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Handicapping
Decision Methods
Basic Statistics
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Handicapping
Reprinted with permission from the author
Race analysis is almost exclusively involved with regression. Handicappers look for
indications of the future by studying the past. Tom Ainslie's advice from 30-40 years ago
that a horse should never be expected to do something it has not already done forms the
basis for most current approaches to race analysis. I suggest the underlying assumptions
are conceptually flawed in a number of instances, and that an awareness of the flaws can
be quite profitable.
Consider the current state of the real estate market in the United States, compared with 5, 10, and 15
years ago. During a similar building boom in the 1980s, regression advocates bought (and sold) property
on the assumption that the real estate market would continue its rate of increase indefinitely. In fact,
it did not, and a number of people suffered substantial financial loss because of that erroneous
assumption. Similarly, current real estate investors may be heading for the same type of losses. In
handicapping, as in real estate investing, studying the past does not necessarily enable accurate
predictions to be made about the future.
Because it is more convenient to believe that recent performance will be replicated, handicappers often
look for the entry that has run well recently at the current distance and class level, with the unstated
assumption that by comparing the recent efforts of each entry, accurate predictions can be made about the
outcome of the upcoming race. Some even use the shortcut "eliminations" suggested by Tom Ainslie, William
Quirin, and others to avoid in-depth analysis--eliminating an entry that failed to beat half the field in
its last race, or that is a router entered in a sprint, or similar.
The "bounce theory" is essential to understand, because it suggests that a very good performance may be
followed by a lesser effort, rather than a repetition of (or improvement on) the very good performance.
There are abundant resources available on the topic, and every serious bettor should spend some time
researching the theory, and thoroughly understanding its implication.
A brief example will clarify the importance of the bounce theory. Two entries duel head-to-head down the
stretch in a driving finish in their last race. Speed, pace, and similar ratings are almost identical.
Which is the better choice to win today's contest? Using regression, many handicappers would tend to avoid
the issue by looking at the races that led up to the duel in their last race, assuming that they contained
indicators that would make the outcome of the upcoming race more predictable.
Regardless of its performance two races back, one of the entries today is more likely to perform better,
and the other is more likely to perform more poorly, than it did in the highly competitive last race. There
are very specific, explicit analytical techniques to help determine which is which. Those issues will be
explored in detail in upcoming posts. I suggest that race analysis that goes beyond simplistic regression
offers substantial rewards to the serious bettor willing to make the effort.
We provide full-service data analysis, data modeling, and software development services for
professional bettors and pari-mutuel investors. Whether you need a database-driven, fully-customized
application developed from the ground up, or modification or upgrade of an existing application, we
can provide cost-effective software solutions to all your race analysis needs. Email us at:
support@ddssratings.com for more information.
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1) Superior information generates superior returns; the higher the quality of
the information used to make decisions, the higher the quality of the decisions
resulting from analysis of that information. “Information” is distinct from “data”;
the vast majority of material used by pari-mutuel investors is raw data—masses of
words, numbers, charts, and graphs—rather than information. Information is data
that has been analyzed, processed, and converted into a form that a potential
investor can use as the basis for decision-making.
2) The value of information is in direct proportion to the availability of that
information; the higher the number of investors with access to the information,
the less valuable that information becomes.
3) The competition in pari-mutuel investing is with other investors; that
competition is only indirectly related to the pari-mutuel events. Most pari-mutuel
investors believe they are trying to “outguess” the other investors regarding the
outcome of specific pari-mutuel events. Nothing could be further from the truth;
the outcome of individual pari-mutuel events is almost irrelevant from an
investment perspective. It is the result over time that is significant.
4) The decision-making skills and pattern-recognition skills necessary for
success in other business and investment activities are every bit as necessary
for success in pari-mutuel investing. Professional bettors recognize this need
and continually develop, fine tune, and train their decision-making and
pattern-recognition skills.
5) The strongest advantage for serious pari-mutuel investors is the average racing
fan's belief that the outcomes of races are either too complex for him or her to determine,
or are unknowable. Both beliefs justify the view of wagering as primarily for entertainment,
justify a near-total lack of cognitive effort to determine the probable outcomes, and
justify losses as the cost of entertainment. Wagering is enjoyable, and winning is more
enjoyable than losing; by focusing on wagering as a business enterprise, there will be
many more opportunities to enjoy the process than if wagering is regarded solely as
entertainment.
We provide full-service data analysis, data modeling, and software development services for
professional bettors and pari-mutuel investors. Whether you need a database-driven, fully-customized
application developed from the ground up, or modification or upgrade of an existing application, we
can provide cost-effective software solutions to all your race analysis needs. Email us at:
support@ddssratings.com for more information.
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The greatest myth in horse racing is that all the information you need to win
is contained in the Daily Racing Form past performances, or in the daily downloads
from BRIS or TSN. It is equivalent to stock traders believing that all the
information they need to make investment decisions is published daily in the Wall
Street Journal.
In both cases, the data provided is valuable, and should form the basis for
further research. In neither case should it be considered the only—or even the
best—source of information. In business terms, the data represents a closed system; everyone gets
essentially the same data, and manipulates it primarily in form, rather than
content. Just as successful entrepreneurs must “think outside the box,” so must
successful investors “think outside the system.”
As interesting and useful as the available data may be, the simple truth is
that the data should only form a part of your investment decision-making process,
rather than forming the entire basis on which decisions are made. The abject
failure of “handicapping software” to show a profit over time for most users is
not surprising—with minor variations, users are attempting to extract a few crumbs
from a continually decreasing piece of the same pari-mutuel pie.
That the data in the Daily Racing Form and the data made available by vendors
is useful is not the issue; the issue is that using only that data as the basis
of a decision-making process is only suitable for recreational bettors and
hobbyist racing fans. Professionals should realize that mindlessly manipulating
the same raw data as everyone else, hoping for insights and advantages unavailable
to the competition, is ultimately futile.
We provide full-service data analysis, data modeling, and software development services for
professional bettors and pari-mutuel investors. Whether you need a database-driven, fully-customized
application developed from the ground up, or modification or upgrade of an existing application, we
can provide cost-effective software solutions to all your race analysis needs. Email us at:
support@ddssratings.com for more information.
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1)
They are unwilling to admit that winning requires more information or
skill than they have.
Novice, recreational, and beginning racing fans should
start with professional grade ratings, rather than trying to do everything
on their own. Not only will it provide continual insight into which entries have
the best chance of winning, it immediately leverages the skill and experience of
professionals in the process of winning.
The myth of the stalwart, lone handicapper jousting the windmills of pari-mutuel
fortune is a holdover from the 1970s and 1980s; it is an outmoded mindset from the
"old days" when people wanted to hide their efforts from others because they were
almost universally losing. Rather than admit they were losing they preferred (and
still prefer) the "emotional comfort" of habitually repeating the same out-dated,
unprofitable, losing strategies year after year. Losses are dismissed as the "cost
of entertainment," and wagering is considered a "hobby."
Conversely, today's racing fan is as likely to be a college student or business
person intent on leveraging pari-mutuel racing into a source of income, rather
than "participating in a sport." In blunt terms, today's successful racing fans
view wagering as a business, not a sport; their belief is that if it cannot produce
a profit, it is a waste of both time and money.
2)
They lack the time for the in-depth race analysis, race modeling,
and record-keeping necessary to gain a competitive edge over other bettors.
Race analysis is a complex activity that requires a serious commitment of time
and effort on a daily basis to stay ahead of the crowd.
Today's successful bettors understand that they need the leverage provided by
professional grade race ratings to be successful. Whether novice or professional,
winning requires more information than that which is available to the casual
racing fan in the Daily Racing Form or data downloads from BRIS or HDW. The best
source of that additional information is DDSS Ratings.
3) They are uncertain which entries offer the best value in each race.
Many racing fans use ratings or software applications that provide a variety of
selection categories, each of which indicates a different order of finish. One or
more of those categories is almost guaranteed to "accurately predict" the outcome
of a given race, but it is impossible to tell which one to use before the
race.
Confusion about value and relative probabilities is a major reason why novices
and recreational bettors tend to overbet exactas, trifectas, and multiple race
wagers such as the Pick 3 and Pick 4. "Laundry list" postings on various
"handicapping forums" of 4 or 5 selections in every race at a dozen tracks create
the impression that boxing all the entries listed is a fast lane to huge profits.
In reality, such wagers can easily cost $10,000 to $15,000 a day, and rarely, if
ever, return more than a small percentage of that amount in wins.
4) They base their wagers on short samples. The average racing fan
believes that the result of a very small number of races acts as a blueprint of
what will occur in another small sample of races. Generally called the "Gambler's
Fallacy" or the "Law of Small Numbers," the concept was popularized by writers
Andrew Beyer and Steve Davidowitz when describing "track biases."
Popular with system sellers for more than 50 years, the "system workout" has
been a staple of both writers and software developers. Most software applications
include a facility to perform "regression analysis" on a limited number of races,
to create the impression that the software selections are profitable. The failure
to correct for outliers--unusually high mutuels that occur infrequently and are
unlikely to repeat--renders such software useless for serious bettors intent on
making a profit from wagering.
5)
They wager by the race and by the day, rather than by the week,
month, or year.
The desire for immediate gratification is the cause of the
Last Race Syndrome
, the situation in which bettors who are behind for the day
ignore solid choices at generous odds to make increasingly wild wagers in an
attempt to "show a profit for the day."
Bettors who continually focus on wagering as a source of income, follow the
implementation strategies developed by professional bettors for their own use
(as with DDSS Professional Ratings), and diversify their risk by spreading wagers
over a number of tracks have the best chance of success. While the "crusher bets"
popularized by writer Andrew Beyer make exciting reading, they are a totally
inappropriate wagering strategy.
DDSS Ratings solve all five of the problems:
-
We design, build, and continually maintain highly accurate, precise data
models for every distance and every grade for more than 25 major and minor
thoroughbred tracks on a daily basis.
-
We perform the preliminary analysis of contender selection and contender
matching in each race.
-
We analyze each race using sophisticated software applications that
evaluate each contenders on 53 different factors using complex, proprietary
algorithms.
-
We assign the most predictive weight to each factor based on the specific
surface, distance, class level, conditions, and track of the current race.
-
We pinpoint the high-value selections and wagering strategies defined by
our extensive data modeling and regression analysis.
-
We provide explicit strategies for implementing the ratings that remove
any ambiguity or need to "interpret" the ratings. The most likely winner, the
most likely placers, and the most productive exacta and trifecta patterns are
clearly and explicitly defined for each race.
-
There is no guesswork involved; you know the best strategies to use for
each and every race situation.
DDSS Thoroughbred Ratings are the perfect complement
to any style of handicapping!
Whether you are a full-time professional or a recreational bettor, our ratings
give you the information you need to win.
Full-time professionals often use our ratings as their primary source of
wagering information and strategies, or use them in conjunction with their own
race analysis.
Trip handicappers use our ratings to pinpoint the strongest contenders to
combine with their personal picks in the exotic pools.
Exacta, Trifecta, and Pick3 bettors use our ratings to identify the most
likely winners and placers in each race for multiple wagering strategies.
Recreational bettors and "weekend warriors" use our ratings to gain the
same advantage over the betting public enjoyed by our professional members.
Because our ratings are complete, recreational bettors can concentrate on winning
and enjoying the races.
DDSS Ratings enable you to:
- Win more
- Lose less
- Save time
- Reduce complexity
- Focus on winning
- Make wagering profitable
We provide full-service data analysis, data modeling, and software development services for
professional bettors and pari-mutuel investors. Whether you need a database-driven, fully-customized
application developed from the ground up, or modification or upgrade of an existing application, we
can provide cost-effective software solutions to all your race analysis needs. Email us at:
support@ddssratings.com for more information.
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Reprinted with permission from the author
I think most handicappers underestimate the leverage provided by using trips as
the focal point of their handicapping. Every number earned by a horse in a
race is based on its performance relative to the other horses, and can only be
meaningful when used within the context of the race.
Similarly, I think most handicappers are intimidated by trips, because they
think they lack the skill to use them profitably. Nothing could be further
from the truth; every bit of "extra information" can prove valuable, simply
because other bettors don't have that information.
The entire mystique of trip handicapping has been overblown to make racing fans
believe that only "experts" with years of intense study and observation can
make use of trips. In fact, trip handicapping is almost mechanical; the useful
details are the ones other observers miss. There is little point in taking
detailed notes about events that will be published in the Daily Racing Form's
results charts for the race for everone else to see.
Initially, the most difficult part of trip handicapping is learning to look at
the horses who are not in the lead, or close to the leader. Because most
attention--both of the track cameras and the racing fans--is focused on the
leaders, events in the middle and rear of the field are less emphasized. It is
in those areas that observations hold the most promise for profit.
The easiest and fastest way to learn how to do trip handicapping is by watching
races that you are NOT betting on. Because you have no investment in the race,
you can watch it more objectively. Focus on the horses in the middle portion of
the field, from third to sixth or seventh in an average field. Remember that to
be a serious contender, it is necessary for a horse--regardless of running style--
to be within striking distance of the leader at the head of the stretch.
Events before the head of the stretch may affect the race outcome, but initially
you should focus most on this critical point in the race.
Any horse
that does
not move into contention--within four lengths of the leader at the top
of the stretch--can be dismissed as a "no go."
That is, the race is
primarily
for training purposes, rather than an all-out effort to win.
All the fractional times, final time, energy expenditures, pace ratings,
speed ratings, and observations for that entry in that race should be ignored
when it runs in subsequent race.
That single step will give you a huge
advantage over the speed, pace, and computer handicappers who mistakenly believe
that every horse in every race is all-out to win, and can be
meaningfully compared with other entries on that basis.
We provide full-service data analysis, data modeling, and software development services for
professional bettors and pari-mutuel investors. Whether you need a database-driven, fully-customized
application developed from the ground up, or modification or upgrade of an existing application, we
can provide cost-effective software solutions to all your race analysis needs. Email us at:
support@ddssratings.com for more information.
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Decision Methods
Race analysis proceeds in linear fashion from highly subjective to highly
objective. The initial decisions about whether or not a specific race offers
an opportunity for profit, whether or not a specific entry will perform better
or worse than it performed in previous races, and whether or not the a specific
entry can compete effectively in the current race are all highly subjective
decisions based on years of experience and the analysis of tens of thousands
of races.
While the mathematical comparisons of various relevant factors are fairly
simple, the initial decision-making process involved in selecting appropriate
races and contenders is relatively complex. The solution to the problem is to
view the process like any other business decision process—and to use the most
effective enterprise resource planning (ERP) and decision support system (DSS)
software available, in conjunction with carefully constructed data models and
statistical analysis.
The correct decisions of experts can be reverse engineered using multiple
regression analysis and a statistical technique called “bootstrapping” to
determine the precise impact values for each relevant factor that the expert
“intuitively” used to make the decision. Bootstrapping is based on the idea
that subjective judgments are not really subjective; evaluations are made on a
subconscious basis that utilizes the information and results of previous
decisions as a “heuristic,” a generic term that refers to a mental shortcut
used in decision-making.
The bootstrap algorithm uncovers those shortcuts and reduces them to a set
of mathematical equations and selection criteria that can be applied to similar
situations in the future. The strength of bootstrapping is that consistent
decision-making criteria will substantially outperform inconsistent criteria
every time; the greater the number of decisions made, the more valuable
consistent decision-making processes become. When bootstrapping is used in
conjunction with carefully constructed data models and appropriate statistical
research techniques, the resulting algorithms substantially outperform the
selections of experts.
The combination of bootstrapping, data modeling, and statistical
analysis enables the creation of software applications that accurately predict
the outcome of races more consistently and more effectively than the experts.
DDSS has reduced race analysis to a set of complex algorithms and
mathematical models that are continually modified according to changes in the
external environment—the same type of modifications made by enterprise resource
planning (ERP) and decision support systems (DSS) software applications used by
Fortune 500 corporations as the basis for multimillion-dollar strategy and
investment decisions.
We provide full-service data analysis, data modeling, and software development services for
professional bettors and pari-mutuel investors. Whether you need a database-driven, fully-customized
application developed from the ground up, or modification or upgrade of an existing application, we
can provide cost-effective software solutions to all your race analysis needs. Email us at:
support@ddssratings.com for more information.
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Reprinted with permission from the author
In the book,
Decision Traps: The Ten Barriers to Brilliant Decision-Making and How to
Overcome Them
, the authors describe a number of methods professionals can use to make better
decisions.
In order of complexity and effectiveness, these decision methods are: intuition, simple screening
and ranking rules, occupation-specific rules of thumb, subjective linear models,
bootstrapping, objective linear models, and multiattribute utility analysis.
Intuition
Intuition is to use emotional responses; signals from the conscious and unconscious mind
about right and wrong based on previous experiences.
Russo and Schoemaker (1990) write, “[intuition] can take account of knowledge you possess
but can’t put into words . . . [and] your mind may be able to process information in a more
complex and subtle way than you could formalize in a decision rule” (p. 120).
However, there are limits to intuition. The “gut feeling” associated with a memory may
have been coded inaccurately or may be associated to an entire situation rather than with
specifics and this is why intuition is ranked as the least effective decision method.
Screening and ranking rules
Screening and ranking rules are simplistic in that they do not consider trade-offs;
“surpluses in one category do not compensate or offset deficiencies in other areas”
(p. 124) and occupation-specific rules of thumb are only applicable to certain situations.
Subjective linear models
The user of a subjective linear model assigns an impact value to categories under
consideration for each choice available, and, for each choice, assigns a number based on
the extent to which evidence favors (or disfavors) the choice in terms of each category.
The result is the sum of the product of each impact value and the number associated with
each choice. A subjective model is reliable, or robust, when small changes in the numbers
or impact values do not change the order of preference between the different choices.
Bootstrapping
The user of a bootstrapping method reverse engineers good decisions to find out which
impact values made a difference and then constructs a model for use in future decisions.
Objective linear models and multiattribute utility analysis
The user of an objective linear model relies on historical data based on outcomes
decisions that have been made repeatedly and where the future is expected to resemble
the past. An objective linear model is constructed in the same way as a subjective
linear model with one exception: the impact value is derived from a statistical
analysis of decision outcomes.
Russo and Schoemaker (1990) write that “objective linear models are . . . ideal for
creating all kinds of estimates and forecasts” except when the future is uncertain.
For critical decisions, it may be more useful to use a multiattribute utility
analysis rather than either subjective or objective analysis. Both of the
latter approaches fail to break each choice into key components and consider
trade-offs in terms of long-term, strategic goals.
References
Russo, J.E. and Schoemaker, P.J.H. (1990).
Decision Traps: The Ten Barriers to
Brilliant Decision-Making and How to Overcome Them.
New York, NY: Fireside.
We provide full-service data analysis, data modeling, and software development services for
professional bettors and pari-mutuel investors. Whether you need a database-driven, fully-customized
application developed from the ground up, or modification or upgrade of an existing application, we
can provide cost-effective software solutions to all your race analysis needs. Email us at:
support@ddssratings.com for more information.
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Reprinted with permission from the author
An area of decision research that may be particularly interesting to providers
of handicapping information is decision aid reliance. Arnold, Collier, Leech,
and Sutton (2004) define reliance in terms of two conditions: acceptance and
influence. Acceptance in the sense of decision aid reliance means that the
user “adopts the aid as a useful part of the decision-making process” (p. 4).
Influence means that, “once the user adopts the aid as a useful part of the
process, the user … allows the process … to become part of the user’s
judgment formulation” (p. 4).
Illusion of control
Kahai, Solieri, and Felo, (as cited in Arnold, et al., 2004) found that
illusion of control results in less effortful thinking prior to making a final
judgment (p. 8). For example, a program that allows users to filter already
existing alternatives while creating the illusion that the user actually
handicaps the races may result in a situation in which the user more readily
accepts the suggestions made by the software. That is, the illusion of control
"granted" by the software increases reliance on the software as a decision aid.
(Kaplan, Reneau, and Whitecotton, 2001).
From a handicapper’s perspective, it may be important to realize that a
particular software package may not necessarily offer freedom of choice and
that it may only create the illusion that there is a decision to be made.
Instead, ready-made decisions based on each category (speed, class, etc.) are
displayed in complicated charts. Rarely is the user able to assign different
weights to each type of consideration; the impact values--both explicit and
implicit--are already programmed into the software.
Overconfidence
Overly confident participants are more likely to disregard recommendations
given by a decision aid and perform significantly worse than less confident
participants (Kaplan, Reneau, and Whitecotton, 2001).
Sieck and Arkes (2005) found that reducing overconfidence through calibration
results in greater reliance and greater performance. One of the participants
in Sieck and Arkes’ study wrote, "Statistical equation gave me more
confidence if it was similar to my original guess. If it was different,
I went with my gut instinct rather than using the equation. If I had
absolutely no clue, I went with what the equation gave me." (p. 48).
It was only when intuition could not deliver a preference that the solution
provided by the decision aid was used.
Sieck and Arkes (2005) write, "our results … reproduced the standard finding
that statistical equations outperform human judges . . . [and] should
generally be strongly preferred over unaided intuition. Nevertheless, as
found here, judges rarely consult available equations and, even when they
do consult, they routinely favor their gut feelings when the 'opinions'
differ" (pp. 49-50).
Self-image
A hypothesized reason for why individuals choose not to use a decision aid,
Sieck and Arkes (2005) write, is due to threats to the decision maker’s
self-concept. Professionals may believe that it is their duty to do what
the decision aid accomplishes and relying on an equation may be interpreted
as a sign of incompetence. There may also be the idea that relying on
intuition is a sign of caring.
In several studies, participants tried to outsmart or outperform the decision
aid. Even in cases where participants were given feedback and descriptions
to support the idea that the decision aid would improve the outcome,
participants still tried to improve on the recommendations provided by the aid.
(Kaplan, Reneau, and Whitecotton, 2001). Of course, skepticism is a good
thing; uncritical acceptance of a decision aid does not lead to better
decisions.
Interactivity
Davis and Kottemann as cited in Kaplan, Reneau and Whitecotton, (2001)
compared participant preference for and use of two decision
aids: an interactive “what-if” tool and a non-interactive quantitative tool.
What the researchers found was that participants preferred the interactive
model, and, even when the participants shifted their beliefs based on being
told that the quantitative model would lead to better outcomes, this did not
change their preference: they continued to use the interactive model.
Recommendations
Sieck and Arkes (2005) suggest that until overconfidence is fully
understood, the most practical recommendation is “to attempt to
increase people’s confidence in the [decision aid], rather than attempting
to decrease it in themselves” (p. 50).
It is natural for decision makers to want to improve decisions and the
decision process. Decision aids should allow users to be a part of the
process and should be designed around the wishes of the users, not the
programmers.
References
Arnold, V., Collier, P.A., Leech, S.A., and Sutton, S.G. (2004). Impact of
intelligent decision aids on expert and novice decision-makers’ judgments.
Accounting and Finance, 44.
Kaplan, S.E., Reneau, J.H., and Whitecotton, S. (2001). The effects of
predictive ability information, locus of control, and decision maker
involvement on decision aid reliance.
Journal of Behavioral Decision
Making, 14.
Sieck, W.R., and Arkes, H.R. (2005). The recalcitrance of overconfidence
and its contribution to decision aid neglect.
Journal of Behavioral
Decision Making, 18.
We provide full-service data analysis, data modeling, and software development services for
professional bettors and pari-mutuel investors. Whether you need a database-driven, fully-customized
application developed from the ground up, or modification or upgrade of an existing application, we
can provide cost-effective software solutions to all your race analysis needs. Email us at:
support@ddssratings.com for more information.
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Reprinted with permission from the author
People tend to be risk-averse (or play it safe) when faced with gains and risk-taking
when faced with losses. Risk-taking tends to occur when perceived consequences of loss are
such that the decision is framed based on the belief that action is preferable to acceptance.
Escalation of commitment is a powerful influence in risk-taking behavior and applied in
many businesses in the form of waiting rooms. When a person has spent some time waiting for an
appointment that person is unlikely to seek an appointment elsewhere because of the desire to
justify the time he or she has already wasted. The negative consequences associated with loss
are often greater than the drive toward potential future gains.
The sunk costs concept is similar to escalation of commitment in that the decision is
framed in consideration of investments rather than future costs and benefits. Rather than
focusing on recapturing investments, or justifying future actions based on time, effort, or
money that has already been lost (sunk), failed attempts should be considered learning
experiences. Sometimes it is just as valuable to know what not to do, as it is to know
what to do.
The problem with taking risks is that when framing is based on a choice between
losses, the focus on the correction of past outcomes at times outweighs potential
future outcomes, even when the probability of success is uncertain.
We provide full-service data analysis, data modeling, and software development services for
professional bettors and pari-mutuel investors. Whether you need a database-driven, fully-customized
application developed from the ground up, or modification or upgrade of an existing application, we
can provide cost-effective software solutions to all your race analysis needs. Email us at:
support@ddssratings.com for more information.
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Reprinted with permission from the author
Order effects are interesting phenomena of cognition. Order effects occur because alternatives
are not evaluated on their own merit. Instead alternatives are compared to previous
experiences and impressions are affected by the order of presentation. When the first
alternative is presented the content is evaluated based on previous experiences and
when secondary alternatives are presented these are evaluated based on the most
recently presented information.
When choices have unique positive features, the comparison process gives an advantage to
the choice that appears in the second position (most recent = recency effect). In particular,
“step-by-step procedures typically show recency effects” and these reflect the decision
maker’s attempt to keep track of a ‘moving average’” (Bruin and Keren, 2003, p. 92).
Bruin and Keren (2003) explain that with few alternatives, and small information load,
so-called “end-of-sequence” judgments show primacy effects. This is caused by a tendency
to anchor on the first alternative presented. However, if there is more complex
information to process, an “end-of-sequence” procedure will produce recency effects.
For example, suppose you need to listen to a number of sales people each offering a
computer package for your business. Each presentation contains a lot of information and
even though a decision represents a significant investment, it becomes boring after the
third or fourth alternative. If Bruin and Keren’s research holds, you will tend to
prefer the most recent presentation to the ones presented earlier. If instead the
presentation consisted of something more interesting and less complex, you will tend to
prefer the earliest alternative.
Applied to handicapping, an earlier alternative (entry or method) might be considered
when the handicapper is wide awake, and able to concentrate well whereas a later
alternative (entry or method) might seem more appealing when the handicapper is irritated,
bored, or distracted.
Framing effects also affect the order of preferences. Results have shown that when
presented with two options that have positive features, a decision maker will have a
preference for the second option (better à best). When a decision maker is presented
with two options that have negative features, a decision maker will have a preference
for the first option (bad à worse).
Reference:
Bruin, W.B. and Keren, G. (2003). Order effects in sequentially judged options due to
the direction of comparison.
Organizational Behavior and Human Decision
Processes, 92
: 91–101.
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Reprinted with permission from the author
McGraw, Mellers, and Ritov (2004) demonstrate that the “overly optimistic beliefs can diminish the
pleasure of outcomes” (p. 282). Calibration is often used as a measure of overconfidence in research.
Someone who is well calibrated has expectations that match their outcomes, or more specifically,
have an average confidence rating that is about equal to the relative frequency of that outcome.
McGraw, Mellers, and Ritov (2004) claim there is a positive correlation in the discrepancy between
expectations and outcomes and the intensity of emotional reactions. For example, the more
excitement a handicapper feels, the more unrealistic his or her expectations may be.
An overconfident person is less pleased by an expected positive outcome than a surprising
positive outcome; and, reacts with dismay to a failure and great disappointment to a
surprising failure.
The results of McGraw, Mellers, and Ritov (2004) study demonstrate that overconfidence
can result in less enjoyment of a task, even though participants succeeded in
task accomplishment.
Participants who were informed about overconfidence effects and
were provided with a baseline with which to compare their results were happier with their
accomplishments and their failures.
The findings imply that baseline comparisons can help
handicappers enjoy the handicapping more, as it would serve as a means to gauge performance
and help create realistic expectations.
Reference:
McGraw, P.A., Mellers, B.A., and Ritov, I. (2004). The affective costs of
overconfidence. Journal of Behavioral Decision Making, 17.
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Basic Statistics
Statistics are not information; statistics are no more than data presented
in a different format. An example of that simple truth is the record of trainer
Bruce Levine from the New York thoroughbred circuit. Some years ago Levine,
then a new arrival to the NYRA scene, brought a stable of highly trained,
well-conditioned horses to Aqueduct. Unlike many trainers who “race horses
into shape,” Levine’s charges were ready to run at first asking. Entries that
had not raced in months, with only mediocre workouts showing in their past
performances, routinely won their first race over the new track.
Knowledgeable New York bettors soon realized that the past performances of
Levine’s entries were useless in predicting performance. Within a few weeks,
Levine’s entries were being bet down to favorite status, based solely on the
fact that Levine had trained them. Trainer records at the time showed this as
an anomaly that created a badly skewed view of reality; “statistically,” Levine
entries going off at odds of greater than 5 to 1 showed a substantial profit
when bet mechanically to win. The implication was that Levine entries going
off at less than 5 to 1 odds were somehow “held back,” or “prevented from
running to their full potential” (a more elegant term than “stiffed”).
Nothing could be further from the truth. The entire “profitable angle”
was based on the first few weeks of Levine’s career at Aqueduct; as soon
as bettors realized the past performances were not useful, they ignored
those records and bet on the basis of the trainer, rather than the entry.
For years afterward, the skewed data was marketed to gullible racing fans
as a “betting angle” that would give them an “insider’s edge” in wagering
at Aqueduct.
The only reason Levine’s entries initially went to post at
unusually high odds was a lack of current information by the bettors at Aqueduct.
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Reprinted with permission from the author
One measure of estimator bias can be found by dividing the actual value by the estimated
value to get a ratio.
The ratio is then subtracted by one to get a percentage error. The calculated value is
called the mean absolute ratio (MAR) and the tracking signal is the running sum
of the forecast ratios divided by the mean absolute ratio.
| A | B | C | D | E | F | G |
|---|
| 1 | Period | Estimate | Actual | (A(t) / E(t)) - 1 | |(A(t) / E(t)) - 1| | MAR |
Tracking
Signal
|
| 2 | 1 | 20 | 15 | = (C2/B2) – 1 | = ABS((C2-B2) – 1) | | |
| 3 | 2 | 18 | 20 | = (C3/B3) – 1 | = ABS((C3/B3) – 1) | = SUM(E2:E3)/A3 | =SUM(D2:D3)/F3 |
| 4 | 3 | 17 | 20 | = (C4/B4) – 1 | = ABS((C4/B4) – 1)) | = SUM(E2:E4)/A4 | = SUM(D2:D4)/F4 |
| 5 | 4 | 10 | 15 | = (C5/B5) – 1 | = ABS((C5/B5) – 1)) | = SUM(E2:E5)/A5 | = SUM(D2:D5)/F5 |
| 6 | 5 | 30 | 11 | = (C6/B6) – 1 | = ABS((C6/B6) – 1)) | = SUM(E2:E6)/A6 | = SUM(D2:D6)/F6 |
| | | | | | | |
| | | | = SUM(D2:D6) | = SUM(E2:E6) | | |
| A | B | C | D | E | F | G |
|---|
| 1 | Period | Estimate E(t) | Actual A(t) | (A(t) / E(t)) - 1 | |(A(t) / E(t)) - 1| | MAR | Tracking Signal |
| 2 | 1 | 20 | 15 | -0.25 | 0.25 | | |
| 3 | 2 | 18 | 20 | 0.11 | 0.11 | 0.18 | -0.77 |
| 4 | 3 | 17 | 20 | 0.18 | 0.18 | 0.18 | 0.21 |
| 5 | 4 | 10 | 15 | 0.50 | 0.50 | 0.26 | 2.07 |
| 6 | 5 | 30 | 11 | -0.63 | 0.63 | 0.33 | -0.29 |
| | | | | | | |
| | | | -0.09575 | 1.670915 | | |
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Reprinted with permission from the author
Sometimes it is necessary to compare the variability of one set of observations
to another set of observations. To do this, it may be necessary to find a
standardized value so that apples are compared to apples and not oranges.
The coefficient of variation is one such value and is determined by taking the
standard deviation and dividing it by the mean (2.92 / 4 = 0.73)
One way to make keep track of estimates is to find the mean absolute deviation (MAD).
Whereas the standard deviation is used when there is an equal chance of under or
overestimating values, the mean absolute deviation (MAD) is used for biased estimates.
To find MAD, which is the average of the absolute values of deviation scores, you can
construct the following table in Excel:
| A | B | C | D | E | F | G |
| 1 | Period | Estimate E(t) | Actual A(t) | A(t) - E(t) | |A(t) - E(t)| | MAD | Tracking Signal |
| 2 | 1 | # | # | = C2-B2 | = ABS(C2-B2) | | |
| 3 | 2 | # | # | = C3-B3 | = ABS(C3-B3) | = SUM(E2:E3)/A3 | = SUM(D2:D3)/F3 |
| 4 | 3 | # | # | = C4-B4 | = ABS(C4-B4) | = SUM(E2:E4)/A4 | = SUM(D2:D4)/F4 |
| 5 | 4 | # | # | = C5-B5 | = ABS(C5-B5) | = SUM(E2:E5)/A5 | = SUM(D2:D5)/F5 |
| 6 | 5 | # | # | = C6-B6 | = ABS(C6-B6) | = SUM(E2:E6)/A6 | = SUM(D2:D6)/F6 |
| | | | | | | |
| | | | = SUM(D2:D6) | = SUM(E2:E6) | | |
Substituting the hash marks with values result in the following table:
| A | B | C | D | E | F | G |
|---|
| 1 | Period | Estimate E(t) | Actual A(t) | A(t) - E(t) | |A(t) - E(t)| | MAD | Tracking Signal |
| 2 | 1 | 20 | 15 | -5 | 5 | | |
| 3 | 2 | 18 | 20 | 2 | 2 | 3.5 | -0.86 |
| 4 | 3 | 17 | 20 | 3 | 3 | 3.33 | 0 |
| 5 | 4 | 10 | 15 | 5 | 5 | 3.75 | 1.33 |
| 6 | 5 | 30 | 11 | -19 | 19 | 6.8 | -2.06 |
| | | | | | | |
| | | | -14 | 34 | | |
Column D is the estimated value, E (t), subtracted from the actual value,
A (t), (15 - 20 = -5, 20-18 = 2, etc.) for each observation.
Column E is the absolute value of each value in column D.
Column F is the mean absolute deviation (MAD) and is found by dividing the running
sum of absolute deviations by the number of observations. MAD can be interpreted
to mean the average absolute error. A smaller MAD is better because it indicates
that the actual value came close to the estimated or forecasted value.
Column G is a tracking signal and is a measure of bias. A lower tracking signal
means that the estimator or forecaster is fairly accurate in predicting values.
A tracking signal that is equal or greater than three is too high and an
experiences estimator should have a much lower tracking signal. Note that
the tracking signal can be either negative or positive.
The goal should be to reduce the average estimation error, or the MAD figure.
In this case, the tracking signal indicates a bias that varies from negative to
positive and from positive to negative. The predicted values are fairly close
for the first four estimates. During the second estimate, the estimator
overestimates the value and then for the third and fourth estimate, the
values are underestimated. For the last estimate, the estimator overestimates
the value.
The greatest bias (over or underestimation) occurs with the fourth and fifth
measurements but the tracking signal is less than three for each of the
estimates so the predictions are fairly accurate.
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Reprinted with permission from the author
One descriptive statistic that is often used in information analysis is the standard
deviation. The standard deviation is a description of variability or how much the
each observation deviates from the average.
To visualize the standard deviation, each measurement or observation can be stacked
up like poker chips with small denomination to the left and larger denomination to
the right. If data is truly random, meaning that each type of observation has an
equal chance of occurring, as the number of observations goes up, the observations
will eventually pile up into a shape that looks like a bell.
This shape is called the bell curve.
The standard deviation is a description of the shape of this curve; the degree to
which the curve is flat or peaked. If you are trying to disprove something, which is the normal
way to go about things in research, to find a large standard deviation is
great. This gives new meaning to the expression: fat chance, doesn't it!
A large standard deviation describes a curve that is wide, more bulbous, and less tall.
In finance, a higher standard deviation may indicate that a particular stock involves
unacceptable risk, as the returns would be highly variable from what is expected of stock
of similar risk.
If you are trying to prove something, you would want to find a small
standard deviation. A small standard deviation means that there is small
variability and the curve is relatively thin, peaked, and tall. This means that
each measurement or guess or estimate does not vary much from the mean or the
expected, predicted value.
To determine the standard deviation: 1) find the mean, 2) subtract the mean from
each observation, 3) square each deviation score found in the previous step, 4) add
each squared deviation score found in the previous step, 5) divide the sum found in
the previous step by the sample size minus one, 6) take the square root of the sum
found in the previous step – voila! There it is.
To find the standard deviation of 3, 6, 8, 2, and 1:
-
Find the mean, which is the sum of all observations divided by the number of observations: 3 + 6 + 8 + 2 + 1 = 20 / 5 = 4
-
Find the deviation scores, which is each observation minus the mean: (3-4) + (6-4) + (8-4) + (2-4) + (1-4) = -1, 2, 4, -2, -3
-
Find the squared deviation scores: (-1 ^2) + (2 ^2) + (4 ^2) + (-2 ^2) + (-3 ^2) = 1, 4, 16, 4, 9
- Add the squared deviation scores together: 1 + 4 + 16 + 4 + 9 = 34
-
Divide the sum of the squared deviation scores by the number of observations minus one: 34 / 4 = 8.5, this number is called the variance.
- Take the square root of the variance: square root of 8.5 is 2.92
| Observation | Sample Data | Deviation score | Deviation score squared |
| 1 | 3 | -1 | 1 |
| 2 | 6 | 2 | 4 |
| 3 | 8 | 4 | 16 |
| 4 | 2 | -2 | 4 |
| 5 | 1 | -3 | 9 |
| Mean: | 20/5=4 | | 34 |
Variance: 34/4 = 8.5
Standard deviation: square root of variance = 2.92
|
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