What is Jeopardy! ?:
A Graphical Exploration from 1984-2009
Jason Crowley, Brenna Curley, and Dave Osthus
Introduction
Jeopardy! has been a popular television game show for many years. The web site J! Archive,
found at www.j-archive.com, contains a wealth of information about this TV quiz show from as
far back as 1984, its first season, until the present. From this web site, we extracted data about
each contestant — information ranging from their winnings each round to state of residence. Excluded from the data are any tournaments or specialty games such as Celebrity Jeopardy! which
we consider to be a different population of interest. In the process of extracting the data, many
inconsistencies were discovered, both due to rule changes over the years as well as irregularities
within the J! Archive web site.
Using the extracted data, we graphically explore a player’s performance both within and across
games. Various plots will illustrate shifts in a player’s place within a game, as well as the effect of
the Final Jeopardy! question on a player’s winning margin. The relationship between consecutive
games played and final winnings is also explored. Linking the data with U.S. Census measurements,
we explore the proportional representation of states on Jeopardy! to see if any states or regions are
outliers with respect to population or time. Lastly, we single out one particular outlier by the name
of Ken Jennings, who won 74 games in a row — by far the longest winning streak in Jeopardy!
history.
Jeopardy! Game Play
The trivia game show Jeopardy!, hosted by Alex Trebek, is played by three contestants over three
different rounds. The clues are actually the answers, so the contestants must give their responses
in the form of a question. The Jeopardy! game board consists of six categories each with five clues.
After the host finishes reading a clue, contestants may buzz in. The first to do so has five seconds
to respond. If a contestant answers correctly, the dollar value of the clue is added to their score,
and they get to choose the next clue — a doubly advantageous result. If they answer incorrectly,
this dollar value is subtracted off their score and the other contestants have a chance to answer. In
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the event that no one answers correctly, the last person with a correct response chooses the next clue.
The first round is the Jeopardy! round. From 1984-2001, clues ranged in dollar value from
$100 to $500. Then from 2001-present they were doubled to range from $200-$1000. In the Double
Jeopardy! round, as the name suggests, clues double in value. So from 1984-2001, clues ranged
from $200-$1000 and then from 2001-present they ranged from $400-$2000. As Figure 1 verifies,
the change to double all the values happened during season 18 — specifically on show #3966, which
was broadcast on November 26, 2001.
During these first two rounds, there are hidden clues called Daily Doubles — one in the Jeopardy!
round and two in the Double Jeopardy! round. If a contestant selects these clues, they get to wager
a dollar amount up to as much as their current total or $1,000, whichever is greater. After wagering,
only they are given the chance to answer.
Average Final Winnings by Season
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Figure 1: Starting in season 18, a jump in average final winnings occurs due to the doubling of the
clue values.
At the end of the show is the Final Jeopardy! round which consists of just one question. To
make it to this round, a contestant must have positive winnings after the Double Jeopardy! round;
if they have $0 or less they cannot participate. For the Final Jeopardy! question contestants are
told the category and have the commercial break to place their wager, ranging from $0 to their
current score. Upon returning, they then have 30 seconds to write down their response once the
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clue is revealed.
The winner after Final Jeopardy! is invited to return to play on the following show as the
returning champion. In the case of a tie, all first place players are invited to return. Before
2003 contestants were only able to return for a maximum of five games. However, starting at the
beginning of season 20, this limit was dropped and contestants are now allowed to return until
defeated.
Maximum Winning Streak by Season
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Figure 2: The maximum winning streak in seasons 20 and 21 are both attributed to Ken Jennings.
Figure 2 illustrates this point. We see a large jump in the maximum number of shows a
contestant was on Jeopardy! with season 20. In fact, this jump was due to a contestant who holds
the record for the longest game winning streak in Jeopardy! history (see The Ken Jennings Effect
section for more information).
Collecting and Cleaning the Data
Before any analysis can be done, data must be available and in a manageable form. This
proved to be the major roadblock in our attempt to graphically explore the intricacies of Jeopardy!. All of the data we could possibly want was available to us on the J! Archive web site.
Unfortunately, it is in a form more suitable to a web browser than a data miner. J! Archive is
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set up in a format such that each show has its own web site, and the user can basically “relive”
the game’s experience. To pull out the needed information off of J! Archive, we wrote a function,
‘jscrape,’ utilizing the XML library in R. This arsenal of functions has the ability to parse the HTML
code of a web site, and allows the programmer to extract data from a given table(s). For more
information about how we pulled the data, as well as how to do it yourself, see our R code at
www.public.iastate.edu/∼jcrowley/chance/CHANCESubmissionRCode.R.
Show ID vs. Player ID
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Figure 3: The departures from the linear trend can be explained by repeat contestants, including
Jeff Kirby who is represented by the enlarged point at approximately (5750, 1600). He is the only
known contestant to return to the show without permission.
One inconsistency with this data set is missing episodes. This is illustrated by Figure 3 which
plots Show ID versus Player ID, a variable we created that uniquely identifies every contestant.
Small gaps can be explained by our omission of Jeopardy! tournaments, which we decided were not
in our target population of shows. For instance, there was a very large tournament around show
#4750. While it appears we have almost all episodes from recent seasons, the coverage before show
#2750 is much more scattered. This is most likely due to the web site developers’ continued efforts
to enter historical shows, or diminished access to early episodes.
Another interesting oddity we see from Figure 3 is the points that stray from the strong linear
relationship present in the plot. After isolating these cases, we looked up these rogue contestants
on J! Archive and in almost every case these outliers were caused by players who were invited back
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to the show due to losses on “poorly worded” or “ambiguous” Final Jeopardy! questions. There are
relatively few of these repeat contestants because it is against the rules for a player to return to
Jeopardy! unless they are invited back. Interestingly enough, according to J! Archive, one of the
outliers — Jeff Kirby on Show #5766, the enlarged point — was a repeat contestant who had not
been invited back. This explains why the horizontal distance of his point from the line is much
larger than the rest of the stray points. Most of the time, contestants who were invited back due
to unfair losses had their second show(s) relatively soon after their original one(s). Jeff returned
for his second show approximately 10 years after his first appearance. He was disqualified from his
winnings after the producers of the show learned of this rule-breaking.
Unadjusted Winnings by Season
Adjusted Winnings by Season
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Figure 4: After adjusting for the rule change which doubled clue values, no discernable trend can
be seen in average winnings over time.
Besides Player ID, we created a number of other variables to help in our analysis of Jeopardy!.
Among these are proportion of questions correct, proportion of Daily Doubles correct, total questions answered and the place each contestant is in at the end of each round. Using these variables,
we are able to further delve into trends within games, as well as possible shifts in player performance over time and space. We also created another variable that adjusts round winnings for the
rule change we outlined in the previous section, where the question dollar amounts were doubled in
Season 18. Figure 4 shows the actual average winnings by season, as well as the average adjusted
winnings by season. We can see that, after adjusting for the doubling of clue dollar amounts, there
5
is little to no trend over time. Since we have fewer episodes available in earlier seasons, represented
by the size of the points, we can see there is more variability in average winnings — a finding in
line with the Central Limit Theorem. After this point, all analysis will be done using adjusted
winnings in order to better compare results across all seasons.
Trends Within the Game
In our graphical analysis of this Jeopardy! data, we explore three main questions related to
trends within the game.
1. How do contestants’ places change throughout the game?
2. Under what conditions does a lead change occur as a result of Final Jeopardy!?
3. Is there a trend between times on show and average final winnings?
How do contestants’ places change throughout the game?
In order to gauge game dynamics, we track players’ places after the Jeopardy!, Double Jeopardy!, and Final Jeopardy! rounds. In Figure 5, we examine the number of players in 1st, 2nd,
and 3rd place at the end of the game faceted by their place after the first round (across the top)
and their place after the second round (down the side). We also shade the bars by the number
of changes that occurred in a player’s place throughout the game. For example, a contestant who
went from 1st to 2nd to 1st place would be considered to have a change of two whereas someone
who went from 1st to 3rd to 1st would be considered to have a change of four. Overall we see that
players tend to stay in whichever place they were in after the 1st round, as shown by the darker
bars being larger than the lighter ones. As expected, the rarest path, albeit not an impossibility,
for a player to take is from 1st to 3rd to 1st place or from 3rd to 1st to 3rd. From a numerical
standpoint, knowing a contestant’s place after the Jeopardy! and Double Jeopardy! rounds both
have predictive value of the contestant’s final place, though to differing degrees. For instance, if a
contestant is in first place at the end of the Jeopardy! round, 56.8% of the time they end up in
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first place after Final Jeopardy!. If a contestant is in first place after the Double Jeopardy! round,
however, they end up in first place 74.1% of the time — an appreciable increase. Likewise, similar
patterns exist for both second and third place.
Tracking Contestant Places Throughout Game
1st after first round
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Figure 5: Players tend to remain in the same place throughout all rounds, as indicated by the
darkest bars.
Under what conditions does a lead change occur as a result of Final Jeopardy!?
In addition to seeing how players’ ranks change throughout the game, we look at the winning
margin between the first and second place players both after the Double Jeopardy! and Final
Jeopardy! rounds. This way the only difference is due to the Final Jeopardy! question. In addition, Figure 6 is faceted on two characteristics: whether or not a lead change occurs due to
Final Jeopardy! and whether or not the first place contestant has a significant lead going in to
Final Jeopardy!. A significant lead is defined as the first place contestant having at least double
the winnings of the second place contestant, thus guaranteeing victory barring any foolish wagering.
Examining Figure 6, we see that lead changes typically occur when the winning margin before
the Final Jeopardy! question is under $10,000. This makes sense, because if a contestant has a
significant lead, they should know to wager only what they can afford without dropping out of
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Winning Margin and Lead Change
Lead change does occur
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Figure 6: Lead changes do not occur in games with a significant winning margin after Double
Jeopardy!
first place. In fact, we see from the absence of points in the bottom right plot of Figure 6 that
no contestants with a significant lead going in to Final Jeopardy! in our dataset have lost their game.
The number of points between the lead change and no lead change plots suggest that the lead
usually stays the same after the Final Jeopardy! question. Therefore, if a contestant is in first place
after the Double Jeopardy! round, they are more likely to stay in that position than not after the
Final Jeopardy! question — a finding congruent with the previous section.
Is there a trend between times on show and average final winnings?
As mentioned earlier, once a contestant has won a game of Jeopardy! they are invited to return
on the following show. Do these more experienced players tend to win more money? To examine
this, we look at the relationship between the number of times each player has been on the show
and their average final winnings. We expect average winnings to increase with number of times on
show. The box plots in Figure 7 illustrate a general increasing trend in final winnings as we look
at players who have been on the show more and more times — confirming our belief. The many
outliers for players who were only on the show once suggest that there were some high-scoring,
presumably close games. We also note that only one person played as many as 9, 10, 20, and 75
games. However, recalling that players were not allowed to continue past five games until 2003,
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perhaps these results would differ if there had never been a limit on the number of games a contestant could play.
Average Final Winnings vs. Show Duration
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Number of Appearances
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Figure 7: There is a positive relationship between number of appearances on show and players’
average final winnings.
Spatial Trends
In our graphical analysis of this Jeopardy! data, we explore three main questions related to
spatial trends.
1. Has the geographical distribution of contestants changed over time?
2. Are some states over or under represented?
3. Do certain states earn more winnings, on average, than others?
Has the geographical distribution of contestants changed over time?
Jeopardy! has been on the air since 1984 and has always been shot and produced in Southern
California. In fact, when the show first began, the only way one could qualify for Jeopardy! was
by auditioning at their California location. These rules changed as the show gained in popularity.
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After Jeopardy! ’s second season, the show started sending out people to different areas of the country to increase the show’s qualification accessibility. Later on, Jeopardy! developed the Brain Bus,
a traveling testing station where one can qualify for the show. Now, hopeful contestants can take
the compulsory 10 question pre-test online, which has virtually no geographic bounds. With this
change over time, we would expect to see the geographic diversity of contestants increase as well.
To test out this hypothesis, we examine the spatial distribution of the first and last 250 games of
Jeopardy! in our dataset.
Number of Contestants First 250 Games
Number of Contestants Last 250 Games
Number
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Figure 8: Eight states are unrepresented in the first 250 games, while only three are in the last 250
games. The states in white are unrepresented.
As Figure 8 shows, there does appear to be a level of spatial dependency over time. During the
first 250 games, there were eight states that had no representation whatsoever, and approximately
20% of all contestants were from California. When looking at the last 250 games, we see an appreciable difference. Only three states were unrepresented and California made up less than 10% of the
total contestants. Though not proven, it is likely these changes are due to Jeopardy! ’s structural
and technological changes made throughout their history, as well as its increased popularity over
time.
Are some states over or under represented?
Looking at the two graphs in Figure 8 leads one to ask the question, “Are some states, such as
California and New York over represented on Jeopardy! ?” California and New York are the first and
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third most populous states in the United States, respectively. Thus, if all U.S. citizens are equally
likely to make it onto Jeopardy!, we would expect California and New York to have the first and
third most contestants, again, respectively. To explore this question, we standardize the data to the
population of individual states. Thus, we can create an expected count of contestants from each
state based on the percentage of the U.S. population who live in that state, and multiplying that
number by 4880, the total number of Jeopardy! contestants in the dataset. We divide the actual
number of contestants by the expected number. If greater than one, the state is over represented.
If less than one, the state is under represented.
Proportional Representation?
Over Represented
Under Represented
Figure 9: The Northeast, West Coast, Illinois, and Georgia are over represented.
As Figure 9 shows, there is a clear spatial trend. The Northeast, West Coast, Illinois, and
Georgia are over represented, while the rest of the country is under represented. To give an idea
of the range we are dealing with, North Dakota is the most under represented state with Utah not
far behind. If all states were equally represented, based on their 2000 population measurement,
North Dakota should have had 11 Jeopardy! contestants, but only one North Dakotan has graced
Jeopardy! ’s stage. On the flip side, Washington, DC is the most over represented part of the
country. Only nine people from Washington, DC were expected to have appeared on Jeopardy!
thus far, but in actuality, 99 have made it on the show — an eleven-fold difference! When looking
at the rest of the map, it is quite obvious that there are two regions of the country that have higher
representation than expected. The question, then, is why? As mentioned earlier, there has always
11
been a testing site in California. Thus, qualifying for the show has historically been much more
accessible to the West Coast. When Jeopardy! implemented their traveling testing center, though
not confirmed, it seems like New York City or somewhere else in the highly populated Northeast
would be a logical first place to go. Another possibility is that the intellectual makeup of the United
States is not uniform. It is possible that people more likely to qualify for Jeopardy! tend to inhabit
the Northeast due to the jobs, schools, and lifestyles offered by that region.
Do certain states earn more winnings, on average, than others?
State
Average Winnings by State
utah
north dakota
kentucky
arizona
ohio
vermont
kansas
delaware
south dakota
d.c.
montana
missouri
connecticut
new hampshire
new jersey
texas
iowa
illinois
washington
california
new york
maine
wisconsin
idaho
maryland
minnesota
virginia
massachusetts
wyoming
tennessee
florida
michigan
colorado
west virginia
georgia
arkansas
louisiana
hawaii
north carolina
pennsylvania
indiana
south carolina
alaska
oklahoma
nevada
rhode island
nebraska
oregon
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mississippi
alabama
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Figure 10: Utah and North Dakota have significantly higher average winnings than other states.
To answer this question, we examine a scatter plot of average final winnings for each state.
From Figure 10, we see that most states have average winnings that are at least in the same neigh12
borhood of one another — between $7,500 - $12,500. Thus, most states do not earn significantly
different amounts than others. There are two states, however, that earn significantly more than
all other states — North Dakota and Utah. As mentioned earlier, there has only been one person
from North Dakota on Jeopardy!, and though he did well, he did not do well enough to win his
game. Thus, North Dakota has such high earnings due to its small representation and commendable
performance. Utah, on the other hand, has been represented in 86 different shows. Thus, small
representation size is not the reason for their success. Instead, they have a much more interesting
cause to their intriguing status. That cause goes by the name of Ken Jennings and is such an
anomaly, he deserves his own section.
The Ken Jennings Effect
Ken Jennings is arguably as famous as Alex Trebek. His name is synonymous with trivia, and
more specifically, winning Jeopardy!. Ken holds the record for the longest winning streak on Jeopardy! with 74 games. This streak blows the competition out of the water, as can be seen in Figure
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Distribution of Number of Appearances
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Figure 11: Ken Jennings appeared on 75 consecutive shows, while the next closest person appeared
on 20 consecutive shows.
In our exploration, we hope to not just identify the greatest Jeopardy! player of all time, but
also take a deeper look into how he was able to put together such an incredible streak. One metric
that sheds light onto his success is the average number of questions answered correctly each game.
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This metric is very important because it works on two levels. One is that a correct answer adds
money to the contestant’s total. The other is that it takes away an opportunity for opponents to
add that money to their total.
Average Number of Questions Answered Correctly
Margin of Victory for Games Ken Jennings Did and Didn't Play
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Games without Ken Jennings
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Player ID
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Margin of Victory ($)
Figure 12: In the left panel, Ken Jennings, the largest point, answered more questions correctly on
average than any other contestant. In the right panel, Ken Jennings’ average margin of victory is
larger than typical.
Figure 12 (left) shows that Ken Jennings answered, on average, just over 35 questions correctly
each game. There are at most 60 questions asked on Jeopardy! every game. Thus, on average, the
other two contestants had to split the other 25 questions. As can be seen, Ken’s average is higher
than any player in Jeopardy! history.
If Ken Jennings answers significantly more questions than his opponents, it would make sense
that his margin of victory would also be significantly different than the other Jeopardy! contestants. To win 74 games in a row, it is unreasonable to believe that every game, or even many games,
came down to the wire. Thus, the next avenue we explore is Ken’s margin of victory compared to
games at large. Figure 12 (right) confirms that Ken’s average margin of victory ($26,011) is indeed
much higher than the average margin of victory in games without Ken ($9,209) — a nearly $17,000
14
difference. Thus, much of Ken Jennings’ success is due to the fact that he did not just beat his
opponents, he destroyed them.
As one can see, Ken Jennings has forever changed the landscape of Jeopardy! and will forever
be the bar to which all subsequent Jeopardy! contestants are measured.
Conclusion
Throughout this exploration of the game show Jeopardy!, many game-related assumptions were
verified graphically. We showed in Figure 5 that often a contestant’s place after Double Jeopardy!
indicates their place after Final Jeopardy!. Figure 6 then shows that games in which lead changes
occur due to the results of the final question are typically games that are relatively close after
Double Jeopardy!. Looking at Jeopardy! in a more geographical sense, we found that becoming a
contestant on Jeopardy! increases in accessibility over time as a result of Jeopardy! ’s attempt to
diversify their contestant demographic. Though geographic diversity has grown, there are still areas
of the United States that are over represented on the show, namely California and the Northeast.
Finally, we showed that not all Jeopardy! contestants are made equal with the analysis of Ken
Jennings. It was not luck that caused Mr. Jennings’ success, but a propensity to accumulate large
leads before the Final Jeopardy! question.
The real tool that makes all this further exploration possible is the compilation of Jeopardy!
data into a rich, clean format. Just as the game of Jeopardy! has become more accessible to the
masses, so has the exploration and analysis of the game. For access to our data and code, please
visit www.public.iastate.edu/∼jcrowley/chance.
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