Originally posted on 08/08/2018:

Hey Danshan11

Let me lay out the 'basic' concept of what I am looking at, in the way of a model. I am certain that I am not the first to look at 'dog plays' in this manner. This is just a theory and I will lay it out so others can check the math, find the 'leaks' and pinpoint the fallacy.

For this example I will use MLB. The parameters will not line up perfectly, but it will explain the concept. I am trying to revise something for the NHL season, but am testing this live against MLB since it's the only game in town right now.

Parameters: MLB - 15 games - 3 games in each series - using a 3 step progression - betting the board - dogs only

There are four distribution outcomes for the winner of a 3 game series:

(a) W - W - L
(b) W - L - W
(c) L - W - W
(d) W - W - W

For this example assume that all the games won were favorites on the moneyline, and the losers were dogs. It would look like this:

(a) F - F - D
(b) F - D - F
(c) D - F - F
(d) F - F - F

Dividing 15 games by the 4 typical outcomes would be 15 / 4 = 3.75. For this example I am expecting no more than a 2 loss interval for series 'a', 'b', and 'c'. I am expecting to lose my progression bet on series 'd'.

The Progression

I have 15 separate 3 step progressions - I will refer to them as 'cells' numbered C1 to C15. I want to assimulate randomness as best as possilbe, meaing that I do not want 2 teams playing 3 consecutive games within the same cell. For my live test I just use the rotation schedule. For example, if a series began on a Mondays and there were 10 games, they would be assigned C1 through C10 in order of the rotation. Tuesdays line-up would begin from the top of the schedule at C11. Night games are days games the following day, and so forth.

This means that while the progressions are actively running, on the first game of a series, the Baltimore Orioles could land on any step of an active progression - Step 1, 2 or 3 - depending on which cell is assigned and what step is active within that particular cell.

I am using a 1 - 3 - 7 progression. This allows me to win 1 unit for every step within the progression. A win on Step 1 = 1 unit, Step 2 = 2 units and Step 3 = 3 units. After a win, the progression resets to 1. Three consecutive losses = surrender loss amount.

The Progression looks like this:

Step 1 = Risk 1 Unit
Step 2 = Recovery Amt Step 1 + 2 units
Step 2 = Recovery Amt Step 1 + Step 2 + 3 Units

So, given these parameters, here is where I need help verifying the math among other things. This is just a basic concept that I am testing to see if it holds enough water. There are several specific things I want to plug in around this, but before anything else, the math has to make sense.

Betting Unit = 1.00 Typical Dog Price for this example = +1.20 1.00 / 1.20 = 0.833

I am risking 0.83 cents to win 1.00

Step 1 Risk 0.83 to Win NET 1.00 Lose 0.83

Step 2 (Loss Amt 0.83 + 2.00 = 2.83) * (0.83%) = Risk 2.35 to Win NET 2.00 Lose 2.35

Step 3 (Loss Amt 0.83 + Loss Amt 2.35 + 3.00 = 6.18) * (0.83%) = Risk 5.13 to Win NET 3.00 Lose 5.13

Cummulative Loss for this Cell = (0.83 + 2.35 + 5.13) = 8.31

This is the math that I need to be checked out. If my progression would be successful in this example 75% of the time in situations 'a', 'b', and 'c', and I would surrender 8.31 in situation 'd' then on way of expressing it over fifteen 3 game series could be:

'a' 3.75 + 'b' 3.75 + 'c' 3.75 = 11.25
'd' = 3.75

The 'a', 'b', and 'c' patterns would produce 3 units continually at a rate average of 1 unit per game.

('a' 3.75 + 'b' 3.75 + 'c' 3.75) is 3 * 11.25 = 33.75

A 3 game sweep pattern would lose a cummulative total of 8.31.

('d' 3.75) is 8.31 * 3.75 = 31.16

Win 33.75 - Loss 31.16 = 2.59

Profit for this example is 2.59

Number of games wagered is 45

2.59 / 45 = 0.057

If the math checks out, then this 0.057 could be the 'mean' to measure the deviation. The ratio of favorites to dogs would determine how this number would move up and down. I am simply curious whether it would have any value as far as measuring deviation swings.

In this example I used 3 dogs over 12 outcomes. I subtituted the word 'typical' for expectation because I am aware that my example does not include many variables. For example: A pattern that is W - W - L. The wins in this pattern could have been 'dog' teams.

Thus, D - D - F. It has been said that 'the dogs' hit at a rate of 40%. That means instead of 3 dogs hitting over 12 games played, 4.8 dogs are hitting within 12 games.

I do not know how to formulate the equation to express this in percentages.

Q: 15 Series - 3 Games each. Favorite to Dog ratio is 9 to 6 for Game 1, Game 2, and Game 3. What is the expectation of a 3 game sweep and how many?

One last piece it that a 3 game sweep at: Gm1 +1.75 Gm2 +2.25 Gm3 +1.60 is going to measure out much differently than a sweep pattern at lower value.

Thanks in advance for everyone's help, and if this problem has been posted 1000 times before...I apologize.