The DoT Matrix -- What's Makes for a Good Player?

Note: The Tournament of Champions started last night. There was a mix-up with the DVD, so I haven't seen the episode yet, but from what I've read the numbers I'm about to throw at you stood up pretty well for one game. We'll see how they do against actual tournament results.

The Jeopardy Tournament of Champions is a two-week tournament during which the thirteen player with the most wins during the regular season return to Culver City to crown a season-long champion. The winner takes home $250,000 and -- perhaps more importantly -- glory.

Predicting a winner has always proven difficult, since so much of the outcome depends on factors that are essentially random (or at least beyond the player's control). Player match-ups, which players see which boards, how they're feeling that day, other players' luck. all factor into determining a winner.

But while there are obstacles to prediction, there are numbers available to help us determine going in which players will need to catch the most breaks to win, and which ones have the tools to make a deep run (mostly) regardless of luck.

Aside from random chance, there are four factors that determine Jeopardy success. In no particular order, you have to 1) know stuff, 2) be good at buzzing, 3) be able to handle difficult material, and 4) know how to wager.

Smarter people than me have hashed out most of what you'd want to know about #4, and I suspect most TOC-level players have spent at least some time playing with the J-Archive wagering calculator. So I'll just look at the first three in the next few posts.

Factor #1 -- Know Stuff

How much does a given Jeopardy player know? We've already established back in Post #1 the baseline level for an average player: 35.56 clues per 60 revealed. But TOC players are anything but average. You don't get to the TOC unless you excel in one or more of the Four Factors. Luck is a big part of the game, but it can't turn a lump of coal into Watson.

So to find out how much a given Jeopardy champ knows, we ask the same questions we asked in Establishing a Baseline. How many Triple Stumpers were there in games involving this champ? And how does that compare with games involving three "average" players? In essence, we want to know how much better the group did as a result of having this player on the "team."

At this point, I have to point out that coming up with useful numbers requires a much larger sample size than just one game. For the purposes of the DoT Matrix, I am only assessing players who saw at least five games worth of material and played against at least ten opponents. That means the DoT Matrix cannot tell us who was the best player to lose to Ken Jennings (much as I might like to know where I rank in that list).

First we use the average knowledge level to determine what percentage of clues an average player can't answer. Our sample gives us a number ("team average," or TA) around 40%. Then we make the same calculation for games involving a given champion. For instance, a 5+-day champ might reduce the "team" average from 40% to 30% (let's call this CA, for "champ average). We then figure out how much credit to give to the champion for the improvement in team performance, as follows:

Answers known per 60 clues faced = (1 - (CA ^ 3 / TA ^ 2) ) * 60

In our example, a champ that posts a CA of 30% in an environment that typically yields a TA of 40% probably knows 50 answers per 60 clues.

So how does this year's field stack up? Here are the rankings based solely on knowledge displayed in regular season play:

Roger 51.85
Joon 50.28
Mark 50.24
Tom K 49.26
Justin 47.19
Jay 44.84
John 43.92
Christopher 43.01
Tom N 41.98
Brian 41.19
Kara 33.36
Buddy 32.31
Paul 31.97

Notice that Erin and Charles aren't in these rankings because they only played 4 games, and both were tournament champions facing specially-written tournament clues. Also, curiously, the TOC alternate Sara would have been fifth in these rankings (48.97) if she were in the field.

But like on GI Joe, knowing is only half the battle.

NEXT: The Force is Strong with This One -- Assessing the Battle of the Buzzers