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© IEEE - 11th International Conference on Computational Intelligence and Communication Networks (CICN 2019)
Dense Neural Network used to Amplify the
Forecasting Accuracy of real-time Human Swarms
Gregg Willcox
Unanimous AI
San Francisco, CA, USA
Gregg@Unanimous.ai
Louis Rosenberg
Unanimous AI
San Francisco, CA, USA
Louis@Unanimous.ai
Rory Donovan
Unanimous AI
San Francisco, CA, USA
Rory@Unanimous.ai
Hans Schumann
Unanimous AI
San Francisco, CA, USA
Hans@Unanimous.ai
Abstract— Artificial Swarm Intelligence (ASI) is a hybrid AI
technology that enables distributed human groups to “think
together” in real-time systems modeled on natural swarms.
Prior research has shown that by forming “human swarms,”
networked groups can substantially amplify their combined
intelligence and produce significantly more accurate forecasts
than traditional methods. The present study explores whether
the rich behavioral data collected during “swarming” can be
used to further increase the accuracy of swarm-based forecasts.
To do this, a dense neural network was used to process the data
collected during a set of swarm-based forecasts and generate a
Conviction Index (CI) for each forecast that estimates its
expected accuracy. This method was then tested in an authentic
forecasting task – wagering on sporting events against the Vegas
odds. Specifically, groups of sports fans, working as real-time
swarms, were tasked with predicting the outcome of 238 NBA
games over 25 consecutive weeks. As a baseline, the swarms
achieved an impressive 25% net return on investment (ROI)
against the Vegas Odds. This was compared to an enhanced
method that used Conviction Index to (a) estimate the strength
of each forecast and then (b) wager only on forecasts of sufficient
strength. The CI-selected wagers yielded a 57% net ROI against
Vegas Odds. This is a significant gain, equivalent to more than
doubling the ROI of the naïve swarm betting strategy.
Keywords— Swarm Intelligence, Artificial Swarm
Intelligence, Collective Intelligence, Human Swarming, Artificial
Intelligence, Collaborative Intelligence, Machine Learning,
Sports Forecasting, Wisdom of Crowds.
I. INTRODUCTION
The technology of Artificial Swarm Intelligence (ASI) has
been shown to amplify the predictive accuracy of networked
human groups across a variety of tasks [1-6]. Prior studies
have shown that real-time “human swarms” can produce more
accurate forecasts than traditional “Wisdom of Crowd”
methods such as votes, polls, surveys, and markets.
For example, a 2015 study tested the ability of human
swarms to forecast the outcome of NCAA college football
games against Vegas betting markets. A swarm of 75 average
sports fans was tasked with predicting a set of 10 college bowl
games. As individual forecasters, the participants averaged
50% accuracy when predicting game outcomes against the
Vegas spread. When forecasting together as real-time human
swarms, those same participants achieved 70% accuracy
against the Vegas spread [2].
Similar performance increases have been found in other
studies, including a five-week study that tasked human
participants with predicting a set of 50 soccer matches in the
English Premier League. Results showed a 31% increase in
accuracy when participants worked in swarms [4]. Human
swarms were also shown to outperform Vegas betting markets
in a 20-week study that involved predicting the outcome of
200 National Hockey League games. By using ASI
technology, human swarms were shown to reduce the
expected error rate by 61% on a subset of games [6].
While prior studies have documented the ability of
artificial human swarms to amplify the predictive ability of
human populations and outperform individual forecasters,
statistical aggregations from large crowds of forecasters,
computer models, and largescale betting markets, no formal
study has studied the estimation of expected accuracy of
swarm forecasts with machine learning. Such a machine
learning model would allow deeper insights into human
swarm behavior, paving the way for the optimization of ASI
systems and the widespread application of swarm-based
forecasting to diverse problems, such as financial,
geopolitical, or sports forecasting.
To address this, the current study develops a machine
learning model that processes the behavioral data from human
swarms, generates a Conviction Index (CI) that reflects the
expected accuracy of the swarm, and predicts the expected
ROI of placing a bet on the game against a largescale betting
market (i.e. the published Vegas odds). The study then pits the
machine learning model against Vegas, computing financial
returns for theoretical bets placed against the real-world odds
and payouts in a full season of the National Basketball
Association (NBA). The model’s betting success against
Vegas is compared to a naïve model of betting on all games.
The present study considered 25 consecutive weeks of NBA
games, requiring human swarms to forecast between six and
eleven games per week, for a total of 238 games predicted.
The study is organized as follows: in Section II, we
introduce the concept of “human swarming" and discuss
biological basis for optimized swarm-based decision-making.
In Section III, a cloud-based technology platform for real-time
human swarming (swarm.ai) is introduced, and examples of
swarms are provided. In Section IV the experimental
methodology behind this forecasting study is described.
Finally, the results of the study are analyzed in Section V.
II. SWARMS AS INTELLIGENT SYSTEMS
Given a population in which each individual has a unique
set of information about the world, how do we best combine
their perspectives and reach an optimal solution? Researchers
have been trying to solve this problem for centuries using
techniques that are now commonly referred to as harnessing
the “Wisdom of Crowds” or simply crowdsourcing [7,8,9].
These methods generally involve taking votes, conducting
polls, collecting surveys, or running information markets.
Most crowd-based methods capture input from each human
participant in isolation (or near isolation) from other members
and then combine the data from the full set of members
through statistical aggregation, either over time or post-hoc.
In other words, these “crowds” are not actually groups of
people interacting freely as real-time collaborative systems,
but instead are statistical constructs for mathematical analysis.
Mother Nature has been working on methods to harness
the diverse perspectives of populations, having explored this
issue across many millions of years of biological evolution.
The successful solutions that evolved in nature do not involve
taking votes, conducting polls, collecting surveys or running
prediction markets – they involve forming dynamic systems
in which the full population is enabled interact in real-time and
converge together on optimal solutions. Biologists refer to this
phenomenon as Swarm Intelligence. It’s one of the primary
reasons why birds flock, fish school, and bees swarm – they’re
able to combine their insights in optimal ways, becoming
significantly smarter together than alone.
The most researched form of Swarm Intelligence in nature
is the honeybee swarm. Studied since the 1950s, the decision-
making abilities of honeybee swarms have been shown to be
very similar to the decision-making processes in neurological
brains [10,11]. Both employ large populations of simple
excitable units (i.e., bees and neurons) that work in unison to
integrate noisy information about the world, weigh competing
alternatives, and converge on unified decisions in real-time
synchrony. In both brains and swarms, outcomes are arrived
at through a competition among sub-populations of excitable
units. When one sub-population exceeds threshold support,
the corresponding alternative is chosen. In honeybees, this
enables the large colonies to converge on optimal decisions to
highly complex problems such as selecting an optimal home
location from among a large set of alternatives [12,13,14].
III. ENABLING “HUMAN SWARMS”
Unlike birds, bees and fish, we humans have not evolved
the natural ability amplify our combined intelligence by
forming real-time swarms. That’s because we lack the subtle
connections that other organisms use to form feedback loops
among members. Schooling fish detect vibrations in the water
around them. Flying birds detect motions propagating through
the flock. Swarming bees use complex body vibrations called
a “waggle dance.” To enable real-time swarming among
groups of networked people, specialized user interfaces and
algorithms are required to close the loop among all members.
To address this need, a software platform called swarm.ai
was developed to enable human groups to link online as real-
time synchronous systems, connecting from anywhere in the
world [15-18]. Modeled on the decision-making process
employed by honeybee swarms, the system allows groups of
distributed users to work in parallel to (a) integrate noisy
evidence, (b) weigh competing alternatives, and (c) converge
on in synchrony on optimized solution, all while allowing
participants to react to the changing system in real-time,
thereby closing a feedback loop around the full population.
As shown in Figure 3, the software used in this study
enables human swarms to answer questions by collaboratively
moving a graphical pointer depicted as a glass puck. Answers
are reached when the swarm moves the puck from the center
of the screen to one of set of answer options. Each participant
provides input by manipulating a graphical magnet with a
mouse or touchscreen. By positioning their magnet with
respect to the moving puck, participants impart their personal
intent on the swarm as a whole. The input from each user is
not a discrete vote, but a stream of vectors that varies freely
over time, enabling the swarm to move, not based on the input
of any individual, but based on the dynamics of the full
system. In this way, the group to explores the decision-space
and converges on the most agreeable solution in synchrony.
It is important to note that participants do not only vary the
direction of intent, but also modulate the magnitude of intent
by adjusting the distance between their magnet and the puck.
Because the puck is in continuous motion across the decision-
space, users need to continually move their magnet so that it
stays close to the puck’s outer rim. This is significant, for it
requires participants to be engaged continuously throughout
the decision process, evaluating and re-evaluating their intent
as they convey their contribution. If they stop adjusting their
magnet with respect to the changing position of the puck, the
distance grows and their applied sentiment wanes.
Fig. 3. A human swarm answering a question in real-time
Thus, like bees vibrating their bodies to express sentiment
in a biological swarm, or neurons firing to express conviction
within a biological neural-network, the human participants in
an artificial swarm must continuously update their intent
during the ongoing decision process or lose influence. In
addition, intelligence algorithms monitor the behaviors of all
swarm members in real-time, inferring their implied
conviction based upon their relative motions over time.
IV. SWARM CONVICTION STUDY
To assess whether the behavioral patterns within the
deliberation data from human swarms can be used to estimate
the expected accuracy of forecasts, a formal study was
conducted using groups of randomly selected human subjects
from a pool of self-reported NBA enthusiasts. Each weekly
group consisted of 28 to 43 participants, all of whom logged
in remotely to the Swarm system. Each subject was paid $4.00
for their participation in each weekly session, which required
them to predict of the outcome of all of the basketball games
being played that night, first as (a) individuals on a standard
online survey, and then (b) as part of a real-time swarm
comprised of the full population.
Across the 25-week period, predictions were generated by
for between six and eleven games per week for a total of 213
games. For each game, participants were required to work
together as an ASI system to forecast the winner of each game,
and converge on their collective level of confidence in this
forecast (“Low Confidence” or “High Confidence”).
Participants were then asked to predict, by working together
as a swarm, how much the team they picked would win by on
a scale from “1” to “15+” points.
Figure 4 shows a snapshot of a human swarm comprised
of 32 participants in the process of predicting the outcome of
a typical NBA game: Washington vs San Antonio. As shown,
four options are provided to choose from, enabling the swarm
to identify which team will win, as well as express a level of
confidence in that outcome. Participants are not voting, but
behaving – continuously expressing their views in real-time.
The Swarm AI system processes the participants’ behaviors
and controls the motion of the full system. The confidence
indicator is helpful as it causes the swarm to split into multiple
different factions and then converge over time on a single
solution that maximizes their collective confidence and
conviction. It’s important to note that Figure 4 shows a
snapshot of the swarm as it moves over time towards a final
answer. The full process of converging upon a solution
generally required between 10 and 30 seconds of real-time
interaction within the swarm.
Fig. 4. Human Swarm in the process of forecasting NHL game
To estimate the relative expected accuracy for each
forecast generated by the ASI system, a dense neural network
(the Swarm Conviction Estimator) was trained using the
behavioral deliberation data captured during each swarm and
used that data to predict the probability that the swarm’s
forecast was correct. This behavioral deliberation data
includes (i) the percentage of users pulling for each target
sampled at various times throughout the swarm, (ii) the total
number of users in the swarm, and (iii) the time the swarm
took to converge on a forecast, among other behavioral
indicators.
The network is trained using the time-varying behavioral
deliberation data from a historical database of 424 swarm
predictions of NFL and NHL games. The range of reasonable
probabilities for each sport differs greatly (e.g. the distribution
of Vegas Odds for NHL is much narrower than the same
distribution for NFL), so the network’s outputted probabilistic
forecast cannot be considered a calibrated probability for a
given sport, but rather a relative measure of the swarm’s
conviction in the chosen outcome. Each relative conviction,
referred to as a Conviction Index (CI), can therefore be used
in a single sport, such as NBA, to rank forecasts from lowest
to highest expected accuracy.
To validate the accuracy and precision of the Swarm
Conviction Estimator in a real-world environment, the
conviction scores were compared to Vegas Odds, and
simulated bets were placed on the outcomes of games. To
decide which games to bet on, an ROI Estimator was
developed to predict the expected ROI of betting on the
swarm’s chosen outcome based on the CI and Vegas odds of
the match. The Vegas Odds were sourced from Sportsbook, a
widely-used online bookie. This ROI Estimator is a random
forest that was trained on a database of 243 swarm NHL and
181 swarm NFL forecasts, each of which had an associated CI
and Vegas Odds.
When the expected ROI from the ROI Estimator is
positive (>0%), betting on the chosen outcome is expected to
be profitable. Games were selected from the pool of NBA
games each week using one of four strategies: (a) betting on
the swarm’s pick in all games, (b) betting on the swarm’s pick
in all games with a positive expected ROI, (c) betting on the
swarm’s pick in all games with an expected ROI above 10%,
and (d) betting on the swarm’s pick in all games with an
expected ROI above 20%. These strategies were designed to
simulate progressively more aggressive betting strategies,
from betting on all games to betting on only a select few games
that are expected to return a significant payout.
The experimental simulations started with a mock wager
pool of $100, and a betting rule directing that a total of 15%
of the gambling pool would be bet each week, regardless of
the games selected to bet on that week. The expected ROI for
betting on each of the swarm’s forecasted outcomes was
calculated using the Swarm Conviction Estimator and the ROI
Estimator, as shown in Figure 5. Simulated bets were placed
each week on each strategy’s selected games, and the
simulated return on the investment was calculated given the
outcome of the bet (win / loss) and the Vegas Odds. The net
return on investment was then added to that strategy’s
gambling pool for the next week.
Fig. 5. System Diagram of ROI Estimation from Human Swarm
Behavior and Vegas Odds
V. RESULTS
The results of the experiment are discussed in two parts.
First, the accuracy and betting performance of the human
swarms over all games is discussed and compared to the
Vegas Odds. Next, the accuracy and betting performance of
the CI-selection methods are discussed and compared to the
uninformed all swarm picks method. To assess whether
human swarms were able to more accurately forecast all NBA
outcomes than Vegas, the swarm’s raw forecasts for all games
each week were compared against the Vegas Odds for the
corresponding game for each of the 25 weeks of the testing
period. Vegas’ expected win rate for these selected games was
calculated as the average Vegas Odds over all games that the
swarm selected as Pick of the Week. Figure 6 shows the
distribution of Vegas Odds for the selected games, and Vegas’
expected win rate: 66.5%. The swarm, on the other hand, had
a win rate of 71.8% across these same games. This is a
valuable improvement, equivalent to outperforming Vegas’
expectations by more than 5%.
Fig 6. Vegas vs Swarm accuracy across all games predicted
To examine the significance of this result, the average
accuracy of each system over the full season was bootstrapped
10,000 times. The average accuracies for each trial are shown
in Figure 7. We find that the probability that the swarm had a
higher win rate than Vegas Odds due to chance was low
(p=.0306), so we can be confident that these swarms were able
to predict the outcome of games with higher accuracy than
Vegas Odds.
Fig 7. Bootstrapped average accuracy for Vegas vs all Swarm picks
In addition, a betting simulation was run for each
prediction set in which 15% of the current bankroll was
distributed evenly among bets on each of the swarm’s
predictions that week. The performance of this model when
betting against Vegas (and including the Bookie’s cut) is seen
in Figure 8. Starting with $100 and investing each week
according to this strategy, the net balance after 25 weeks
would be $124.74, or an ROI of 24.7%.
A bootstrapped simulation was performed to estimate a
90% confidence interval around this result, where 10,000
simulated seasons were generated by randomly selecting with
replacement among the games that were seen each week. We
find that the 90% confidence interval over the ROI of this
betting strategy is [-7.48%, 61.69%], indicating that we are not
confident that betting on all swarm picks would return a
positive ROI (p=0.112).
Fig 8. Cumulative simulated betting performance of fixed
bets on all games predicted
So, while the swarm was significantly more accurate at
predicting outcomes than Vegas Odds, we cannot be confident
that betting on the swarm outcomes would return a positive
ROI. Two factors could have contributed to this difference: (a)
Vegas Odds includes a 2-5% “Bookie’s Cut” in all outcomes
to allow sportsbooks to make money, impacting the ROI
simulation, but averaged out for the Accuracy analysis, and
(b) the compounding nature of the simulation’s bankroll
increases the variability of the success of this betting strategy
relative to Vegas Odds.
To assess whether the behavioral patterns in these swarms
could be used to precisely forecast the outcome of games, we
next compared the performance of CI-selection methods to the
performance of Vegas Odds over the selected games. To do
so, the Expected ROI of each of the 238 games was calculated
using the Swarm Conviction Estimator and ROI Estimation
machine learning programs. The Expected ROI of each game
was used to determine if the game should be bet upon. Three
strategies for betting on these values are compared: (1) betting
on all games with an expected positive ROI, (2) betting on
games with an expected ROI above 10%, and (3) betting on
games with an expected ROI above 20%. Of the total 238
games, these betting strategies selected 202, 137 and 92 games
to bet on respectively.
The accuracy and ROI from these selections of games,
referred to as the CI-selected games, was compared against the
accuracy and ROI from betting on swarm picks over all
games. The simulated performance of all models when
betting against Vegas (including the impact of the Bookie’s
cut) is shown in Figure 9. In these simulations, the higher the
expected ROI cutoff of the betting strategy, the higher the
season-end ROI. The strategy with the highest ROI was the
CI-selected 20%+ method, which returned a 56.6% ROI over
the 25-week season.
Fig 9. Cumulative simulated betting performance of all vs. CI-
selected games at various thresholds
The final ROI of each method is shown in Table 1. To
assess whether this amplification of ROI is significant
compared to the all-swarm-picks method, the season-end ROI
of each selection method were compared over 10,000
bootstrapped season simulations. The CI-selection methods
were found to frequently outperform the all-swarm-picks
method over a full simulated season (up to 77% of the time),
but not frequently enough to be confident that the CI-selection
methods were outperforming the all-picks method due to
random chance (p=0.23).
The probability that each of these methods returned a
positive ROI due to random chance was calculated over these
10,000 bootstrapped seasons as shown in Table 2. Notably, the
20% CI-Selected games generated a positive return on
investment 89.11% of the time, meaning that this betting
strategy had roughly an impressive 9 in 10 chance of ending
the season with a financial gain.
Selection Method
ROI (end
of season)
Probability of
Outperforming
All Swarm Picks
Probability
of Positive
ROI
All Swarm Picks
(238 games)
24.7%
-
88.80%
Expected ROI > 0%
(202 games)
29.5%
0.3304
88.87%
Expected ROI >
10%
(137 games)
39.5%
0.3059
87.55%
Expected ROI >
20%
(92 games)
56.6%
0.2330
89.11%
Table 1. Simulated betting performance of all vs. CI-selected games
at various thresholds
To investigate why the ROI can be doubled as compared
to the All Swarm Picks method, but statistical significance
was not found, the bootstrapped season-end ROI histogram
was plotted in Figure 10. The variance of the bootstrapped
ROI of the most aggressive strategy (Expected ROI > 20%)
was high in comparison to the All Swarm Picks method, likely
because of the small sample size of the method: it selected
only 40% of games to bet on.
Fig 10. Bootstrapped average accuracy of all swarm picks vs CI-selected
picks (expected ROI > 20%)
As games were selected with high expected ROI, the
simulation ROI increased. This suggests that the Swarm
Conviction Estimator and ROI Estimation programs are
translating the swarm behavior into an accurate relative
ranking system that can be used to select games where the
Vegas Odds are inaccurate, and a positive ROI can be
expected. These programs can, in turn, be used to bet on
games and improve the ROI of the Swarm Intelligence system.
VI. CONCLUSIONS
Can the unique deliberation behaviors captured from live
human participants during real-time swarm-based forecasts be
analyzed to assess the likelihood of forecast accuracy?
Furthermore, can such an assessment be used to identify the
strongest forecasts among a set of forecasts (e.g. the best bets
against the Vegas odds)? The results of this study suggest
strongly this may be the case. As demonstrated across 25
consecutive weeks of forecasting the 2017-2018 NBA season,
a machine learning program, configured to analyze the real-
time behavioral characteristics of swarms of approximately 35
typical sports fans, was able to both select outcomes of the
games more accurately and outperform the betting success of
the swarm itself. In fact, although both swarm-based methods
were able to outperform the Vegas betting market at predicting
the outcome of select games each week, the machine learning
program more than doubled the ROI of the unaided swarm’s
betting strategy and did so without training on any NBA data.
It’s important to note that this study was limited by the
availability of training and testing data: only one season of
each of the three sports in this study was available for training,
and only one sport was used for testing. Future work with
more extensive historical datasets may enable even more
accurate results. Additionally, the games covered in this study
were not forecast probabilistically, due to the lack of suitable
data to perfectly calibrate the Conviction Indexes to NBA.
Future work aims to generate probabilistic forecasts. In
addition, future work will investigate the success of behavioral
swarm analysis in different settings, will strive to improve to
optimize the CI for general and calibrated settings, and will
refine the method in which bets are placed to allow for more
sophisticated betting mechanisms (i.e. using the Kelly
Criteria), as we believe there remains substantial room for
improvement when optimizing a wagering strategy against
Vegas Odds based on swarm-based predictive intelligence.
ACKNOWLEDGMENT
Thanks to Chris Hornbostel and David Baltaxe for their
efforts in coordinating the weekly sessions that generated
NBA basketball predictions. Also, thanks to Unanimous AI
for the use of the swarm.ai platform for this ongoing work.
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