interesting paper for the smaller pick three player

[Robert Fischer]

https://www.econ.washington.edu/user/ellis/econ482/horse1105.pdf

Ellis argues that favorites are over played by showing that by far the most often outcome is that 1 or 0 favorites will win during the pick three sequence. That combined with the higher payouts for those sequences is the basis of his value opinion.

[Capper Al]

https://www.econ.washington.edu/user/ellis/econ482/horse1105.pdf

Ellis argues that favorites are over played by showing that by far the most often outcome is that 1 or 0 favorites will win during the pick three sequence. That combined with the higher payouts for those sequences is the basis of his value opinion.

The website comes up with a warning.

[GameTheory]

Take the "s" out of "https"

[Robert Fischer]

http://www.econ.washington.edu/use...2/horse1105.pdf

[garyoz]

You need to click through on the secure server (with s).

A really nice little study--has nothing to do with bet size (e.g., not just for small bettors).

Quoting:

Note that the highest premium to be found relative to the win-parlay bet, 80%, is when exactly one favorite wins its race in the three-race sequence. ..snip... it is clear that the lowest premium relative to the win-parlay bet, 16%, occurs when all three favorites win their races in the three race sequence. The premium is also subpar when favorites win exactly two of the three races in a pick three sequence.

This is consistent with behavior in which the bettor is willing to take a chance on a longshot in one race, but too risk-averse to leave out the favorites in the other two races. A subset of this case occurs when a horse other than the favorite wins the first leg, and favorites win the second and third legs of the sequence. This pick three outcome only occurred 11 times at the Santa Anita meet, but the regression presented in Table 5 suggests a very small premium, 14%, in this event....snip... Including favorites on pick three tickets can be viewed as purchasing insurance, albeit incomplete insurance; after all, the favorite is more likely than any other horse to win a given race. But that does not mean that the favorite is likely to win the race. Actuarially speaking, given the 20% takeout rates on pick three wagering pools, the racetrack is a terrible place to purchase insurance!

So optimal pick 3 tickets have one favorite and never (ever) bet a ticket with 3 favorites (based upon Santa Anita, Fall 2000). Also, field size is irrelevant, it is all reflect in the off odds.

[rrbauer]

Don't know whether to laugh or cry. The P3 has been around since the mid-90's (Calif) and we're just now figuring out that overplaying favs in the 3-race sequence is not good? First, understand that in the buried, downstream legs that we don't know which horse will be favorite. Then, if we accept the "favs win 1/3 of the time" that the probability of 3-favs winning is .33 x .33. x .33 which works out to about .035 which is about 28-1. If you follow P3 wagering at all you know that the payouts on P3's that involve 2 favs going into a 3rd fav do not even come close to 28-1. Maybe 10 or 12 to 1. Everything works against the scenario in terms of probability; and, if that's not enough, in the rare instance when 3 favs win the P3 seqence the payoff doesn't compensate for the risk. A double whammy!

[formula_2002]

https://www.econ.washington.edu/user/ellis/econ482/horse1105.pdf

Ellis argues that favorites are over played by showing that by far the most often outcome is that 1 or 0 favorites will win during the pick three sequence. That combined with the higher payouts for those sequences is the basis of his value opinion.
I wish he included the a/e (actual wins/expected wins) for each of his three groups (0, 1, 2, and 3 favorites).
Then you could determine how significant the deviations were from the expected mean .80.
It would also be interesting to see the results when the favorite wins in the different legs.

If he would run the analysis with different data, perhaps 4 more times we could start to judge if the data in the first set really represented the environment he is testing

[garyoz]

Don't know whether to laugh or cry. The P3 has been around since the mid-90's (Calif) and we're just now figuring out that overplaying favs in the 3-race sequence is not good? First, understand that in the buried, downstream legs that we don't know which horse will be favorite. Then, if we accept the "favs win 1/3 of the time" that the probability of 3-favs winning is .33 x .33. x .33 which works out to about .035 which is about 28-1. If you follow P3 wagering at all you know that the payouts on P3's that involve 2 favs going into a 3rd fav do not even come close to 28-1. Maybe 10 or 12 to 1. Everything works against the scenario in terms of probability; and, if that's not enough, in the rare instance when 3 favs win the P3 seqence the payoff doesn't compensate for the risk. A double whammy!

This study is an academic study, not based on assumptions, just the data and relatively sophisticted econometrics. No need to make assumptions "if you follow p3 wagering..." such as your analysis.

The overbet favorites in pick-3's, what the author refers to "as insurance bets," create an inefficiency in the P-3 market--making P-3's using one favorite in the sequence overlays. This study documents that. May seem like common sense, but its always nice to have it confirmed--even if it is a very small sample.

[formula_2002]

Based on the information given, I calculate the following ROI's

0 favorites, less than .62
1 favorites, less than .61
2 favorites, less than .64
3 favorites, .54.

Handicapp your way out of those roi's :D

I'll stick with craps ;).

[chickenhead]

Based on the information given, I calculate the following ROI's

0 favorites, less than .62
1 favorites, less than .61
2 favorites, less than .64
3 favorites, .54.

Handicapp your way out of those roi's :D

I'll stick with craps ;).

ROI for what? There is no innate ROI to anything. It has to be tied to an action, an investment.

[Robert Fischer]

Based on the information given, I calculate the following ROI's

0 favorites, less than .62
1 favorites, less than .61
2 favorites, less than .64
3 favorites, .54.

Handicapp your way out of those roi's :D

I'll stick with craps ;).

can you share the math ?

I don't understand how "2 favorites" is a lower expectation than 0 or 1 favorites. The study showed only 19% of the winning sequences to be of the "2 favorites" variety and the median payout was only $52.
While 34% of the sequences had "zero favorites" and paid a median of $278.

[Robert Fischer]

^
were you using more horses for the sequences without all 3 favorites? In practice you could know your cost and expected median return for the "3 favorites", but would the cost part of Roi start to depend on field size or eliminating non-contenders in the other sequences?

[formula_2002]

can you share the math ?

I don't understand how "2 favorites" is a lower expectation than 0 or 1 favorites. The study showed only 19% of the winning sequences to be of the "2 favorites" variety and the median payout was only $52.
While 34% of the sequences had "zero favorites" and paid a median of $278.
2 favorite example:
1 fav x 1 fav x 7 none favorites (his average field was a bit more than 8 entries)= 7 plays. Those 7 plays represent one of three possible sets.
You also have, 1X7X1 and then 7x1x1 for a total of 21 plays at $1 per.

He won 33 plays at an AVERAGE payout of $72. total returned was 33x$72= $2376.
total bet was 21 plays x 176 races X$1 = $3692.
ROI= $2376/$3692= .64.
Right?

[Topcat]

Thank you-I'm always intested in new studies.

I think Dick Mitchell covered this off pretty well in his Common Sense Betting book. I think it is the best money management book out there.

[chickenhead]

lets see here.

avg of all payouts is $317

176 wagers

8 horse avg field

8x8x8 = 512 combos, X176 = $90,112 wagered to buy everything

return is $317 X176 = $55,792

ROI 61.9%

which implies a 38.1% takeout. Which means it's a useless sample size, it's not big enough for you to figure out the takeout from it, so forget about trying to extrapolate anything else from it.

either that, or for whatever reason, that's not a valid treatment of the data.

[formula_2002]

lets see here.

avg of all payouts is $317

176 wagers

8 horse avg field

8x8x8 = 512 combos, X176 = $90,112 wagered to buy everything

return is $317 X176 = $55,792

ROI 61.9%

which implies a 38.1% takeout. Which means it's a useless sample size, it's not big enough for you to figure out the takeout from it, so forget about trying to extrapolate anything else from it.

either that, or for whatever reason, that's not a valid treatment of the data.


Why the winning pick 3 play could return less than the pick 3 pool take out.
Suppose there are 4 horses in each of the three pk3 legs.
The win probabilities in each leg for each horse is the same 10%, 20%, 30%, and 40%.
A total book of 1.00 (no take-out in either the win or pk3 pools).

Your pick three ticket consist of the three favorites.
You bet $1
A fair return is 1/ (.4x.4x.4) =$ 7.5 for each $ you bet
Or 6.4% of the exacta pool for each $ you bet.
.
If the pool had $100 in it you get your $7.5

But suppose the pool had but $80 in it.
Now you can only get .064x $80= $5.12

Of course there could have been $200 in the pool, then you would have gotten $15.!!!

[formula_2002]

Why the winning pick 3 play could return less than the pick 3 pool take out.
Suppose there are 4 horses in each of the three pk3 legs.
The win probabilities in each leg for each horse is the same 10%, 20%, 30%, and 40%.
A total book of 1.00 (no take-out in either the win or pk3 pools).

Your pick three ticket consist of the three favorites.
You bet $1
A fair return is 1/ (.4x.4x.4) =$ 7.5 for each $ you bet
Or 6.4% of the exacta pool for each $ you bet.
.
If the pool had $100 in it you get your $7.5

But suppose the pool had but $80 in it.
Now you can only get .064x $80= $5.12

Of course there could have been $200 in the pool, then you would have gotten $15.!!!

Then again if you had the only winning ticket you would get all of the $100.
If you had to share the pool with 49 other tickes, you would only get $2.

So its really has to do with the number of tickes sold on the winning combination , not all the stuff I mentioned in the previous note.

[Tom]

If it ain't real results, it ain't reality.
The real data is out there - go calculate roi's from real results.
Anything else is fun with numbers. :sleeping:

[garyoz]

The purpose of the study was not to suggest "favorite X all X all" bets but to demonstrate that favorites were overbet, by what the author hypothesizes to be "insurance" wagers by pick-3 players. You are imputing something the author is not addressing. It is a narrowly focused study.

[formula_2002]

If it ain't real results, it ain't reality.
The real data is out there - go calculate roi's from real results.
Anything else is fun with numbers. :sleeping:
His results were real, his analysis was poor.(or "I" just can't value them)

You should not use all these "averages" and "medians," and you need lots of data.

The analysis also should be done on an incremental odds basis, keeping the mean difference as small as possible (like 1%). The smaller the mean difference and the greater the amount of data allows for more accurate analysis.
Also, its not the amount of Franklin's you won, it's the amount you should have won (a/e)


When I do this kind of stuff, I use real numbers and lots of them.
I just haven't found results that appeal to people.. ;)

[formula_2002]

The purpose of the study was not to suggest "favorite X all X all" bets but to demonstrate that favorites were overbet, by what the author hypothesizes to be "insurance" wagers by pick-3 players. You are imputing something the author is not addressing. It is a narrowly focused study.
My point is, he is missing the point.
In the sample size he used (small for the odds being considered) there is no statistical difference in the four sets of roi's.

[Robert Fischer]

2 favorite example:
1 fav x 1 fav x 7 none favorites (his average field was a bit more than 8 entries)= 7 plays. Those 7 plays represent one of three possible sets.
You also have, 1X7X1 and then 7x1x1 for a total of 21 plays at $1 per.

He won 33 plays at an AVERAGE payout of $72. total returned was 33x$72= $2376.
total bet was 21 plays x 176 races X$1 = $3692.
ROI= $2376/$3692= .64.
Right?

thanks ,
That looks correct to me.
Darn'd All-button :) .

[Robert Fischer]

My point is, he is missing the point.
In the sample size he used (small for the odds being considered) there is no statistical difference in the four sets of roi's.
Isn't .54 a significant difference from .61-.64 ?

[garyoz]

Isn't .54 a significant difference from .61-.64 ?

Good point. But once again the study is not about hitting the "all" button, so I don't think that is how I'd analyze its validity. But rather it is demonstrating what everyone intuitively knows, favorites are overbet in pick-3's. It is an academic piece using a small data set. Personally, I like to see academic analyses applied to handicapping. Remember this is a working paper and not a published article.

IMHO, all the posts in this thread make good points. However, I wouldn't term this analysis "sloppy."

[chickenhead]

Why the winning pick 3 play could return less than the pick 3 pool take out.
Suppose there are 4 horses in each of the three pk3 legs.
The win probabilities in each leg for each horse is the same 10%, 20%, 30%, and 40%.
A total book of 1.00 (no take-out in either the win or pk3 pools).

Your pick three ticket consist of the three favorites.
You bet $1
A fair return is 1/ (.4x.4x.4) =$ 7.5 for each $ you bet
Or 6.4% of the exacta pool for each $ you bet.
.
If the pool had $100 in it you get your $7.5

But suppose the pool had but $80 in it.
Now you can only get .064x $80= $5.12

Of course there could have been $200 in the pool, then you would have gotten $15.!!!

For a single race, sure. No different than if you bet all horses to win in a race, you might lose more than the track take on that race. Over a large enough sample, you'll get back ~ your bet amount minus the track take. No?

The pool has to be large enough to provide payoffs in tune with the odds, if any pick 3 pools are they would be the socal pools, so I'm assuming they are. Don't know how to figure that one off the top of my head, tho.

[Tom]

When I do this kind of stuff, I use real numbers and lots of them.
I just haven't found results that appeal to people.. ;)

You do not know the odds when you bet a pic 3 or 4.....so your study, if it uses them is not valid to what you really are betting.

[classhandicapper]

I wish he included the a/e (actual wins/expected wins) for each of his three groups (0, 1, 2, and 3 favorites).
Then you could determine how significant the deviations were from the expected mean .80.

I agree.

Whether there is value or not is only partially related to the premium to the parlay. For example, big favorites tend to outperform the take and big longshots tend to underperform. So even if you are getting a bigger premium to the parlay with a couple longshots, it may still be a worse bet because those lomgshots are so sharply overbet in the win pool (and vice versa).

[formula_2002]

You do not know the odds when you bet a pic 3 or 4.....so your study, if it uses them is not valid to what you really are betting.

I made no study of PK3' other that to calculate a few fair values once in awhile.
I'M STILL WORKING ON THE WIN POOL. ;)

[formula_2002]

Isn't .54 a significant difference from .61-.64 ?
It's a good question.
.54 is 1.62 standard units from the mean.
Many consider anything beyond 2 standard units "significant".
It's not in a special place.

Thats how I look at it, but I'm not a statistician..