a more meaningful ROI calculation (a/e)

[formula_2002]

This is from one of my post on the "selections" forum.

"Every few I days I run the results through my programs and tally things and like;
actual wins/expected wins, for the Pinnacle line, my line(s) and the final "public's" line.

Thats how I found out that the actual winners were out performing the "lay" side of ALL lines, and underperforming the "take odds" side of all the lines.

I've been using that a/e calculation since the early '90's (my Prodigy days). The more I use it, the more appreciate it.

expected winners= 1/(odds+1)

a/e also yields the % for a dutch play.
It also, imo, yields a meaningful ROI figure."

[douglasw32]

Man I wish I knew what this means ... sounds great!

[formula_2002]

Man I wish I knew what this means ... sounds great!
Lets say you bet every horse in today's Preakness.
Bris list the WPS pool subject to an 18% takeout.
if you sumed 1/(odds+1) for all the 9 horses. The sum should be about 1.22.
Say a 50-1 shot won the race. Just about everyone would say 'Hey, I bet a dollar on each of the 9 horses and got back $51, for an roi of 51/9=5.66"
I would say, "Hey, you should have won 1.22 times, but you only won one."
I'm sure the winning players could care less about how many times he should have won..a win is a win,
but in the long run, playing every horse in the race will catch up to you.

This is of cousre an extreme example.

If you are a serious player, you should always compare the number of actual wins to number of expected wins, (a/e).

[Dave Schwartz]

Joe,

Please permit me to simply for the audience:




That is called "pool impact value" or "PIV" in the vernacular we have been using at HorseStreet for the last 10 years or so.

It is, as you say, a much better indicator of performance than "impact value."

The concept of "impact value," which I first heard of in Frederick Davis' Percentages and Probabiltities (1973 - Millwood Publications), uses a similar but slightly different formula.

Both IV and PIV are dependant upon "wins divided by expected wins." The issue is how one derives the expected wins.

With the original IV approach as defined in William Quirin's Winning At The Races six years after Davis was (basically) percentage of winners divided by percentage of starters.

The better way to compute IV is to consider field size of the races the individual horses were entered in. Thus, a horse coming from a 10-horse field should be expected to win 0.10 races, while a horse coming from a 5-horse field should be expected to win 0.20 races.

With PIV we logically expect a horse that gets 10% of the wagering pool to win 10% of a race. Thus, if you lump together all the horses that had 23% of the pool wagered on them, they should have gotten 23% of the total wins.

Please note that this is superior to the "booking percentages" approach you have outlined because it takes into consideration differences in track takes from one track to another. As you know that can be a substantial difference from NYRA to TUP, for example.


We have also "invented" another one: DV or "Dollar Value." This one compares the $net for each class of horse (i.e. rank of 1st, rank of 2nd, etc.) with the average $net in the sample for all horses. (Recall that $net is the average return for $2.00; i.e. $2.10 is a +5% advantage while $1.80 is a -10%.)

Generally, the average $net in a large sample will be around $1.55. Thus, if a horse is expected to to return a $net of $1.80 he could be said to have a DV of 1.16. In other words, he could be expected to return 16% more than the average horse.

The beauty of this is in exotics. Imagine that if you take a 1.20 DV and a 1.30 DV and multiply them together you get a combined DV of 1.56. When that 1.56 is multiplied times the $1.55 average the result is $2.42, which is, of course, highly profitable.

This is highly instructive because it indicates that two such unprofitable win bets can (theoretically) be combined into a profitable exacta bet.

Carried a step further, it can be used to determine whether a given trifecta combination is profitable/playable.

Note that the actual payoffs do not need to be known in order to test for playability! If one assumes a profitable $net between two horses, changes in the payoffs result in a changing of the probabilitities of the combination itself and the $net remains unchanged.

Does it work? Not perfectly, because there is still an adjustment as the animals move from one odds group to another, but basically, yes.


Regards,
Dave Schwartz

[formula_2002]

Joe,

The issue is how one derives the expected wins.


Dave, I'll grant that what you say about adjusting for take out is academically correct, and I often use it when developing a system.

My current data base sums 1/(odds+1). This allows me to establish the take and breakeage for each race, and adjust to total pool odds.

But I don't use that figure when trying to calculate my "advantage" .

I dont find IV useful in my calculations.
PIV?, It does my heart no good to know I've beaten the plubic, only to lose to the track.
I calculate all odds, exacta,tris,quads..ect the same way. 1/(odds+1)=probability.

If the odds are 2-1 at belmont and 2-1 at xdowns,
I still have to win 33% of my plays. When Pinnacle cut's the take to 2 1/2%( :rolleyes:)) , my 2-1 shot must win 33% of my plays.
( But I would rather play against the 2 1/2% take.)

Either way is ok as long as you understand that when adjusting for breakage, the roi must be 1+ breakage in order to be even. When not adjusting, its simply 1.
Betting every horse in the field using your cals, the
Pimlico horse has to win that single race 1.22 times, my beast only needs to win once. :D
Joe M

[Overlay]

The better way to compute IV is to consider field size of the races the individual horses were entered in. Thus, a horse coming from a 10-horse field should be expected to win 0.10 races, while a horse coming from a 5-horse field should be expected to win 0.20 races.

With PIV we logically expect a horse that gets 10% of the wagering pool to win 10% of a race. Thus, if you lump together all the horses that had 23% of the pool wagered on them, they should have gotten 23% of the total wins.

Dave,

Your discussion raises the same question in my mind that I had when I ran across Mike Nunamaker's Modern Impact Values, which took field size into account in calculating its impact values, or the article where Gordon Pine discussed A/E ratio. I'm not saying that Nunamaker's measure, or PIV, or A/E ratio, is not superior to Davis/Quirin-style impact values (the percentage of winners with a given characteristic divided by the percentage of all horses with that characteristic, irrespective of odds or field sizes) in determining the true strength of factors. What I had trouble getting around was what I perceived (perhaps incorrectly, given the current state of computing and data bases) as the difficulty of gathering the past information needed to calculate them (field sizes and/or post-time odds of each individual horse in each individual race in a given sample), as compared with just having to know the aggregate percentage figures employed in the Davis/Quirin approach. Perhaps this is an example of the advantage rightly going to someone who has the time or capability to do that kind of in-depth research, but I always looked at it as a trade-off between time expended and marginal value gained. Is there a way around this to arrive at those alternatives to impact values in a manner that is not as time/labor-intensive as I perceive them to be?

[formula_2002]

Reading Benter's paper in the book "Efficiency of Racetrack Betting Markets"
for the 100th time, his "er", expected return on $1, (his roi), is calculated using tote board odds.


He adjust the tote board odds for take out to find his probability.
See table 8 of the paper.

His expected wins are base on tote board odds.
His probability estimates are based on tote board odds, adjusted for take out.

I think he's got the right idea ;)

[Dave Schwartz]

I think he's got the right idea

That, of course, would be your choice, but bear in mind that was from a long time ago.

He also used FoxPro, as do almost all the Asian teams today. Why? Because everyone who ever worked for him took a copy of his program with them and it was written in FoxPro.

[Turfday]

Guys.....I still hate geometry and never got past it and you all are WAY, WAY, WAY beyond my scope.

I simply wanted to share my Bettting Value Averages formula with you...it's much like a baseball players SLUGGING percentage, as opposed to a BATTING average.

I use this for trainers, jockeys, trainer-jockey combinations, sires and post positions.

My constant factors are field size, finish position and closing odds. The factor that varies is time (date). Calculations incorporate all of the aforementioned with our software adjusting for "what happened lately" is more important than "what happened in the past" and is weighted according.

For example, a third-place finish position at long odds in a big field may be worth more points than a win in a small field at short odds in a small field.
This is why I liken this to a slugging percentage in baseball...a homer being worth more than single.

My main categories, as noted above, are trainers, jockeys, trainer-jockey combinations, sires and post positions. There are a number of sub-categories underneath those main categories (especially for trainers).

For post position, every single distance that a given racetrack runs is broken down by individual field size and formulated accordingly to include the "lately" vs. "past" weighting as well. This, in theory, helps account for any changes that a track has made (surface or configuration).

By incorporating the "lately" vs "past" weighting, whether you buy it or not, provides a much greater sample size in the various categories or for specific distances or field sizes. Same, of course, is true for the other categories...trainer, etc. Therefore, instead of looking at minor, short term samples, I am able to look at larger, more meaningful stats.

My search engine allows search for last 365 calendar days, last 1,095 calendar days or "all-time" ...dating as far back as Jan. 1, 1995. However, as you can imagine, even though a given trainer may have been "hot" five or six years ago, that would show in his "all-time" win percentage, but not have much to do with his Betting Value Average if he has been cold since.

So I pick out the search time frame...last 365 days, last 1,095 days or "all time" and then decide on a sample size to search for.

I then have a "consistency," a "value" and a "combined" category to search by. "Combined" meaning "consistency" + "value" divided by two.

As an example, according to my BVA's, using the last 1,095 day search and 300 starters as a sample size, trainer Steve Miyadi (No. Calif.) is the best trainer in the country with a .434 BVA in the "combined" category. What's interesting, is that if I searched using 600 starters, he STILL would be the best trainer in the country.

Using the same search criteria, the best value trainer right now is Michelle Lovell (Texas) with a .416 BVA. Miyadi is the best consistency trainer with a .598 consistency BVA (as opposed to his combined BVA which includes his value BVA).

Comeback in a month or two because, of course, things change.

Do you guys incorporate or equate sample size into your software?

[Dave Schwartz]

Bob,

Interesting outlook. I like it. In fact, I began research into a time decay/relevance model a couple of months ago, although it probably will not be ready for a couple more months.


Sample size is always a consideration, of course.

I cannot speak for all of our users but personally I use a 6-model attack (if you will) to decide what wins a "race like today." The following models are created dynamically just before post time.


1. Race Type Model
Last 100 races:
Same circuit
Same surface
Distance +/- .5f
Similar track condition
field size +/- 2
similar age
same sex
similar race type
class level +/- 3 levels

2. Long Term Pace
Last 100 Races:
Same Track
Same surface
Distance +/- .5f
Similar track condition
field size +/- 3
similar age
same sex
Race Type: maiden or non-maiden
class level +/- 4 levels
Same number of front runners

3. Pace Shape
Last 30 races:
Same Track
Same surface
Same Distance
Similar track condition
similar age
same sex
Race Type: maiden or non-maiden
Same # of E's and EPs


4. Recent Pace
Last 12 Races:
Same Track
Same surface
Same Distance
Similar track condition
similar age
same sex
Race Type: maiden or non-maiden

5. Short Term Pace
Last 10 Days:
Same Track
Similar surface
Similar Distance (i.e. sprint/route)
Similar track condition


These 5 models are combined to build a Fibonacci-based consensus point system which is used to select the contenders. (4 horses; 3 if the field size is under 8)

The first model is then used to produce a line.

That line is then adjusted with the tote board using an approach we call smoothing.

After an adjustment for ties, the contenders combine to produce about 79% winners.

Generally, if one attempts to play against the worst bet among the contenders, the remainder will be profitable.


BTW, all of this is done in about 60-90 seconds before post time. I actually played a race once when the handicapping did not start until the first horse was loading the gate. (It was a large field and I got the wager in just before the gate opened.)


Regards,
Dave Schwartz

[Turfday]

Dave....

Unfortunately, I am not even close to the complexity of your program. I only wish that my software guru would have time to convert my stuff to predictors.

Yours is actually a program that looks for outcomes based on factors you mentioned.

My program provides valuable, statistically relevant indicators, which we (as humans) have to "program" ourselves using brain power as predictors.

There is a $600,000 plus Pick Six carryover at Hollywood Park today. The third race kick offs the sequence at 1 1/8 miles turf.

As an example, Denise Breuer, trainer of the 2/1 m/l favorite (in a six-horse field), is 1/41 with turf horses in her career. Blind Harry, the horse in question, has two in the money finishes on turf (one recently).

I have no way of predicting if trainer Denise Breuer (1/41 on turf) is going to win her second turf race today (she might simply because it's a six-horse field), but I normally avoid betting on short prices with trainers who don't win in a specific category that pertains to today's race. But I have no way of "predicting" this, except to judge myself.

Problem is, it's the Pick Six opener. Hard to leave off your ticket in such a small field, but not one I would bet on.

[hurrikane]

Bob,

if it helps you any this 3 horse kcked out as a big time false fav.
But the trainer is enough to tell you that. Consider too that she is 14-0 for the last 365 days and the horse has never done anythng in a grass route or even on the turf before.

But the due column bettors would be all over this pup.

[hurrikane]

Dave,

I'm curious how you have found your DV to work across all exotics. And any application in the pick x races.

have you found it to be any type of indicies for payout?

Interesting idea.

[Dave Schwartz]

Hurrikane,

We have only used it thus far in exactas. It works.

Of course, without the "odds smoothing" you get a completely different set of values and they don't work so well.

Dave

[dancingbrave]

I must admit that some of you guys on this forum seem really advanced - makes me feel really basic.

UK Racing must be a lot easier to win at than US racing as all I have ever used is a modified kelly staking system, some sectional timing, own ratings and trying to predict the shape of the race. This has produced on average 20% profit to stake for 13 years consecutively.

US racing seems too hard if you guys go to these extents to make profit.

[Dave Schwartz]

DB,

Since winning is relative to the competitive level of the other participants, the bar may well be a bit higher in the US (where there seems to be a computer on every desk).


Regards,
Dave Schwartz

[dancingbrave]

I would disagree with the computers argument. i think it is more a combination of:


1 - UK racing being lower margin due to fixed odds format.

2 - Exchanges.

3 - Fixed Odds being different between various books offering shopping opportunities.

4 - Fewer races but much stronger markets.

5 - A bigger casual bettor market because of off track outlets being numerous.

I'm sure there are a few of you that average over 10% profit to stake annually - it is beyond my comprehension how that is possible on US racing - Hats off to you guys.

[sjk]

I see many people I work with who have computers but would not have the capability to beat the races.

At the same time some of the posts from the off-shore players show me that they have a very sound basis for their play.

I guess we all give it our best and let the chips fall.

[formula_2002]

I would disagree with the computers argument. i think it is more a combination of:


1 - UK racing being lower margin due to fixed odds format.

2 - Exchanges.

3 - Fixed Odds being different between various books offering shopping opportunities.

4 - Fewer races but much stronger markets.

5 - A bigger casual bettor market because of off track outlets being numerous.

I'm sure there are a few of you that average over 10% profit to stake annually - it is beyond my comprehension how that is possible on US racing - Hats off to you guys.

It is beyond my comphension also!!

What vig does a fixed odds bookmaker use?
Are match plays offered?

Thanks
Joe M

[dancingbrave]

Vig typically for fixed odds bookmakers in UK is 2% per runner. So an 8 horse race would be 16%, however if you have 15 different boks producing similar but slightly different fixed odds for the race in the morning that reduces to about 2-4%. In addition there are exchanges, that despite high fees typically 4% on winning bets have vig less than 2%.

So typically if you are serious and are on the ball in terms of shopping around for best odds you are betting against 3% vig and have the advantage of fixed odds and knowing larger bets won't affect your returns.

So a bettor that has a 25% edge can make 22% profit whereas I'd say if a bettor in the US has a 25% edge I'd estimate he'd struggle to make 6% profit to stake with the vig, breakage, pool betting being against you.

With the better information available in north america it astounds me that people can get an edge big enough to make it worthwhile.

btw - match ups typically not offered in UK other than very occasionally.

[formula_2002]

Vig typically for fixed odds bookmakers in UK is 2% per runner. So an 8 horse race would be 16%,



I'm a bit confused about that. What is the sum of his book for the whole race(sum 1/odds+1) ? 1.02 or 1.19 ? It can not be both.
Here, at a track with a 15% vig(take) the sum is 1.176+breakage.
Does the book break to a dime or nickle?

So many questions ;)

[dancingbrave]

There is no breakage with fixed odds. a typical bookmaker would set his odds eg:

1 - 5/2
2 - 7/2
3 - 4/1
4 - 5/1
5 - 10/1
6 - 12/1
7 - 12/1
8 - 25/1

A theoretical percentage of 116% - sometimes a bit higher and the customer can choose to fix the odds as offered or get the SP which is the fixed odds price as determined by an independant body at the start of athe race (same for all bookmakers). But you can see if a different bookmaker is offering horse 1 @ 11/4 and horse 4 @ 6/1 the theoretical profits for the bookmakers goes down and the margin the bettor is betting against goes down if he shops for the best odds.

[formula_2002]

There is no breakage with fixed odds. a typical bookmaker would set his odds eg:

1 - 5/2
2 - 7/2
3 - 4/1
4 - 5/1
5 - 10/1
6 - 12/1
7 - 12/1
8 - 25/1

A theoretical percentage of 116% - sometimes a bit higher and the customer can choose to fix the odds as offered or get the SP which is the fixed odds price as determined by an independant body at the start of athe race (same for all bookmakers). But you can see if a different bookmaker is offering horse 1 @ 11/4 and horse 4 @ 6/1 the theoretical profits for the bookmakers goes down and the margin the bettor is betting against goes down if he shops for the best odds.

Thanks. To me thats just less than a 15% vig on the book.
I'd like to see some fixed (or as some would have it, set) odds offering here.
Joe M