Beating the Mogul Game — An Exercise in Applied Mathematics

I have often wondered about how to rank sports teams.? This goes way back to when I was 10 years old, when I ran across a magazine at summer camp that purported to do this for NFL football.? And so I wondered for many years, looking at similar problems and wondering how a ranking of teams could be generated from a win-loss history.? I finally came to a conclusion when I played the Mogul Game.

The Mogul Game has 148 rich people, and they vary from the super-rich (Gates, Buffett, Ellison) to the not-so-rich (I think they got a kick out of putting Donald Trump at/near the bottom of the list, much as he boasts to Forbes that he is much wealthier than they calculate).

After playing the game idly for a little while, I concluded that if I wanted to win, I would have to capture and analyze data from the game in order to win it.? And so I did, recording who was richer than whom.? I went through four phases:

  • Doing qualitative comparisons when I wasn’t certain of who was richer.? Who had the two parties beaten and lost to?
  • Comparing the trial ranks when the difference was greater than 10.
  • Looking at the highest ranked persons that a given set of contestants had won against, and the lowest ranked that they had lost to.
  • Looking at the average of the highest rank won against and the lowest rank lost to as the best proxy for a contestant’s own rank, unless it violated the results of an actual contest.? In hindsight, I should have adopted that rule much earlier.

It took three days of off-and-on playing to master the game.? Not all that important, but as I mentioned above, the method can be applied with some modifications for ranking sports teams in an unbiased way.? The same could be applied to any competitive activity where there is a win/loss result.? There are two changes for other activities, though.? Games are not necessarily transitive.? Rich person A is richer than B.? B is richer than C.? A will always be richer than C.? In competitions, Team A can beat team B one day, and lose the next.? Also, Team A can beat team B, which can beat Team C, but C can beat A.? So, if I were doing this for baseball teams, my ranks would drive probabilities of one team beating another.

Why would this be necessary when one can simply inspect the win-loss percentages?? Teams with good records may have weak schedules, and this takes account of the strength of the teams played in assessing the strength of a team.? I’m not sure what they do with ranking College Football or Basketball teams, but this would be a more bloodless way of making the comparison.? Granted, it takes a certain number of contests before there is enough density of information to create a ranking, but given a list of wins and losses from an entire season, this method should be capable of ranking an entire league.

I know this is an odd post for me, but I found it to be an interesting project, and it does have other applications.? Thoughts?

6 thoughts on “Beating the Mogul Game — An Exercise in Applied Mathematics

  1. hi David,

    An obvious application would seem to be ranking companies within an industry sector. Would not a fund manager improve their probability of outperformng a benchmark that is not so vetted?

    Just wondering. Interesting stuff. I had no idea you were such a NERD!! hehehe

    Cheers!

    – TomOfTheNorth

  2. David — I took a couple of tries at the game. While I recognize many of the names, guessing the exact level of wealth is akin to asking which of two people, both 200 yards down the road, is a few feet closer.

    Meanwhile, you set the bar pretty high with 80 straight!

    Those of us interested in college football will get to see some of the non-transitivity of results in action.

  3. Another example of someone doing something the complicated way and wasting tons of effort. Did it take you three days of playing to figure out this simple method, or were you just trying to beat the game? If you just wanted to beat the game then why just look up their wealth?

    1. Okay, asdf. I did not spend three whole days at it, but you can prove me wrong by looking up their net worths, and beat my score of 80. Show me how bright you are.

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