Friday, April 18, 2008

More Fun with Sports and Probability- How Important are Matchups?

Previously, I used Tecmo Super Bowl III to demonstrate that 1 game cannot tell you who the better team is. Replaying from the beginning 50 times is better.
Since then, I've been trying to find a basketball game for the SNES that we could learn interesting things from about real-life sports. However, none of the SNES games keep track of the stats that I would need.

Before the NCAA tournament, several websites used Monte Carlo simulators to simulate the tourny 10,000 times using different types of data. The Monte Carlo predictions were highly accurate this season as the favorite teams romped. However, none of them gave results of particular matchups. For instance, most gave a good chance to Davidson of making the Elite 8. But, they gave a better chance to Georgetown. What I would be more interested in knowing is this:
If Georgetown had a 55% chance of beating Davidson then, in all the simulations in which Davidson won, how did they fare against simulated opponents in the next round? Which opponents did they do the best against?

Because, I might have picked Davidson in my bracket to upset Georgetown in the 2nd round if I knew the odds of Davidson also beating their possible 3rd round opponents were pretty good. Matchups matter.

I have found that Tecmo Super NBA Basketball is useful to examine probabilities of outcomes in the playoffs, and see how seeding/matchups work out. (*Disclaimer* Nothing in this post took me more than an hour to do, so don't be concerned about how I'm wasting my time ).

The game uses data from the '91-92 seasons. I simulated the season and got these standings:

Golden State and Portland have dominant records, with the Bulls not far behind. Here are the brackets:
The top seeds in the West were Golden State and Portland. In the East they were Chicago and Cleveland. It takes about 10 seconds to simulate the playoffs on the emulator (the computer only gives game scores, not stats for these games. It does compile individual stats as the season progresses but not a full box score). So, in my make believe Monte Carlo simulator, this is how it turned out in 30 simulations:

Championships won:
Portland- 10 times
Golden State - 7
Chicago - 4
Phoenix - 2
Detroit - 2
Lakers, Utah, San Antonio, Cleveland, and Indiana all had 1 apiece.

Golden State is an interesting case for matchup issues. They had the NBA's best record but don't win the majority of championships. Why?

In the simulation, Golden State wins the title 23.3% of the time. The win their first round series 27 of 30 times, but get upset in the 2nd round 50% of the time.

The majority of their 2nd round matchups are against the Lakers (who advance to the second round 2/3 of the time). The Lakers win their 2nd round matchup 14 of 20 times (70%).

So, Golden State is a very good team relative to other teams in the league, but the Lakers match up well against them and beat Golden State more than Golden State beats them.

Another example is Utah. Utah only gets out of the 1st round in just 3 of the 30 simulations. However, in one of those simulations it wins the championship! Utah beats Portland in 1 of 3 (33%) series. This might suggest that Utah matches up better against a Portland team than a better San Antonio team which loses to Portland 26 of 30 times (87%).

So, matchups matter. Golden State has a tougher 2nd round matchup, so it struggles to live up to its seeding. It wins 11 of the 12 series in which it gets past the 2nd round, indicating it's better on average than most teams but not the Lakers.
Utah has a tough 2nd round matchup, but if it could just get past San Antonio it might upset Portland fairly often.

These are the things I think about.

1 comment:

JTapp said...

I should have also noted that Portland and Chicago never failed to advance to the 2nd round. Those were the only series that never saw an upset.