Single Season Replays

[rowech]

I know the replay results of a single season won't be as accurate as say strat-o-matic. However, has anyone played single season replays enough to see how things end up?

[Amaroq]

There was a thread complaining about it at one point - the poster was basically arguing that after some large number of unattended replays of the same season, he was seeing the 'real' division winners win their division again only 50% of the time, so only one World Series in 4 had the correct matchup.

I actually thought that sounded about right. [:D]

[risk_doc]

A variety of things go into the won-lost record that are random in this game such as player streaks (I have noticed that Puresim models the hot and cold spells for players quite accurately, even my 100-100-80 third baseman will go through streaks of several games without a hit).  Another key factor is injuries.  Also, the AI manager may use players differently that they were actually used during a season.  Also, I have noticed that when I replay a replay league, the player ratings aren't always the same from replay to replay.  This is probably due to a random deviation that is programmed into the scouting function.  Also, weather and stadiums (are they using the right stadiums for the team and year?) can also have a major impact upon player and team results.
 
When all is said and done (and all of the random factors are added together), there is quite alot of variation that can occur from season to season in Puresim (and also in real life baseball).  Now, as a statistician, the question does come up as to whether the central limit theorem (ie., the sample mean converges to the true mean as the sample size becomes quite large) applies if enough sample seasons are run.  The answer to this question is yes.  However, the mean result will not likely match up to the actual season result since the actual season would represent just one sample from the distribution and there is a small probability that it would exactly match the mean.
 
Sorry for the statistics lecture.  If you were wondering, I have a Ph.D. in economics from Iowa State University with a field in econometrics / statistics.  One of my research (and consulting) specialties is the application of Monte Carlo simulation to problems in risk management.  Thus my internet moniker, "risk_doc".

[PadresFan104]

lol... Monte Carlo simulation was something I had to know about for my PMP certification...

[risk_doc]

Monte Carlo is becoming more mainstream now that there are a variety of Excel add-ins, such as @Risk and Crystal Ball, that can do it. Also, it is much easier to apply than the probability calculus and set theory that I had in graduate school.

[rowech]

I'm a high school math teacher so it doesn't bother me any.  Just wondered if anyone thought stats came out decently, records decently, etc.  I know it won't come out perfect but I worry it won't come out even close. 

[risk_doc]

Depends upon how much of a "statistical outlier" was the actual season that was played. Did the most talented team win it all or was there a variety of random factors (weather, injuries, etc.) that contributed to the eventual results. Also, Prosim does allow you to replicate general manager styles, but does is there enough error in the AI manager versus the real manager to cause a divergence in results?

In sports, the most talented team does not always win the championship. However, the central limit theorem would suggest that after a large number of simulated seasons, the average results should show the most talented team (on paper) coming out on top most of the time.

For example, the 1985 Royals were not even close in terms of being the most talented team on paper; however, due to a variety of circumstances (team chemistry, luck, Dick Howser, George Brett's incredible performance in the playoffs, Don Denkinger) they won the World Series. If you simulate that season several times, you will probably find that the Royals won't win the AL West the majority of the time. The California Angels were probably the most talented team in the division (as proved out during the following season).

The beauty of team sports is the intangibles that go into the results. A game that faithfully recreated each and every actual season's results would be a very dull game to play in my honest opinion. The beauty of Puresim, is that each time you resimulate even a single season (say 1985 for example), it is a whole new ballgame. Sure, there will be teams that don't have much of a chance (i.e., the '85 Pirates) but each season is a new start with the potential for new results.