means the subsequent bet (in this case u48.5 -110), using the 7% push frequencies (which you acknowledged) would be about 51.95%, which is a NEGATIVE EV BET AT -110! This directly contradicts your original statement that:

You generally shouldn't middle a sane bet unless you think the second bet is 0EV or better on its own.

This statement stands on its own in the original post. I did not take you out of context. Your claim that I "ignored that 48.5 was fair value" has no relevance here. You later added this "1c, 2c" qualifier to bail you out. So are acknowledging that my first point of middling -110 2 point NFL totals is generally correct (about 76% of the middle opportunities meet the criteria, all except over 36, 39, 40, and 43), or not? Forget your 1c, 2c, backout. If you stand by your original statement, then you are wrong, plain and simple.

As far as my second point is concerned, it appears you are not disputing it, with this reply:

Correct. It's also irrelevant to any position you could accuse me of having at the time you first posted, oh, wait, except for the fact that I'd already said/agreed that you should middle sufficiently large bets with a coinflip (5% is not sufficiently large). Thanks for repeating that- maybe the next person who comes along will see it before posting, now that it has been repeated 4 times.

The correct number is not 5%, it is actually 5.5%, which would equate to a 55/45 edge -110. So I guess I was not repeating your figure. I indicated 6.5% as a minimum, which is not correct.

So my two points again:

Point 1. Sane (1% kelly) bets on NFL totals GENERALLY SHOULD BE MIDDLED if you can get two points on a subsequent bet, even if the subsequent bet alone is -EV. (in fact over 76% of all NFL 2 point middles meet this criteria, as indicated above)

Point 2. Large bets on NFL totals betting @ kelly (roughly about 5.5% (corrected) of bankroll, which equates to an edge of 55/45 at -110) GENERALLY SHOULD BE MIDDLED even if the subsequent bet is a coin flip, and the odds (-110) on the subsequent bet reduces it to -EV.

I don't really care if this is repeated, but it is important for those who want to maximize EG betting NFL totals.

[tomcowley]

You responded to the OP without reading the thread, where I'd clarified, you know, exactly what you were talking about, and you didn't add anything (correct) beyond what Data said. Data and I both know what we were saying, and neither of us were advocating factually incorrect positions.

Your whole problem is that you are looking at this as some fixed problem, where you have the opportunity to make all these bets at the same time, and no probabilities ever change. You can't quote, or even make up, any numbers that dispute any specific example I gave. The fact that you have a bet on o46.5, for some amount (1% in your example), with some assumed edge at the time you bet it, IMPLIES ABSOLUTELY NOTHING ABOUT THE WIN PERCENTAGE OF AN ACTUAL OR SYNTHETIC u48.5 THAT YOU CAN BET LATER. NOTHING AT ALL. You are *assuming* that your estimate of the win% of o46.5 remains the same, which isn't implied by anything that I said, or by reality. Hell, it could even be a halftime line to make u48.5 game.

Your point 1 is still completely wrong- when middling a +EV 1% bet, the size of the middle is irrelevant, only its edge matters: -2c or worse, don't middle it, ever (on -110). It doesn't matter if the middle is 2 points or 15 points (by a halftime line) if the buyback bet is worse than -2c. You're making bad assumptions to state anything beyond this

Your point 2 is ignoring one very important factor- THAT YOU STILL THINK YOU HAVE THE SAME EDGE AS AT THE TIME YOU MADE THE FIRST BET. There's absolutely no reason for this to be true in practice. If you have even a 7% bet, and at halftime, you estimate a 66% win%, and can buyback at coinflip -110, you should let it ride. In your example, even if you overbet with a 6% bet on o46.5, that you estimate to win 55% of the time, let's say the line- and your estimate of win%- both move. The line goes to 48.5, and your estimate is that you now win 60% of the time- so that you have a 6% position at 60% to win, and can buyback on a coinflip- and you still let this ride.

Trying to base *present* decisions on *past* estimates of edges is impossible. Trying to generalize rules based on *past* edges is silly- whenever the rules are right, it's by luck. When you base your rules and decisions only on 1) your current position, 2) the line you can bet, and 3) your estimate of win% on both, then you have rules that are applicable to pretty much any situation you find yourself in, and that don't require any assumptions about past edges.

[BigCap]

Your point 1 is still completely wrong- when middling a +EV 1% bet, the size of the middle is irrelevant, only its edge matters: -2c or worse, don't middle it, ever (on -110). It doesn't matter if the middle is 2 points or 15 points (by a halftime line) if the buyback bet is worse than -2c. You're making bad assumptions to state anything beyond this

My point assumes that the handicapper has calculated the edge and bets accordingly. When he can get a middle line somewhere else, he uses my rules to make the subsequent bet. Simple.

Your point 2 is ignoring one very important factor- THAT YOU STILL THINK YOU HAVE THE SAME EDGE AS AT THE TIME YOU MADE THE FIRST BET. There's absolutely no reason for this to be true in practice. If you have even a 7% bet, and at halftime, you estimate a 66% win%, and can buyback at coinflip -110, you should let it ride. In your example, even if you overbet with a 6% bet on o46.5, that you estimate to win 55% of the time, let's say the line- and your estimate of win%- both move. The line goes to 48.5, and your estimate is that you now win 60% of the time- so that you have a 6% position at 60% to win, and can buyback on a coinflip- and you still let this ride.

Are we talking about halftime bets, where the probability changes based on the progression of the game? No, we are not. We are talking about a big edge player who perceives a 55/45 edge to bet 5.5% of his bankroll. Again, if he can get a -110 with a 7% middle frequency, he should take it.

If you are going to continue to bring up how probability changes based on the middle number, save yourself the effort.

[tomcowley]

My point assumes that the handicapper has calculated the edge and bets accordingly. When he can get a middle line somewhere else, he uses my rules to make the subsequent bet. Simple.

This is meaningless at best- which is actually an improvement over your inital point 1.

Things that go in a spreadsheet to calculate optimal middles:
Utility function
Current position
Lines available for betting
Probability of each outcome

Things that do not go in a spreadsheet to calculate optimal middles:
Original edge
Number of points in the middle
Whether it's a spread or total
Push percentages
The sport involved

Are we talking about halftime bets, where the probability changes based on the progression of the game? No, we are not

One of us is talking about how to middle in any situation, and one is talking about how to middle extremely stale/off-market numbers or after 7% moves that don't influence your opinion.

We are talking about a big edge player who perceives a 55/45 edge to bet 5.5% of his bankroll. Again, if he can get a -110 with a 7% middle frequency, he should take it.

And why do you take it? Because it's a very slightly -EV (-1.7c) negatively correlated bet, not for any other reason. It has nothing to do with the middle frequency. You'd take reverse middles at -1.7c (or .38% below breakeven) in this situation (for example, a 40% to win hedge at +148.3 or +147.6) if you could get them.

[Dark Horse]

pseudoscience [(sooh-doh-seye-uhns)]

A system of theories or assertions about the natural world that claim or appear to be scientific but that, in fact, are not. For example, astronomy is a science, but astrology is generally viewed as a pseudoscience.

Your stuff on hot zones is almost as amusing as your stuff on streaks. Of course you refuse to back it up with the slightest hint of evidence but you expect people to believe you because you use some math/science terminology in your "explanation". Most of us see it for what it is: pseudoscience.

Call it whatever you want and embrace your ignorance on the subject.
God forbid that something would have escaped your attention. Why should I care and why would I share specifics? Those who know, know that they know. The fact that someone as arrogant as you lacks this edge offers more than enough counter amusement for me.

Go crunch some data, based on laws that others have discovered for you. And try to forget that, before their discovery, they surely fell under your definition of pseudo-science. It's all voodoo outside of that little box, so no candy from strangers. Not only can I not remove the plate before your head, I have no desire to do so. And I wonder, in a pseudo-scientific kind of way, if that makes me cruel... But the answer I get, every time I flip another tarot card, is 'no way Jose!'.

[Dark Horse]

For the more openminded, non-linearity is far from a non-scientific concept.

[reno cool]

The sad thing in gambling, and I assume in other fields is that those that are creative and discover new things are rarely as successful as those that take someone else's ideas, hammer them to the max, and proclaim themselves great entrepreneurs.

[Dark Horse]

That doesn't fly in gambling. Inherent in sports betting is the quest for an edge. And just as inherent is the wisdom of not sharing the fruits of that quest with the world. That's where typical science and sports betting differ.

[Art Vandeleigh]

I for one am rooting for you DH (not necessarily rooting against anyone).

If you can show an angle that is predictable to the extent that it is profitable, and not a temporary anomaly such as the number 21 coming up five of the last twenty spins on a fair roulette wheel, that would be greatly terrific.

Since sports is filled with non-linear beasts such as human ballplayers, umps/refs, coaches/managers, all who are prone to good and bad days and good and bad decisions, I can't rule it (profitable angles) out completely, even if the closing Pinnacle line does reflect that in the long run, -140 favorites win more frequently than -130 favs, -220 wins more frequently than -200, +130 dogs win S/U more frequently than +150, etc.

[donjuan]

So Dark Horse comes up with absurd claims like "hot zones" and streaks being relevant but refuses to provide anything to actually support the claims and hides behind not wanting to give up the info. That's fine if you don't want to give up your data or info, but don't expect anyone else to take you remotely seriously. And until you elucidate your views or provide even the smallest smidgen of proof, I will continue to call your ideas exactly what they are: pseudoscience.

[Dark Horse]

The fact that you expect winning edges to be presented to you in scientific papers merely proves you understand very little of the sports betting industry.

I'm afraid you have confused the strong math by some good sports bettors here with a misconception that this would be their only edge.

As to scientific approach. A real scientist does not dismiss what he doesn't know, but rather admits that he doesn't know. That is the starting point of all research. The fact that you discard what you don't understand is a rather unfortunate embrace of ignorance.

As to proof. I'm not here to prove anything to you. I was pointing you in a direction, but that was obviously too much to bear. I can assure you that what I referred to is common knowledge to many sports bettors. Like any data cruncher lacking initiative, you insist on ready made answers, because original research of even this simple nature is, apparently, beyond you. You're like a frog in a crowded little pond, who's unwilling to climb a little hill because there may be an ocean on the other side.

In short, your arrogance is misplaced. Any pseudo-scientist worth his salt would have little trouble tracing it to a deep-seated insecurity. To someone who has put all his eggs in one basket, the thought of starting from scratch outside of that single expertise must indeed be unbearable. Good luck to you.

Final answer.

[BigCap]

This is meaningless at best- which is actually an improvement over your inital point 1.

Things that go in a spreadsheet to calculate optimal middles:
Utility function
Current position
Lines available for betting
Probability of each outcome

Things that do not go in a spreadsheet to calculate optimal middles:
Original edge
Number of points in the middle
Whether it's a spread or total
Push percentages
The sport involved

The discussion is about middling NFL totals. I never generalized the discussion. My points were worded specifically toward NFL totals, and they are valid for that type of bet. The bettor already understood his estimation for the total score, and bet accordingly.

Assuming an edge yielding a 1% kelly bet, 76% of all NFL totals should be middled assuming that the bettor can get two points, as these middle frequencies exceed the 4.81% minimum threshold.

[Art Vandeleigh]

Math dummy needs help.

6 NHL games tonight, each listed at O/U 5.5

Four of the games are shaded a bit to the over (52%/48%), two games to the under (48%/52%)

Book A lists the Grand Salami as over 33 goals total -110
Book B lists GS as under 34.5 -110.

I'm sure middling is +EV, but anyone know how much, and how to go about calculating it (ahem Mr. Ganch)?

Better off taking one of the bets only?