Rob Crowne said:
First I'd look at the equity in your current wager. The line is really between 2.5 and 3, so we'll go with the win percentage that is between those two numbers, 58%..
58 times you lose $1,000
42 times you win $22,000.
Let it ride equity: $8,660 per wager
So what are you options on New England? The first would be an even scalp. The problem with dealing with sums this large is it limits your ability to shop for lines. Your best bet would be NE -140 at Bookmaker.
A bet amount (not win amount) of $14,416 (-140). You have guaranteed yourself $8,583 per wager.
Even scalp equity: $8,583 per wager
Another option is to dog scalp it. You can bet enough to guarantee you would not lose if NE happened to win.
$1,400 to win $1,000 on NE.
58 times you win $0
42 times you win $20,600
LLoyd, good stuff. I have some comments, one correction and one request. This is not in any way a critique of your work. It is just simply intended as a classroom discussion to add to the learning process.
COMMENTS ON THE PROBABILITY CALCULATION
(1) How did you arrive at your probability calculation for -2.5 points and -3 points to arrive at the midpoint percentage assumption? It looks like you may have used the money line conversions of each point spread as the basis. For accuracy, you might want to consider using one of the many push-percentage charts out there to calculate the probabilities without the built in skewing of the lines. When using standard money lines, the bid and asked are skewed by the vig. The midpoint is also not accurate because standard lines include a skewing against the favorite and do not reflect the true probability either. Using push percentages gets rid of all the built-in errors created by the bookmakers.
I am not using ML conversion. I have a chart that lists the game win rates for each spread and that's what I used
(2) Why did you use the -2.5 (-115) line as the true measure of probability instead of the original line maker's line of -3.5, or the midpoint line of -3? The best way to calculate the probability is via an expert handicap of the game, but in the absence of that, how do we choose between the line maker's handicap and the public handicap? That is always a difficult question when making hedging calculations.
You are right, the best time to hedge would be as close to game time as possible so you have the most accurate numbers. But he asked me so I answered based on what it was at the time he asked
In my opinion, in this case the public adjustment has probably resulted from bettors looking for the potential middle by grabbing +3.5 in the hope that they may get -3 or -2.5 later (as they did).. The number -3 makes the best middle in NFL betting, and is very profitable. The line, once it settles at -2.5 will probably adjust back up to -3 when those looking for middles come back on the favorite. Late public love of the favorite may well push it right back to -3.5 on game day. That all means that the line of -2.5 (-115) has probably been skewed by the people seeking a middle, and would not be the most accurate measure of true probability.
In other cases, particularly when using a late line, the public assessment is probably better than the linemaker's line because, in most cases, the line maker is not trying to calculate true probability, while the public is trying to make that calculation.
If we are not handicapping ourselves to assess true probability, which may be very different from any line posted (the whole idea behind handicapping and betting) then the choice of which line to use must be made on a case by case basis. That said, I believe that for safety sake, if you are going to use lines to determine probability, the line that produces the highest loss probability for the side you have already bet should be used to determine the probability of losing your original bet and winning the other side. In this case, that would be the asked side of a line of -3.5, which is -1.75. For those who don't know, the money line of -1.75 translates to NE winning 63.6 times in every 100, and NYG winning the other 36.4 times.
That's certainly a way to do it. If that was the case, hedging would be even less enticing
CORRECTION OF EVEN SCALP:
I think the amount you calculated as the amount JD would need to bet on NE in the even scalp equity choice is in error by $1000. The answer should be $13,416. Depending on how you came at the problem, it looks like you either forgot to subtract out, or mistakenly added in the $1000 amount that JD already bet on the Giants. I believe the $14,416 is his total bet, not his necessary NE bet. No big thing mathematically It's a common mistake that I also make all the time. Although the extra $1000 may have caused JD to come looking for you if he made the Even Equity choice. LOL
I answered all this in a previous thread. Thank you again for catching my error
REQUEST/SUGGESTION
Math geniuses such as yourself often think things that are obvious to them are obvious to everybody. Trust me, they're not. My guess would be that few people here understand how you arrived at the per bet equity, or even that per bet equity means the average amount per bet that one will win or lose over the long term. What's easy for you, isn't easy for the rest of us in many cases.
In addition, you often approach the solution to the problems differently from the way I come at them. Even though we both get the same answer, it is always good to know a second method of solving the problem, and I would really appreciate seeing how you did it.
Finally, when the numbers can't be proved, such as your numbers in the Even Equity situation above, it is much easier to find the error by looking at your actual calculations than by having to start from scratch myself, and then try to figure out where the mistake may lie, and who is making it -- you or me.
My suggestion is that if you are doing a hand calculation, for the benefit of both the mathematically inclined, and for those who need to learn how to do the calculations. that you provide each step in detail with explanation as to why you took that step wherever necessary. That is much more helpful from a learning standpoint than just being presented with the final numbers. In other words, it may be helpful to many people for you you to be a teacher in addition to being a problem solver. Try to picture everything the non-math folks might not understand, explain it and demonstrate it. For instance, in calculating the Let It Ride option, I know it is obvious to you and me, but some people may need the calculation completed to see how you got to the Equity and learn how to calculate it themselves.
Of course, some things realistically require a calculator. Nobody, for instance, wants to sit around drawing Pascal's Triangles to figure out probability now that there are calculators to do it instantly, and no one sits around with compound interest charts.. If you use a calculator on line, the location would be appreciated, and an explanation, wherever necessary, as to how to fill in the numbers. If you use a hand-held scientific or business calculator, maybe a quick explanation of the plug in numbers and buttons to use would be helpful to some.
I am particularly interested in your workout of the Even Scalp Equity if you did it by hand. My request is that, if you can, please provide your calculations for that option. You can present your algebraic formula if that is what you use. Thanks. .
If someone doesn't understand any lingo I am using they are welcome to ask and I am happy to answer. I do not use algebraic formula's when I figure things out. I am FAR from a math genius. I am more of a stats savant. If you had seen my math grades from 11th grade on you would understand. I don't use an algebraic formula because even though that is likely a more efficient way, it's just not the way I am comfortable with. For scalps I just use the SBR arb calculator
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My responses are in bold/italics