The Math of "bad lines"

[SunDevil]

This wasn't getting any commentary in the other thread so I figured I'd post it on its own....


Some very interesting math for y'all:

Break-even required win %age for a +100 dog = 0.5000
Break-even required win %age for a +120 dog = 0.4545

0.5000-0.4545 = 0.0455

Break-even required win %age for a +435 (Pinnacle's line on the match) dog = 0.1869
Break-even required win %age for a +605 (CBS's "bad" line on the match) dog = 0.1418

0.1869-0.1418 = 0.0451

0.0455 > 0.0451

Hence a player finding & playing a dog at +120 when other books are at +100 is actually mathematically betting into a worse "bad line" than a player betting into +605 when other books are at +435.

So now, a VERY dangerous precedent has indeed been set by allowing cancellation of the +605 wagers....because a player is actually picking up a bigger edge for themselves by scoping out a +120 when the market is at +100 than is the player finding a +605 when the market is at +435. Is the next step allowing cancellation of those "bad line" +120 wagers?

I await the arguments against my logic - numbers don't lie.

 

[SunDevil]

Also, given a finite amount of capital (for example $2000, but any number will work) with which to scalp, the following analysis is interesting:

Scalper A has $2000 to play with and finds one side of a game at +100 and the other at +120. Few would call one of these a "bad line" but Scalper A can play $1047.62 on the +100 side and the remaining $952.38 on the +120 side and guarantee himself a profit of $95.24 on the game.

Scalper B also has $2000 to play with and finds one side of a game at +605 and the other at -435. As we have seen in numerous threads here, most are willing to call +605 an "OBVIOUSLY bad line". However the best profit Scalper B can guarantee hismelf is $94.40 (by playing $1702.92 to win $391.48 on the -435 side and playing his remaining $297.07 to win $1797.32 on the +605 side).

So again we see that a player (with any fixed finite bankroll) betting into a +100/+120 situation is actually betting into a "worse" line than the player betting into the -435/+605
situation.

This is what happens when you try to quantify what constitutes a "bad line" and why the book must eat their mistake.

 

[raiders72001]

Sun- You make a very good point. Dave wouldn't have cried if everyone had the tennis match at +100 and CBS had it at +120 because a normal person just eyeballing these lines see them as much closer than +435 and +605. The math tells a different story.

 

[SunDevil]

Thanks silver&black. It's just another situation of the books wanting the best of both worlds. Players whine when the +/- spreads get so wide when big favorites are involved and the books use the (truthful) defense that they are earning the same vig as they are on events with tighter favorites. But now when it's convenient the book leans on the fact that "the spread between the numbers is so large that it's obviously a bad line". They can't have it both ways.

 

[3rdlong]

Excellent post, SunDevil.

 

[TTinCO]

I missed this in the other thread, but you do have one hell of a point SunDevil.

[This message was edited by TTinCO on June 30, 2003 at 12:59 AM.]

 

[PatrickMcIrish]

Nice work.

 

[SunDevil]

Thanks guys. No prob. The day a book can quantify what constitutes a "bad line" in advance I'll take my hat off to them.

 

[Java]

Sundevil-
I'm the last person you'll find defending CBS, but I'm not sure your math is right:
1) You are not looking at relative ratios, but rather at absolute differences. This may not be correct.
2) Your 0.0451 is a lot bigger chunk of .1869 and .1418 than .0455 is a chunk of .50 and .4545
3) +605 is 39% more than +435, so I would think that +139 to +100 is the proper comparison.

Admittedly, I don't usually think of the lines in the way you presented, so I might be in the wrong frame of mind. I won't stand by this take, I'm just throwing out my initial thoughts. I'll give it some more thought. Sun, let me know if you see where I'm going wrong, or if your logic needs a band-aid.

Clever post.

 

[SunDevil]

Java, the reason I posted my 2nd post in this thread was to make the %ages of the 1st post more tangible to people. Either one makes the same point. Any scalper with a finite amount of money and/or limits on their play sizes would be happier to see a +120/+100 situation arise than a +605/-435 takeback. The profit you can lock in is greater. End of story.

 

[Java]

Okay, Sun, how does this sound?
I think you need to compare the zero-juice true lines. Allow me to explain....

Assuming 20-cent lines:
Then +120 matches up with -140, which means the zero juice line is: -130
The chance of fav winning this is 130/230 = 56.52% (dog: 43.48%)

+100 line is the takeback of -120, so the zero-juice is -110 ---> 110/210 = 52.38% for the fav (dog: 47.62%).

At +605, the favorite would be -725, and the zero-juice line at -665. Chance for favorite = 665/765 = 86.92% (dog: 13.08%)

At +435, the favorite would be -525(?). No juice is -480, so 480/580= 82.76% (dog: 17.24%)

So for +100/+120 case: 47.62 - 43.48 = 4.14
and for +435/+600 case: 17.24 - 13.08 = 4.16

I'm still not sure if it right to compare the percentage differences this way, but I think the zero-juice lines are what should be compared, not the with-juice lines.

 

[SunDevil]

Java, I tried to make my analysis independent of the spread between the dog price & favorite price as this varies dramatically from book to book when dealing with large favorites (your ?s confirm you feel the same). However your analysis really only confirms my point that the difference between a line that is deemed by many to be "obviously bad" (i.e. a +605 vs -435) and a line that very few would deem to be bad (i.e. +120 vs +100) is truly negligible no matter which set of numbers you look at.

I still prefer the analysis of my 2nd post in this thread though. The actual $ profit that can be locked in is a more practical measuring stick than the percentages.

 

[raiders72001]

To find true odds. Ex. +250/-300

+250 is 3.5 in decimal odds, and -300 is 1.33

Now, the true odds are:

3.5 * (1/3.5 + 1/1.33) = 3.625 which is +263
and
1.33 * (1/3.5 + 1/1.33) = 1.381 which is -263

And an easy way to convert american odds to decimal odds (and vice versa), is like this:

If american odds is over +100, then divide it by hundred and add one, and it's in decimals: +250/100+1 = 3.5

And if american odds are under -100, then divide it by hundred and forget the minus sign, and then divide number one with that value, and add one: 1/(300/100)+1 = 1.33

 

[Java]

Sun-
I now see your point and realize were talking about two different betting strategies.
You are trying to compute the advantage of a scalp betting both sides. I was thinking in terms of placing only a single bet. This is based upon advice I once got:
If you find -140 and +150, you are better off just picking just the one you like best (compared to consensus line). This increases the risk but also increases the payout. If the true line was -140 and you can bet +150, then in the long run, you will be ahead (assuming you stay away from stiff books).
This is a fullness-of-time, long-view. It has maximum win (though with increased risk).

 

[mathguru]

Sun Devil, that is pretty tasty math I must admit. Great work with the 2 dime breakdown as well; I am impressed with your performance.

It may be that +120 is an obviously bad line when it is at +100 most places, i dunno.

Sounds like the Johnson Twins fell asleep at the wheel.

 

[SunDevil]

Absolutely Java. The perfectly risk-neutral person should never waste their time playing both sides of a scalp, only the "right" one. Problem is that almost all of us are to some extant risk-averse and that's what leads people to play both sides.

I wonder where where SPV has gone tonight. I'd love to hear him try to poke holes in my analysis above since he was the leading proponent of the "obvious bad line" talk.

 

[SunDevil]

Thanks Guru. (As must be quite obvious by now) I get off on cornering people on faulty, inconsistent logic. I'm dying to hear some rep of CBS say that "No, we'd never cancel something like a +120 when it should be +100, but we'll cancel THIS +605 as it is OBVIOUSLY a bad line." because then they'll have contradicted themselves beyond a shadow of a doubt. Alas, Johnson only gave us a +250/-240 example to deal with - not quite enough for me to corner them on.

 

[raiders72001]

I agree with you guys about playing the right side instead of scalping. Also I think a big mistake that people make is when they make a great series bet, basketball for example, then they are up 2-0 in the series and play the other side. They have a great bet and want to secure a little win instead of just taking the big win on the original bet.
The only time I would hedge a bet is if I played a team at 100-1 to win the World Series and the payoff was huge. Then I would hedge but otherwise don't minimize the great bet that you have made.

 

[Otherwize]

Sundevil and Java, nice work guys! Shrink take note of some of the more helpful posts in a long while. However Java, your math and Sun Devils are more illustrative than most of us see; they may be flawed in that the old math we all learned long ago is gone. I wish it still worked on a zero juice formula.

Funny thing is, I'm crunching the numbers SunDevil and they still work. Damn I hate math for being so correct!

 

[mathguru]

Allow me to reiterate that Sun Devil might be the poster of the month with this display. No joke, great showing Devil.

And who said that ASU didn't turn out some sharp math students? "Not I" said the dog.