Saturday, August 11, 2007

"The Chris Allen Basketball League - Recap"

Back in February, I "announced" the creation of a basketball league similar to (but much simpler than) the Chris Allen Football League. And, now, I've finished the season.

First off, a recap of my basketball algorithm:
- Each possession, the probabilities for points were as follows: 52% for 0, 6% for 1, 32% for 2, and 10% for 3.
- Much like in the football league, each team gets a rating depending on how they do each week, and those ratings affect the probabilities for subsequent games. Good ratings increase the chances of two-pointers and decrease the chances for a zero-point posession, and bad ratings do the opposite.
- To increase the complexity a little bit, each team also has a "tempo" that is randomly determined before the season. The length of each game is the average of the two team's tempos.

Early on in the season, I was starting to doubt whether the ratings system was allowing teams to deviate much from the average. I thought there was too much random variability, and so even if a team had a decent ratings advantage going into a game, it wouldn't greatly affect their chances of winning. Well, fortunately, I was wrong. After a full 30-game season, we have distinctly "bad" teams and "good" teams. The best team in the regular season was San Diego (27-3), and the worst two teams were Tucson and Maine (4-26). Those records are skewed enough to one side that the ratings system is clearly self-sustaining. And since every team started at the average, I bet the discrepancy between good and bad will be even higher next season.

Does tempo make a difference in terms of the outcome? Well, a shorter game means the underdog has a greater chance of winning. But in a system where the outcomes determine the ratings themselves (and vice versa on down the line), do the two effects cancel out? In other words, teams with high tempos play longer games, and thus, those games conform to the ratings more. However, teams with high tempos are also less likely to get extreme ratings in a game, so it's harder for them to deviate from the average, and thus, harder to get an "extreme" rating one way or the other. Well, to help and settle this, I determined the correlation between games-away-from-500 (absolute value) and tempo. The result: -0.06, which is hardly an indication of significance. Negative means teams with lower tempos are more likely to deviate from the mean, which I suppose makes sense over the long run, although it is very slight. Maybe next season, since we'll be starting the league out with already-established ratings, we'll see a correlation here.

Perhaps the most interesting thing that happened during the season is that one conference became primarily "offensive", and one conference became primarily "defensive". Teams play more intra-conference games (22) than inter-conference (8) during the season, so it is possible for an entire conference to gain a specific "character". In the last set of games of the season (all intra-divisional games), Western Conference teams averaged 74.9 pts/game, while Eastern Conference teams averaged 59.9 pts/game. That doesn't mean the Western Conference is "better", only that the Eastern Conference games are lower-scoring. In the previous set of games, composed entirely of inter-conference matchups, each conference went 8-8. It's harder for one conference to get "better" than the other, since conferences play against each other, and they beat each other up. But they can certainly bias the ratings towards "offensive" or "defensive".

It's interesting to see how the scores became more varied as the season progressed. Early in the season, you often wouldn't see scores above 90 or below 50. But in the last set of games, there were three scores of 90 or above, and four below 50, including an absolutely dismal 21 points. That's what happens when the worst offense plays the best defense. Yes, as you would expect from the previous paragraph, this was an Eastern Conference game.

Which is better, being offensive, or being defensive? If the ratings are the same, I don't think it makes a difference in the algorithm, because either way affects the expected values of the scores the same. As an underdog, it might be easier to win if the game is offensively-oriented rather than defensively-oriented, but I don't have the math to back that up. Personally, I don't think it matters. The fact of the matter is, the most successful teams this season have a good offense and defense. There is one division winner with a bad offense but an excellent defense, though. And I can't seem to find any teams with a similarly great offense but bad defense that have had a successful season. Hmm...

Now, the playoffs. One thing I'm doing differently in the playoffs than in the football league is that now, the ratings won't change during the playoffs. The ratings you take into the playoffs with you will be the ratings you have for the entire playoffs. In the football league, the ratings changed throughout the playoffs. And since teams were playing other good teams, and thus "beating each other up", even the teams with good ratings had their ratings dwindle as the playoffs went on. And the result was that the team in the weaker conference won the Big Bowl, because it had endured less damage to its ratings. So, instead, ratings are fixed for the duration of the playoffs. (And, it's just easier this way, come next season.)

Now, the season results: Pittsburgh defeated San Diego in the championship series (best-of-three) with a one-point victory in Game 3. I found it exciting, but it's kind of hard to translate a game based on this algorithm into a interesting narrative like I did with the "Big Bowl".

Last Year: "Raleigh Disc Golf, Part 3". This post had 10 comments, some of which actually had to do with disc golf, but most concerning Amber's successful attempt to send me a letter with 39 one-cent stamps on the envelope. (Of course, you'd need 41 now.)

Tomorrow: "Engagements".

Today's random thought:

- Brief scare one morning this week, when my car didn't start. Turns out, it was just the five-year-old battery that needed to be replaced anyway. But any time something like that happens to a car with 158,700 miles on it, I have to wonder, "Is this it?"

1 comment:

Jeff said...

21 points in the Eastern Conference - that's just like the real NBA, whatever that is.