I will try and update the standings once per week. During the early part of the season, I'll just list the current projected win totals. Once we get deeper into the season, I'll project playoff spots and overall totals...

(Note that the projected wins takes into account number of games in each league. So two teams with an identical .548 current winning% might be projected to have a slightly different number of total wins due to how the current wins are distributed)

Based on projected wins in each league, here are the spreads between max wins and min wins, by league.

60M: 92
80M: 70
90M: 67
100M: 42
120M: 65
200M: 97

Obviously, these numbers will most likely decrease since it's doubtful some of these 4-16, 5-15 teams will end up with 120 losses. A similarly for the 16-4 and 15-5 teams.

Even looking at all the teams in each league, here is the standard deviation between wins...

60M: 22.5
80M: 16.5
90M: 20.2
100M: 12.2
120M: 18.4
200M: 21.8

The 60M and 200M themes are seeing the most variance. It's amazing to see such variance in a league (200M) where we all have similar players.

Quote: Originally Posted By schwarze on 12/03/2009The 60M and 200M themes are seeing the most variance. It's amazing to see such variance in a league (200M) where we all have similar players.

Although its not my field, I'm fascinated by the concept of randomness and probability in all aspects of life. I've done a lot of reading on the subject (at least for a layperson) and I'm convinced that most people don't fully understand how much variation there can be in a system where the only variable is randomness. I suspect that you would see similar variations in a league consisting of identical teams with identical lineups, managerial settings and pitcher designations with all management decisions made by the WIS computer.

Hmmm, sounds like a potential theme league idea.

Well, it is my field, and while you could figure out all the probabilities and distributions analytically, it's also a super easy problem to simulate.

When playing WiS, similar questions come up often, in my mind at least. Take thejuice6's tournaments, where the exact same team might play in two or more rounds of a tournament and have a vast change of fortune from one round to the next. Or simply wondering how pumped up you should be about winning 100 games, or how bummed about losing 100.

Anyway, I've thought about it a lot, but with it coming up in this thread I've finally been motivated to write a simulation. Took all of about 10 minutes to write and a minute to run 1000 simulated seasons.
(It took longer to type up the results!)

24 teams playing a standard WiS season--every game a 50/50 proposition:

Mean number of wins in best record: 93.75
Mean number of losses in worst record: 93.58

(This is actually symmetric, of course. The difference here is sampling 1000. More are needed for a more exact answer.

Mean range between most and least wins: 25.33
Mean standard deviation: 6.45

(schwarze -- is the standard deviation you reported above for *projected* wins?)

Maximum number of wins: 104 (3 times)
Maximum number of losses: 105 (4 times)
Number of "leagues" with at least one 100-game winner: 47 (4.7%)
Number of "leagues" with at least one 100-game loser: 43 (4.3%)
(these are actually symmetric, as well)

Number of "leagues" with both 100-game winner and 100-game loser: 1

So, what else do you want to know?

Quote: Originally Posted By sgsmith on 12/03/2009
(schwarze -- is the standard deviation you reported above for *projected* wins?)

Yes

Good stuff sgsmith...

I still think it would be cool to run a hands-off theme league.

Here's one I've always been curious about: what's the average record for each place within a 4-team division in a 50/50 league. Here it is:

1st - 87.8
2nd - 83.0
3rd - 79.0
4th - 74.2

Overall, a little more than two-thirds of divisions were won with fewer than 90 wins.

My sense is that in our actual leagues, that happens far less often than two-thirds of the time, so we can comfort ourselves that we're measuring skill to some degree -- we're not just flipping coins here.

Of course, the existence of owners who have played 85,000 games and won 56% of them is sufficient evidence of that!

Do we get a link this time around?

No. They've never done a link for round 2.

Oh ok, shows how often I've been there! LOL