...the site uses an electronic 1000 sided die to determine it's basic results...presumably because baseball deals in so many 3 digit numbers---.310, .405, .788 etc...

...let's say there is a player who has a .299 AVG and no walks and there are no other effects in the game to alter his AVG....to get a hit all he has to have is a "die roll " between 1-299 and he has a hit...he has 299 successful hit numbers out of the 1000 possible numbers...

...let's say that in SIM play he achieves exactly 700 PA which for him would be 700 ABs...there is a very, very small chance he will get 700 different die rolls in his 700 PAs...there is a very, very, very minute chance that all 700 will be above 299...in which case he'll bat .000...

...no alteration to his stats, no introduction of streaks, no being cursed by hateful programmers, just incredilby bad "luck"....

...and the SIM is much more complicated than that simple example...sometimes his "target" number will be 250, sometimes 400...and there is no telling when he'll get a die roll of 325...if he gets it when the target is 250, he's out...if he gets it when the target is 400, he has a hit...

Good post John.

In various volumes Bill James has done simulations of massive numbers of "seasons" worth of performance for a single player, using career average numbers.

With nothing like the SIM's level of complexity - just random results from a number of independent trials with fixed probabilities - he demonstrates just how dramatically performance across a season's-worth of plate appearances can vary.

When you compound that with all the variables the SIM takes into account in altering those probabilities for any given PA (park, fatigue, quality of opposing pitcher, L/R pitcher, quality of range in the defense, etc) one can very easily expect extreme fluctuations in performance with no additional variation programmed in.

Not to be contrary to, uh, contrarian, but the SIM isn't complex at all. In fact, it distills baseball stats and yearly trends into fairly simple calculations for each pitch and each AB and each game situation.

Now, given that each pitch and each AB is the result of these fairly simple, but long formulae is remarkable, but hardly complex.

In fact, the misnamed Log5 doesn't use logarithmic functions at all. It's merely a multiplicative function comparing yearly league stats and individual stats. If it really used logarithms and imaginary numbers and integrals and string theory.... now THAT would be complex.

...i'm not sure why he called it "log5"...it's certainly very bayesian and logs are often applied to odds ratio formulas to give more understandable results...perhaps there is something essentially log5ish about it...

.299 Hitter with no walks and 700 PA's-A fascinating player

He would produce a standard deviation of 1 80% of the time. The standard deviation would be equal to 7%. So if the .299 hitter hit between .280 and .320 with th same 700 PA's, he would be 1 of the 80% to fall within the 1 standard deviation group. Is that right?

Most of us have experienced the kind of weird variation that John's example invokes.

On my current teams, the same Bobby Abreu is playing on two very similar teams, both in $80m leagues in RFK Stadium.

One of them has 174 PA, 3 HR, 15 RBI, a .215 BA and .322 OBP.
The other one is 113 PA, 4 HR, 22 RBI, a .337 BA and .398 OBP.

Given the same talent and similar context, the rest is just luck.

What drives must of us stir crazy is when bad luck sticks to one player -- or one lineup spot or roster position -- and won't go away.

I've used both Sandy Koufax and Joe Wood in their best years in the same rotation spot on one high-cap team that is in first place just barely. If either Sandy or Joe came anywhere close to expectations, the team would have a sizeable lead. Instead, Koufax went 2-7 and Wood is 1-8. Two other Joe Wood '12 iterations on other teams in the league are 7-5 and 7-7.

And then I get to wondering how much luck is involved in real life: when Barry Zito can't live up to his high-value contract or when a Walt Dropo comes along and has one sensational season and then falls into mediocrity. Luck in the form of random outcomes must be more of a factor in the sim than in life, but I wonder if luck isn't a much larger factor in real life than most of us are accustomed to thinking that it is.

Quote: Originally Posted By outbacker on 5/14/2008
.299 Hitter with no walks and 700 PA's-A fascinating player

He would produce a standard deviation of 1 80% of the time. The standard deviation would be equal to 7%. So if the .299 hitter hit between .280 and .320 with th same 700 PA's, he would be 1 of the 80% to fall within the 1 standard deviation group. Is that right?

yeah outbacker that would be true if the league you played in were identical to the league the player played in real life. Open leagues surely aren't identical to MLB competition and theme leagues are often high cap which provide much better than average pitching. Therefore, it is hard to estimate where one standard deviation would fall.

My 1 Standard Deviation is only a guess on my part. And this only takes into account the .299 Hitter with 700 PA's and without any Pitching factors. Without, any kind of Mathamatical foundation, I'm certainly at a distinct disadvantage in trying to establish, any kind of intelligent discussion relevant to the .299 Hitter with 700 PA's. Netherless I consider this to be a fascinating and important topic.

There's just so much luck that goes into it. Taking the .299 hitter as an example, here's what a typical "hot" streak might look like (log5 of actual hitter/pitcher matchup and then the number rolled):

260/240
320/310
290/260
230/540 (hit)
300/600 (hit)
200/140
300/280
300/700 (hit)
200/150
320/295
300/170
400/390
360/280
250/380 (hit)
220/670 (hit)

that's 5 hits in 14 at-bats or .357

Quote: Originally Posted By outbacker on 5/14/2008
.299 Hitter with no walks and 700 PA's-A fascinating player

He would produce a standard deviation of 1 80% of the time. The standard deviation would be equal to 7%. So if the .299 hitter hit between .280 and .320 with th same 700 PA's, he would be 1 of the 80% to fall within the 1 standard deviation group. Is that right?

The standard deviation of the batting averages of players with 700 PA who hit .299 is .017. Discounting all other forms of variation (park, pitcher), due to random variation alone, 68% of hitters would hit between .282 and .316, 95% would hit between .264 and .334, and 99.7% would hit between .247 and .351. So there is quite a bit of variation even though all players have a .299 chance of getting a hit each time. Couple this with differences in parks, pitchers, league quality, salary cap, extemes on both ends are bound to occur.

Thank you

And then I get to wondering how much luck is involved in real life: when Barry Zito can't live up to his high-value contract or when a Walt Dropo comes along and has one sensational season and then falls into mediocrity. Luck in the form of random outcomes must be more of a factor in the sim than in life, but I wonder if luck isn't a much larger factor in real life than most of us are accustomed to thinking that it is.

...while "luck" is almost certainly a greater fact in a computer simulation than real life, i really agree with your last sentence...i think one of the keys to long term careers as a player, manager and gm is the equanamity that comes from realizing how much luck plays a role in the relative short term...

these are the sorts of threads i love, as a guy who teaches statistics to undergrads. i can't weigh in at work, really, but i can't wait to see what else has been said by the time i get home!

The book Baseball Between the Numbers by the crew at BP looks at some of this stuff...I'd highly recommend it for those into statistics (baseball statistics and "real" statsistics as well!), which is probably about 80% of the users on this site...

...a great book, from chapter 1-3:

"Protection is overrated. There's no evidence that having a superior batter behind another batter provides the initial batter with better pitches to hit; or if it does, those batters see no improvement in performance. Additionally, it's very rare that a situation arises in which run expectation actually drops after the pitching team walks the batter at the plate. Therefore, if the pitching team does walk a batter because it would rather pitch to the following man, it is almost alwaysmaking a mistake by opening the door to a big inning."

"Sorting a lineup in descending order of OBP yields the most runs, but players with a high SLG can offset a low OBP as early as third in the lineup."

"Intentionally walking a batter in a correctly ordered lineup is nearly always a bad decision."

...now my own opinion is that such analysis based upon computer modelling is somewhat overstated in dealing with real life situations, but we are actually playing in a computer model here on WIS...also, that particular model ignores base running ability and the possible propensity of some hitters to hit into DPs more than others, but it's interesting stuff and offers a good starting point for some WIS managerial decision making...