Great post!  I think most people severely under-estimate luck (or variation in the sim). 

Everytime I have a team that doesn't make the playoffs, I just assume it was poor luck. Of course, when I have a team that wins a bunch, I assume that it is because I'm just awesome. Thats positive thinking!

Bumped up Mr. Boogerlips' recent statistical variance post.  He had virtually the same team over a three-year period and its win total ranged from 81 wins (a mediocre team by most regular season standards) to 99 wins (a pretty good team by most standards).  Leaving aside quality of competition and other "outside" factors, it's interesting that one season probably isn't dispositive in terms of determining whether you have a "good" or "bad" team.

I've noticed that when SIM'ing a couple teams against each other, it takes several hundred games for a reliable pattern to emerge and sometimes the result after 500 games (about the equivalent of three seasons) is quite different than the result after 200 games.        

Statistically if you had a flat 50% chance to win every game, the 95% confidence interval for your team would be 68 to 94 wins.  For a 103 win team the range is 91 to 115 wins. 

By the way, season 3's team -- the 110-game winner -- starts the playoffs Saturday.  We were first in wins (19 more than 2nd place), first in runs (83 more than 2nd place), first in ERA (0.02 better than 2nd place).  Any chance we DON'T get knocked off in the first round? 
 

?You obviously have a better team than your first round opponent although the dead-ball vs live-ball era pitching may even things out a tad.  I think your team wins in 4.   BTW, I checked the numbers* and that seems to be the mostly likely result of a five game series-- that is your team wins in 4 games ~25% of the time.  Of course you still face a 35% chance of losing the series.

*Based on a flat 58.3% chance of you winning each game.

good post, i studied it longer than I should have, but enjoyed reviewing. Thanks.

I'm a bit surprised at the size of the Ragan variance.  Other than that everything looks pretty much like I would expect...

This is a great thread, and should serve as a strong counter argument against the occasional conspiracy theories thrown out about WIS embedding streakiness into the algorithm, or about there being randomly generated "good/bad" versions of a player.  When you control for the external variables that are present in a typical OL, most of the perceived anomalies disappear and the player stats look remarkably consistent, as you would expect from an algorithm that is based purely on the underlying stats and randomly generated probabilities.

Here's another example, from the 3000 Hits Progressive.  The way this league works is that each owner takes a player with 3000 hits and progresses his career.  Each season you use the actual season of your player, but twist his teammates.  I have Palmeiro, so season 1 uses 86 Palmeiro and twists the rest of the 86 Cubs, etc.  Through 9 seasons, Palmeiro is now on his 3rd franchise (Cubs, Rangers, Orioles).  Interestingly, Jamie Moyer was his teammate in real life in 6 of those 9 seasons, and each time I have used the 2002 version of Moyer.  The league is 100M, with DH and average AAA.  Parks stay pretty much the same year to year.  Overall caliber of competition is pretty constant year to year. 

Here's six seasons of 2002 Moyer:

Player	Lg Season	Twist Year	G	GS	CG	SHO	W	L	SV	SVO	IP	H	R	ER	HR	BB	SO	WHIP	ERA
Moyer, Jamie	1986	2002	39	39	0	0	18	10	0	0	242.0	253	114	109	39	39	101	1.21	4.05
Moyer, Jamie	1987	2002	41	39	1	0	16	15	0	0	256.0	262	138	131	37	63	111	1.27	4.61
Moyer, Jamie	1988	2002	37	37	0	0	19	12	0	0	236.0	251	111	109	33	70	112	1.36	4.16
Moyer, Jamie	1989	2002	39	39	1	0	15	17	0	0	253.7	275	130	126	31	57	112	1.31	4.47
Moyer, Jamie	1990	2002	42	40	0	0	10	17	0	0	263.7	298	147	126	41	59	122	1.35	4.30
Moyer, Jamie	1994	2002	43	38	0	0	12	11	0	0	259.7	262	129	124	41	75	132	1.30	4.30
Moyer, Jamie	Total		241	232	2	0	90	82	0	0	1511.0	1601	769	725	222	363	690	1.30	4.32