On Wednesday, we published an article by David Goldenberg about “Jeopardy!” great Ken Jennings’s amazing 74-match “Jeopardy!” win streak in 2004, called “Why Ken Jennings’s ‘Jeopardy!’ Streak Is Nearly Impossible To Break.” In it, Goldenberg explains how much of an absurd outlier Jennings is and examines some reasons that Jennings’s performance may be even harder to match than we would guess. This caused The Boss to tweet this comparison to a certain 56-game hitting streak:
Ken Jennings’ streak is as unbreakable as Joe DiMaggio’s. http://t.co/F4wIn818dH
— Nate Silver (@NateSilver538) May 6, 2015
Here at FiveThirtyEight, we love a chance to disagree with the big guy. So let me take this opportunity to dissent: With no disrespect to Jennings, awesome though he is, his record is breakable. Joe DiMaggio’s isn’t.
Don’t get me wrong: Jennings is amazing, and his streak may very well last until the end of time (or at least the end of “Jeopardy!”). Goldenberg’s article has some great detail, like how seemingly minor rule changes about how much practice players get with the buzzer make it a lot harder for someone of Jennings’s caliber to dominate as much as he did. There are a couple of points Goldenberg makes that I would argue against, and a couple of things I think he gets flat wrong, but we can safely accept the gist of it.
So let’s start with The Streak. Er, The Jennings Streak.
First off, let’s be perfectly clear: If a contestant isn’t as talented as Jennings, or nearly so, they’re not going to win 74 games in a row. If someone has a 50 percent chance of winning each game (which would be above average), they’d have about the same chances of winning 74 as they’d have of winning the lottery twice in a row and then dying in a plane crash.16 So the frequency with which a streak like Jennings’s can be created is really a matter of how often someone like Jennings will come along and how often he or she will (or can) win. To help me break this down, I’ve enlisted the help of Alex Jacob, an old friend of mine who was a very successful professional poker player and recently won over $150,000 in a six-game “Jeopardy!” win streak. He applied a gambling-based win-maximization strategy to do it.
Jacob believes Jennings had a “mind-blowing advantage” for a number of reasons, including “his ridiculous knowledge base, his time spent practicing the buzzer and getting used to the pressures of the game, and the massive psychological edge that comes with being the bajillion-game returning champion.” But he also believes the talent pool hasn’t dried up: “There is still plenty of untapped elite ‘Jeopardy!’ talent. I used to live in Las Vegas, where they hold the Trivia Championships of North America, and I’ve competed against some unbelievable players there, guys who have auditioned for the show and are still waiting for a phone call.”
Recall that “Jeopardy!” only started allowing winners to stick around for more than five matches in 2003, and Jennings’ streak came in 2004. At the time, it wasn’t immediately clear whether Jennings was a singular talent or whether the game might be deterministic enough for long streaks like that to be normal. Every year that passes with no one matching or even approaching Jennings’s record makes the former explanation seem likelier — but it has still been only 10 years.
And it’s not even clear that Jennings is the best “Jeopardy!” contestant in the past 15 years: He has been beaten twice by Brad Rutter, who was a five-time champion in 2000 and has never lost a match to a human.17 Counting all his tournament victories, Rutter is now 19-0 in “Jeopardy!” contests, most of which were against tougher competition than Jennings faced. Heck, if he plays enough Masters tournaments,18 Rutter could top Jennings’s win total himself!
Let’s say Rutter is a wild card, but one who’s relevant and establishes that Jennings isn’t unique.19 If we assume that Jennings-quality players come along about once every 10-15 years, how often would they win 74 games?
Here’s where there’s at least a small problem with how Goldenberg calculates Jennings’s odds. He concludes that Jennings got pretty lucky, as he should have only a 21 percent chance of winning 74 games, even given the way he completely dominated play. But this calculation assumes that if Jennings misses Final Jeopardy, the other contestant will get it right about 49 percent of the time, which is how often contestants usually give the right response to the Final Jeopardy questions clue.20 But if Jennings gives the wrong response in Final Jeopardy, the odds of his competition getting it right are likely way below average. This exact situation didn’t happen enough to examine directly, so I instead looked at the last five years of Final Jeopardy: In the 51 percent of cases in which the defending champion replied correctly, each of his or her opponents also answered correctly about 60 percent of the time.21 In the 49 percent of cases where the defending champion had the wrong response, each of his or her opponents got it right just 35 percent of the time. Plugging that back into Goldenberg’s calculation22 for the likelihood of Jennings’ streak, the average streak for Jennings jumps from 47 up to 69 games, with about a 33 percent chance of winning 74. And this average should likely be even higher because Jennings is better than a typical defending champion.
It may seem like just a trivia contest, but there is actually considerable strategy involved in “Jeopardy!,” including how much to bet and which clues to pick. While Jacob declined to go into the details of his strategy since he probably still has matches in his future, he did say that “even the best players can improve their winning chances by making good strategic decisions.” For example, he disagrees with Goldenberg’s conjecture that potential streak-breakers might play for money instead of to win. This bothered me a bit, too: While playing to maximize money may be a good strategy for many, for anyone who has a chance of going on a Jennings-like streak, staying on the show will always be worth much more than whatever could be made in a single game. (Jennings netted over $2.5 million.) In fact, if contestants play to maximize money instead of wins, this could benefit a potential many-win champion — if those contestants are his or her opponents.
Jacob even suggests that the real-life Ken Jennings might have done better if he had employed better strategy:
Ken was pummeling his opponents. With such a mind-blowing advantage, you could make the argument that he should have been betting the minimum on a lot (maybe all) of his daily doubles in the Double Jeopardy round, at which point he was usually on pace to finish with a lock game,23 having amassed a big lead (19-game champion David Madden used this strategy). My gut is that compared to betting the minimum, a correct response probably doesn’t increase Ken’s chances of a lock as much as an incorrect one decreases them.
And, indeed, in the final, doomed game of Jennings’s streak, Jennings lost over $10,000 on Daily Doubles in the Double Jeopardy round. If Jennings had bet the minimum on those, he would have had a lock game going into Final Jeopardy,24 and right now we might be discussing the impossibility of breaking his 148-match win-streak.
So I’m going to make an estimate and say that the odds of a Jennings-quality player — particularly a future version who has digested everything the Internet has to offer about trivia and optimal strategy — may have more like a 50 percent chance of matching Jennings’s streak. That may sound far-fetched, but “Jeopardy!” is fairly deterministic — the best player can win a very high percentage of the time. (It’s more like tennis than golf in that way.) Combine that with our best estimate above, and that means that we should probably expect a Jennings-type streak to come along every 20-30 years.
So let’s return to the original question: How does this compare to DiMaggio’s hitting streak? The odds of that being beaten vary somewhat depending on what assumptions analysts make and how they frame the question. From SABR.org:
There appear to be two points of view about the nature of the DiMaggio streak. The first is that it was a binomial event of extremely low probability but one that actually happened in 1941 — something like actually witnessing the occurrence of 100 straight heads in coin tossing. The second is that it is an example of a superior hitter exceeding even his own normal capabilities.
But here’s what baseball has that “Jeopardy!” doesn’t: a long history. There has been a lot of baseball played in the past 100+ years, and no one has really gotten close to DiMaggio. There have only ever been six hit streaks of 40 or more games, including DiMaggio’s, but let’s charitably assume that 40-game hit streaks can happen about once every 15 years. Further, let’s charitably assume that a batter in the midst of a 40-game streak has an 85 percent chance of getting a hit in each game — this is about the outer edge for a player with a .400 batting average or better who doesn’t walk very often. That would place each mid-streak player’s odds of matching DiMaggio at about 7 percent. So every 15 years, some amazing batter gets a 7 percent chance of getting a 56-game hit streak. That means we would see a streak like DiMaggio’s once every 200 years! All records are meant to be broken, but whoever breaks Jennings’s streak is not just unlikely to see DiMaggio’s streak broken in their own lifetime — it probably won’t even happen in their grandchildren’s lifetimes.