For those that don't understand the value of 2

[beetman]

That Statfox article is horrible. Stick with Ganchrow's calculator.

[BuddyBear]

I'm mad that I missed thread.

Took forever to find, but I found it. It's worth it....Page 3 is a bit boring and there is some reconcilation and "mutual respect" among posters that occurs.

Just keep in mind ASU was +2.5 and got steamed to +1/PK right before kick-off and Texas proceeded to hand it to ASU. I think Texas was covering all but 2 minutes of the game. I lost my under bet on that game too

Anyway....i am heading to bed.

http://forum.sbrforum.com/players-talk/51828-i-hate-when-line-movement-tricks-me-into-thinking-im-right-side.html

[donjuan]

Just keep in mind ASU was +2.5 and got steamed to +1/PK right before kick-off and Texas proceeded to hand it to ASU. I think Texas was covering all but 2 minutes of the game. I lost my under bet on that game too

So what was the fair line on the game, in your opinion? Texas -30? Excuse me while I laugh at anyone who thinks that closing lines at Pinnacle are off by 10+ points.

[BuddyBear]

So what was the fair line on the game, in your opinion? Texas -30? Excuse me while I laugh at anyone who thinks that closing lines at Pinnacle are off by 10+ points.

Umm...the fair is line is +2/+2.5/+1 or whatever it was....

But the right side was Texas -whatever that night. That's not the point. You keep trying to change the argument. You just couldn't bring yourself to admit that you were not on the right side instead choosing to engage in a highly convulted discussion. If you want to live in a delusional world and have a ticket that said ASU +2.5 and say to yourself, "Well, ASU should have covered that spread..." then you are being intellectually dishonest. 10 minutes into the game you should have known it was a losing bet, but not a bad bet.

Dude, listen, I get your reasoning and don't disagree with you. If you liked ASU that night, getting ASU +2.5 was defintely the right (and only) price to play them. It was a good bet then, it is a good bet now, and it always will be a good bet considering it closed at +1.

However, stop being a dick. Everyone gets your speel on here....your a numbers guy, not a people person. We get that. Your posts on here are so ridiculous and condescending and it's huge turn-off. Go join the MENSA forum if you think you are all that.

Why don't you just post your plays on here and demonstrate to all of us how great you are???

[donjuan]

Umm...the fair is line is +2/+2.5/+1 or whatever it was....

By fair line, I mean the line that is perfectly efficient (game falls on each side 50% of the time).

But the right side was Texas -whatever that night. That's not the point. You keep trying to change the argument. You just couldn't bring yourself to admit that you were not on the right side instead choosing to engage in a highly convulted discussion. If you want to live in a delusional world and have a ticket that said ASU +2.5 and say to yourself, "Well, ASU should have covered that spread..." then you are being intellectually dishonest. 10 minutes into the game you should have known it was a losing bet, but not a bad bet.

I was saying it was the correct side, not that it "should have" won. I had it at around 53%, in line with market numbers. I expected it to lose quite often, sometimes in a blow out. That's how PDFs work.

Everyone gets your speel on here....your a numbers guy, not a people person. We get that. Your posts on here are so ridiculous and condescending and it's huge turn-off. Go join the MENSA forum if you think you are all that.

My goal here, for the most part, is to stimulate and engage in serious sports betting discussion.

Why don't you just post your plays on here and demonstrate to all of us how great you are???

Because my goal is not to show you how great I am. It's to correct errant thinking and engage in serious sports betting discussion. I have learned a lot from Ganchrow, Thremp, etc. in the last year and am definitely not above learning more. For example, up until a few months ago I focused too much on EV at the expense of EG. I didn't realize that making -EV hedges was optimal for EG, such as the following situation:

You and a friend agree to bet on the flip of a coin. The flip will be fair and your friend offers you +105 on heads. Another friend is there and offers you -101 on tails. You have a 10k bankroll and there is no max bet. What are your optimal bet sizes on each bet?

[beetman]

There is no such thing as a results-oriented "right side" in a sporting event. Betting baseball is a good way to disavow yourself of the notion that there's such a thing as "the right side" after looking at the results.

[Ganchrow]

You and a friend agree to bet on the flip of a coin. The flip will be fair and your friend offers you +105 on heads. Another friend is there and offers you -101 on tails. You have a 10k bankroll and there is no max bet. What are your optimal bet sizes on each bet?

When offered an unconstrained pure arbitrage on some number of independent events, the Kelly-optimal solution is to wager on each outcome a percentage of bankroll equal to the probability of that event occurring.

In other words, provided a pure arbitrage exists, Kelly bet sizes should be determined completely irrespective of payout odds.

So whether you're being offered +105/heads & -101/tails or you're being offered +10,000/heads & -9,999/tails, or +100,000/heads & +500 tails the Kelly-optimal allocation would be exactly the same in each scenario -- 50% of bankroll on heads and 50% of bankroll on tails.

Strange but true.

[beetman]

Also, the optimal bet sizes should be $5094.77 on heads and $4905.23 on tails on the first wager, and on subsequent wagers, 50.9477% of bank on heads and 49.0523% on tails.

[beetman]

Oh, I guess not.

[Ganchrow]

It does certainly appear that for whatever reason Pinnacle has a higher estimate of NCAA basketball push probability for the 2-point versus the HPC (around 5% or so for Pinny versus approximately 3.9% for the HPC).

Even assuming the HPC figures 100% accurate this would not generally be indicative of an exploitable discrepancy at Pinnacle, tending only to reduce (rather than eliminate) implied vig for the relevant buy/sells involving the 2-point to around 1% (assuming the central Pinny values to be unbiased).

See the attached spreadsheet for a mechanism to compare Pinnacle values (which would need to be entered manually) versus the predefined calculator probabilities (which may be edited on the "Predefined Probs" worksheet). Only bolded cells may be edited.

[raiders72002]

Closing lines at Pinnacle is the generally accepted method. The majority of your post is a jumbled mess with totals being the only thing worth even mentioning.

I'm not sure what I'm backfitting exactly, either. What other method would you use to determine push percentages other than past results over a reasonable sample size? A magic wand?

Don- Let's use baseball as an example because that's the sport that I love. Here's the jumpled mess.

You have to take ball parks into consideration. A ground ball pitcher has an advantage vs a fly ball pitcher in parks with lots of home runs when the winds blowing out. Weather is a factor.

When it's cold outside I'll back a guy throwing in the high 90s vs a guy in the 80s that lives on the corners. Try going outside in 39 degree weather and having feel on the ball to paint the corners. I t's not fun taking one off the handle if a guy's throwing 97 MPH.

Does the umpire squeeze the plate? This hurts control pitchers.

You have to look at the SP previous game. Some SP are affected by the amount of pitches thrown the previous game which may make a 7 inning starter down to 5 as an extreme example meaning the RP, which is undervalued , will pitch more innings. Other SP aren't affected by the previous games pitch count.

H/A- There are years that I loved playing Bos at home because of the discrepancy in win percentage in home games compared to away. Other teams aren't affected that much.

So basically what I'm saying is that if a game at Wrigley Field is played when it's cold and the wind is gusting out you better play the team with the SP that's a ground ball pitcher throwing heat against a flyball SP that lives on his control.

Throw out every calculator in the world when capping the above game.

[raiders72002]

DonJuan

Closing lines at Pinnacle is the generally accepted method.

Once again the data is bad because Spiro's lines are sharper than Pinny's if you want to talk NBA.

Now we are getting back to more jumpled mess. If BW steams a game you want to hit the line before the move. If the public steams a game then who cares. I'll fade the steam.

[Ganchrow]

There's no question that pathological effects such as (for example) especially high or low scoring volatility will impact the value of marginal half-points. Obviously, this isn't taken into account by the HPC.

The HPC (and for that matter the above-linked spreadsheet, as well) is intended only as a guide to determine valuation in the typical case. Users are encouraged to consider exogenous factors when making a final determination concerning marginal half-point value.

This doesn't imply we should completely discard the HPC in pathological cases but rather that we be sure to be cognizant of its weaknesses, and use the computed values as a baseline case from which we can perform further analysis.

[jjgold]

This all is coming from Shrink? He is the number one square/whale on the forums. Kenny had to drop over 200k the last 7 years. I might take his local State picks serious but anything else he needs sone guidance. Kenny loves action.

[raiders72002]

This doesn't imply we should completely discard the HPC in pathological cases but rather that we be sure to be cognizant of its weaknesses, and use the computed values as a baseline case from which we can perform further analysis.

I'll play games strictly on line moves a lot and who's moving it.

Kenny had to drop over 200k the last 7 years. I might take his local State picks serious but anything else he needs sone guidance. Kenny loves action.

However, stop being a dick. Everyone gets your speel on here....your a numbers guy, not a people person. We get that. Your posts on here are so ridiculous and condescending and it's huge turn-off. Go join the MENSA forum if you think you are all that.

Why don't you just post your plays on here and demonstrate to all of us how great you are???

There is no such thing as a results-oriented "right side" in a sporting event. Betting baseball is a good way to disavow yourself of the notion that there's such a thing as "the right side" after looking at the results.

[durito]

Raiders -- you are the one claiming that ONE GAME from yesterday at Pinnacle proves something. I am not claiming anything either way. Just asking for some actuall proof.

Here some current lines at pinnacle.

South Carolina 2 -105
LSU -2 -105

S. Carolina 2.5 -117
S. Carolina 1.5 105

LSU -2.5 105
LSU -1.5 -117


NC Charlotte 3.5 -105
Massachusetts 3.5 -105

NC Charlotte 4 -117
NC Charlotte 3 105

Massachuestts -4 105
Massachuestts -3 -118


La Salle 7.5 -105
Temple -7.5 -105

LaSalle 8 -117
LaSalle 7 105

Temple -8 105
Temple -7 -117

Air Force 5 -105
San Diego St. -5 -105

Air Force 5.5 -116
Air Force 4.5 105

San Diego St. -5.5 105
San Diego St. -4.5 -116

[donjuan]

There is no such thing as a results-oriented "right side" in a sporting event. Betting baseball is a good way to disavow yourself of the notion that there's such a thing as "the right side" after looking at the results.

Exactly. My entire argument in the post Buddy Bear referred to was AGAINST being results-oriented. By "right side" I meant with respect to the odds and number I got. In baseball, just as with any sport, there is no right side but rather right price.

Ganchrow,

Correct, although I arrived at the solution in a different way.

Raiders,

You always want to make adjustments, but that does not mean you should completely disregard your models. For example, last night I did not play Arizona -17 because of the fact that they were going to rest their starters if they got a decent sized lead (conference tournament, having to potentially play 4 games in 4 days), in spite of the fact that I had this as a play under normal conditions. That said, I think people tend to think up abnormal conditions so they can justify going with their "gut instinct".

[Ganchrow]

Here some current lines at pinnacle.

South Carolina 2 -105
LSU -2 -105

S. Carolina 2.5 -117
S. Carolina 1.5 105

LSU -2.5 105
LSU -1.5 -117

And filling out the above:

<PRE>Spread LSU So. Car.<BR>1 -127 +113<BR>1½ -117 +105<BR>2 -105 -105<BR>2½ +105 -117<BR>3 +117 -131</PRE>

So to give an example of using this data with the above linked spreadsheet:

Assuming no bias, these pricings would give us the following implied probabilities:

<PRE>MoV Prob<BR>1 3.4%<BR>2 5.0%<BR>3 4.8%</PRE>

versus HPC probs of

<PRE>MoV Prob<BR>1 3.5%<BR>2 3.9%<BR>3 4.7%</PRE>

Or, taking the HPC push probs as given, this would give us (based on an unbiased Pinny ±2 market) EVs at Pinnacle of:

<PRE>Spread LSU So. Car.<BR>1 -3.8% -1.6%<BR>1½ -3.6% -1.5%<BR>2 -2.4% -2.4%<BR>2½ -1.5% -3.6%<BR>3 -1.3% -3.9%</PRE>

[raiders72002]

You always want to make adjustments, but that does not mean you should completely disregard your models. For example, last night I did not play Arizona -17 because of the fact that they were going to rest their starters if they got a decent sized lead (conference tournament, having to potentially play 4 games in 4 days), in spite of the fact that I had this as a play under normal conditions. That said, I think people tend to think up abnormal conditions so they can justify going with their "gut instinct".

agree somewhat with abnormal conditions as justification but those are the plays that I try to exploit.

[raiders72002]

Raiders -- you are the one claiming that ONE GAME from yesterday at Pinnacle proves something. I am not claiming anything either way. Just asking for some actuall proof.

I got a little testy yesterday. Back to normal today. It'll be fun to watch how these numbers play out for the rest of the NCAA year.

[Justin7]

I took a look at Pinny's drop down numbers. As of Friday afternoon, there are 3 games on the "2". The average sell-off price is 11 cents. You'll note that games off a flat line (e.g. Stanford -2 -109 / Wash St +2 -101) value the half-point higher for the side with higher juice. This is simply a result of the win percentages based on that spread.

I would accept Pinnacle's buy/sell prices as compelling evidence that you should buy onto or off of the "2" in all of these NCAAB games (at least in "normal" totaled games).

Most of the other half-points are at 10 cents. The "1" is trading at 7/9.

[donjuan]

I would accept Pinnacle's buy/sell prices as compelling evidence that you should buy onto or off of the "2" in all of these NCAAB games (at least in "normal" totaled games).

Not sure I follow your reasoning here. If Pinnacle offers a bet at -106 and you can find it at -105 elsewhere, that alone is not a reason to bet it.

[raiders72002]

Don - He's saying if you like the bet and can find a book that you want to play it at, then buy for 10 cents.

[donjuan]

Sorry, meant to say "that alone is not a reason to buy points" rather than "that alone is not a reason to bet it".

[durito]

Don - He's saying if you like the bet and can find a book that you want to play it at, then buy for 10 cents.

Unless there is some -105/-105 book that lets you buy and sell pts that I am unfamiliar with, then you are stuck making this bet at a -110 shop and laying -120, whereas pinnacle is only charging -117 or whatever.

If you believe what's said in the pinnacle pulse, they have said they believe they are getting a better price whenever anyone buys/sells pts. Given that they charge 26+ cents on and off the 3 in the NFL, It's possible they are in fact overcharging off every number.

[raiders72002]

C'mon- All books don't have the same line and all books don't have the same juice. If this were the case then you would never have to find any other book then Pinny.

You find a book that beats the Pinny line and buy for 10 cents.

[raiders72002]

If Pinny has it -14cents/+11 they still get the best of it because it's between 11 and 14 in their opinion.

[Ganchrow]

First off, I'd really like to put to bed the incorrect usage of the term "juice" when it fact it's "payout odds" that are what's really intended. Assuming an unbiased market, "juice", "vig", or "theoretical hold" is equal to the negative of player EV on a given bet.

If a market's offered at +120/-130, then if you believe the market to be unbiased, there's no "high juice-side" and "low-juice side" -- both sides, by definition, have the same juice.

Similarly, if one bet is offered at -110/-110, while the other is offered at -120/+100, the favorite at -120 is not higher juice than the favorite at -110. It's actually lower juice.

(In fact, I'm actually in ongoing negotiations with the chairman of the US Senate Judaical Committee right now, it's my sincere hope that the committee will approve a measure stipulating that anyone in the Think Tank caught misusing the term "juice" as above while crossing state lines, may be legally ridiculed, shot and then ridiculed some more. There might be some veto risk, however, as I was told the President still need to times together a myriad of different factors.)

So now with that off my chest I can proceed.

From a mathematical perspective, considering only the nominal "cent" increase to US odds (e.g., 12¢ to buy and 10¢ to sell) tells only a sliver of the actual story. A more complete consideration is the push probability implied by buying or selling off the 2-point. Using the spreadsheet I linked to above (which I know you've already downloaded and perused, right?) the determination of implied Pinnacle probabilities is just a simple matter of copying the central figure and payout odds (NOT the "juice"!) from the drop downs. These may then be easily compared with the push probs from the HPC (or your own push probs if you so desire), and then the Pinnacle EVs (assuming the HPC accurate) may then be examined. (I gave an example of using the spreadsheet in this post.)

What we find is this:

1. where discrepancies do exists, Pinnacle is almost always overestimating the push probability versus the HPC
2. with the notable exception of the 2-point, the implied Pinnacle probabilities are generally close to the HPC (historical) values
3. in the case of the 2-point, Pinnacle is rather uniformly assuming a push probabiling of about 5.0% versus about 3.9% for the HPC

When I first started dabbling in sports betting one of the first things my handicapper and I did was head to out Vegas for a few weeeks to basically get the lay of the land (we also knew little about precious little about the offshore world). At the time it was early basketball season and being a friendly guy, I'd chat up the locals. Since I neither really knew nor cared much much about sports current events (nor do I now), the priamry topic of conversation was betting mechanics.

"When it comes to NCAA Basketball," more than several 'sharps' uniformly declared, "always pay for the 2-point."

Later, when I discovered the forums, I found much the same opinion prevalent. That the 2 is the most point in NCAA Hoops really seemed to be conventional wisdom. Perfunctorily, it certainly sounds reasonable. Most baskets earn a team 2-points, so why shouldn't that be the most common MOV? Right?

Speaking from experience, I seldom find it a wise to blindly take as fact prevailing "wisdom" when said fact represents easily verifiable mathematical claims, so I pulled the data and examined the historical results.

The results were pretty unambiguous. Among single-digit MoVs the 2- was actually rather on the low side for small spreads. It wasn't as low as the push prob as on the 1-, but it was far from being the most commonly pushed spread (inclusive of smoothing). The 3.9% figure I deduced later found its way into the HPC.

After reading through this particular thread I decided to looked at the issue again. Going back to 1997, and including all data through March 13th, what has the historical push probability of the 2- been since the 1997 season?

All Games

For a radius of 2 (so including games with spreads from PK through 4):
462/11,571 or 3.99% of games ended with a favorite MOV of exactly 2 (margin of error ≈ ± 0.36%)

For a radius of 3:
599 games out of 15,361 or 3.90% (margin of error ≈ ± 0.31%)

I then looked to see if the results were substantially different for tournament games than for regular season games. This is what I found:

Regular season

For a radius of 2:
447 games out of 11,163 or 4.00% (margin of error ≈ ±0.36%)

For a radius of 3:
579 games out of 14,832 or 3.90% (margin of error ≈ ±0.31%)

Post-season

For a radius of 2:
15 games out of 408 or 3.68% (margin of error ≈ ±1.83%)

For a radius of 3:
20 games out of 529 or 3.90% (margin of error ≈ ±1.63%)

So nope, nothing doing there. In fact the posts-season push probs were actually lower than for the regular (although not even nearly to a statistically significant extent).

The last thing I looked at was how this differed with time. I looked at 1990s post-season push probas (although regrettably only stretching back as far as 1997. Here's what I found:

1997-1999 Post-season

For a radius of 2:
3 games out of 50 or 6% (margin of error ≈ ±6.72%)

For a radius of 3:
7 games out of 78 or 8.97% (margin of error ≈ ±6.43%)

So this might shed some light on what's going on. This is largely speculation but here I go -- After the 90s some "sharp" (and I actually have an idea which "sharp" this might be -- he doesn't post on this board, btw) noticed that an inordinate number of NCAAB Tournament games with spreads of about 2 landed on a fave MoV of 2. This was all out-of-proportion with the regular season push frequency and he noted it. He also told some people. A lot of people. It sounded good and he could easily
point to the evidence. No analysis of statistical significance was given, however.

"I have it on good authority," many budding "sharps" whispered, "that the NCAA Tourney 2- is a very important point."

And so it's passed around like a $50-whore that "Sharps buy the Tourney 2".

But to this day I can find no rationale for this claim other than, "everybody knows that the 2 is important", and "Pinnacle is charging over 10¢ for it!"

Come on. This is supposed to be the quantitative part of SBR. My philosophy is generally this ... "With no compelling evidence to the contrary go with Pinnacle. With compelling evidence to the contrary, recheck your evidence, then try to determine out if a reasonable explanation for the discrepancy exists."

Well guess what. A reasonable explanation does exist.

Moths orient themselves using the sun. A by-product of this is that they'll tend to orbit to madly terrestrial light sources. This can be tragic (for the moth, anyway) when the terrestrial light source in question is a flame (as beautifully recounted by Richard Dawkins in The God Delusion). But that unfortunate side effect (and that it's all that it is) doesn't mean such behavior is on a species-wide scale without evolutionary import. While ideally moths wouldn't be trapped by flames, from a species-wide perspective it's an acceptable for the greater good of improved navigation.

Same goes for Pinnacle.

Here's what we know:

1. Players tend to buy points a lot more frequently than they sell points, tending to inflate the implied push probs for all points
2. There was a brief period during the 90s when buying the 2-point for 10¢would have been extremely profitable (although not to an extent even bordering on statistical significance).
3. Conventional wisdom seems to hold that the NCAA BB 2-point is always of high value, and can be of even more value during the Tournaments.
4. The historical record clearly demonstrates that the push proba of the 2-point should probably be right around 4% on average
5. Pinnacle is imputing a push prob of 5% for the 2- pretty much across the board

This last point is a very important one. Pinnacle's not just saying that one or two games have inflated value for the 2- (a claim which I might easily believe), but rather that all these games have a push prob of about 5% for the 2-point.

Well guess what -- such a claim is easily verifiable. The math just isn't that hard and on average that's not true historically. Period.

Now of course I can't be certain that Pinnacle isn't using some fancy scoring distribution model to determine that the historical push rate of the 2- is an anomaly and should in reality be much higher. I definitely can't rule that out.

But as per Occam's famous shaving implement, I think the simpler explanation is much more likely. Many more people buy points than sell points, people apparently love to buy the 2-point, so they simply charge more for it. We're not talking a huge difference here, mind you. Based on the HPC (or the spreadsheet) Pinnacle's 5% implied prob would generally reduce effective juice to about 1% on the double sell, but raise it to over 4% on the double buy. If many more people buy than sell, then that's just good business. They're not eliminating juice for players who sell the 2 ... just slightly reducing it.

Anyway, that's just my take.

[Justin7]

A minor point in your analysis, Ganchrow...

If your radius 2/3 analysis includes the push rate for the "Pk", which is always 0, you're deflating the value of 2.

Instead of using similar spread games, I would check how often a game lands on the "2" for games spread -1.5 to -2.5. I'd exclude games with a total over 150 also (at least for determining the 2 between quality teams, which tend to rarely have such high totals).

And for Juan/Raiders, let me clarify what I was saying earlier... If you are betting on a game, and you can buy onto or off of the "2" for 10 extra cents, that appears to be better than the straight side without buying the hook.

[raiders72002]

incorrect usage of the term "juice" when it fact it's "payout odds" that are what's really intended. Assuming an unbiased market, "juice", "vig", or "theoretical hold" is equal to the negative of player EV on a given bet

street talk - heavy 2, more juice, means the payout on -2 is less then on +2 assuming you risk the same amount of money.

That's why my arguments aren't as articulate. Means the same, different lingo.

[Ganchrow]

If your radius 2/3 analysis includes the push rate for the "Pk", which is always 0, you're deflating the value of 2.

I think you've misunderstood.

The r-radius push rate for a MoV of m refers to the probability of a favorite MoV of exactly m for spreads ≤ |m-r| and not the other way around. You have it backwards.

Instead of using similar spread games, I would check how often a game lands on the "2" for games spread -1.5 to -2.5.

Yes, this would be a radius of 0.5. Across the entire data set this gives us a value of 4.09% with a sampling error of 0.65% over 3,588 games. That's why i generally use slightly larger radii. As I've mentioned before this is based on Stanford Wong's methodology.

We've had this conversations before in other threads AND in person. You must have been too drunk to remember.

I'd exclude games with a total over 150

This does not produce a statistically meaningful change. No change at all for for a radius of 0.5 (still 4.00%), an increase to 4.01% for a radius of 2, and a decrease to 3.88% for a radius of 3.

[Ganchrow]

street talk - heavy 2, more juice, means the payout on -2 is less then on +2 assuming you risk the same amount of money.

That's why my arguments aren't as articulate. Means the same, different lingo.

Heavy 2 is fine. That works.

But referring to payout odds as "juice" is a close cousin to the ignorant belief (which as I recall was a notion of which you and I were actively dissuading people when this board first opened) that higher nominal money lines of given width are most costly than lower nominal money lines of given width.

The usage is just plain wrong.

[durito]

Thanks ganch.

I hope SBR pays you well.

[raiders72002]

referring to payout odds as "juice" is a close cousin to the ignorant belief (which as I recall was a notion of which you and I were actively dissuading people when this board first opened) that higher nominal money lines of given width are most costly than lower nominal money lines of given width.

Ganch, by far, is the most helpful person on this board.

[Patrick McIrish]

Good stuff guys, nice read.