My apologies in advance for the ignorance of this question, but I'm grappling with a basic law of probability. Let's say you draft a decent team that should win 90-100 games in an OL, all other things being equal. But through random chance -- not a particular weakness in the lineup, rotation, ballpark selected or opponents faced -- nearly everyone on the team underperforms and it goes 35-46 in the first half of the season. Unusual, but I've had it happen.

Would probability then dictate that the team will probably go on a tear and overperform during the second half of the season so its performance "evens out" over the course of a full season? Or would the laws of probability dictate that the team should perform exactly as it would ordinarily be expected to perform in the second half of the season? But, in that case, how does the season "average out?"

The same basic question applies if Greg Maddux `95 gets shelled five games in a row or Babe Ruth `27 goes homerless for 20 games. If the laws of probability dictate that things even out over the long run, do opponents have more to fear from a team or a player that has been underperforming and is overdue to "catch up," or should their expectations be exactly the same as usual (all other things being equal)?

If I studied the law of large numbers, I guess I would know the answer -- but then again, if my grandmother had wheels, she'd be a car.

Thanks for your help.

if the results are truly random then his expected peformance in the 2nd half is exactly what it would've been before his slump. seasons don't even out. there can be significant random variation in just one season. If you're expecting to reduce the standard deviation in the "long run", then the long run is 20 seasons or 50 seasons, not one season.

It doesn't work that way. Evening out happens over very large numbers. Way more than 162. If you've got a .577 team, you're likely to play .577 ball the rest of the way. It was rather unlikely you would go 35-46 - but that doesn't make it *more* likely that you'll go 62-19 the rest of the way.

Agree with both posts above. It's important to understand that by "evening out over the long run" that does not mean "performing better than expected so that the overall performance averages out." It means "performing as expected over a long enough period of time that the early performance deviation basically becomes only a very small fraction of the whole."

Example: you flip a fairly balanced coin 10 times and get 2 heads. (20% H).

Over your next 10 flips you expect 5H, 5T so that after 20 you should have 7 total heads (35% H).

Over the next 10 flips you expect 5H, 5T so that after 30 flips you have 12 total heads (40% H).

After 1000 flips you expect to be at 497H, 503T (49.7% heads).

And so on. The "law of large numbers" means that you will slowly approach 50% Heads....if you flip millions of times that early run of 8 tails in 10 flips basically washes out - but not because the coin starts suddenly turning up heads more often.

Maybe it's just the fact that I notice the slumps more, but does anyone else feel like we see a lot more negative streaks (individual and team) than positive streaks lately?

Here's a test. Enter the same exact team in 3 (or more) open leagues and see if they perform better with a different mix of players in each league.

If they perform the same (or worse) in all the leagues, then maybe you just drafted a poor team. It's not uncommon to have players perform below their stats (i.e., especially if you took a HR team or a team that doesn't normalize well)

Thanks for all the posts, especially the post by Contrarian, which made me fully understand the concept for the first time. I'm not always the shiniest penny in the roll, no particular pun intended.

And my team that was 35-46 at the halfway point has now inched its way to 61-61, tending to confirm my suspicion that, over a long enough period of time, this is probably a thoroughly mediocre 90-win team rather than a truly terrible 70-win team. I'm going to follow schwarze's suggestion and enter it in a couple more leagues just to test this thesis, since I'm a glutton for punishment.

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the past is the past

all you know at the halfway point is you will probably end up with 82 wins and miss the playoffs

Here is the other thing to remember... contrarian's post can just as easily be applied to a .570 team (or a biased coin)

A .570 team would be expected to win 57 of every 100 games and about 92 games over a 162-game season.

If you assume that, just like a coin flip, a deviation to the high side is just as likely as the low side. 8 heads are just as likely as 8 tails.

So if 57 wins is the mean and the distribution is even, then 47 wins is just as likely as 67. So if your team was "cold" and played at .470 in the first half, then got "hot" and played at .670 in the second half, the odds of both of those things happening were exactly the same.

For what it's worth I recently had a team go 11-21 in its first 33 games, then 82-48 the rest of the way finishing at 93-69 to win the Div.  That seems actually abnormal to me because for some reason whole teams seem to "slump", or play under expectations, and there doesn't seem to be any rhyme or reason to it.

As I suspected, my Inca Gold team that prompted ths thread wasn't as bad as my 35-46 (.432) first half record indicated.  Since the All-Star break, they have gone 36-21 (.632) and are now 71-67 (.514) overall.  They will most likely finish with between 85 and 90 wins, and they have an outside chance at the wild card.

I'm still convinced that they are neither as bad as their .432 first half start nor as good as their recent .632 performance indicates.  I think they are a decent but unspectacular 90-95 win , 570/.580-ish team.  Contrarian, jfranco and others have been patient enough to explain that an anomalous run of bad luck isn't subsequently counterbalanced by an anomalous run of good luck to even things out.  Over time, the random variations will simply have less effect on the overall W/L percentage and the team will gradually trend closer and closer to what the SIM gods intended from the get go.  Nevertheless, the contrast between the first and seond half numbers is creating the illusion that things are somehow trying to "even out."

I'm definitely going to play this team in a few more open leagues, because now I've gotten obsessed with finding its "true level" of performance.  My commitment may seem a little curious for a team whose upside I only believe to be a 95-win season at best, but I've done stranger things in my life.

On the flip side of the coin, I have a Screaming Liners team that is now 79-35 (.693).  They started the season 7-0, then slumped to a very mediocre 19-20, but since then have rattled off a pretty amazing 60-15 (.800) run.  I don't thnk I've ever seen one of my teams play .800 ball for so long a stretch, and I'm waiting for them to come back to Earth, because they're not nearly that good.

But in their case, the anomaly is easier to explain, because Cy Williams is turning in an outsized 54 HR/152 RBI performance through 114 games at Yankee Stadium III.

I guess in fairness to myself, I should play the "good" team for a few more seasons in other OL's to determine ts "true level" of performance as well.  Just out of curiosity, how many of you play the same team over multiple leagues and keep a record of its overall performance and the variation in individual seasons?  No, nutty, I'm not asking you.

bump^

It's been shown statistically in real sports that there's no such thing as "hot" and "cold" players. That streaks are really just come out of a "random walk" of the numbers. I teach statistics and I still can't get that through my head when I watch sports.

One little correction. If a team should win 57% it turns out that over a given period, winning 47% would have a slightly different probability than winning 67%. See the binomial theorem for confirmation.

Or for a little less mathematically intensive proof. If a team should win 92% of its games, winning 102% would obviously be less likely than winning 82%.

when judging a player statistically there is not hot and cold, but what about mentally when  players do go through streaks where they can see the ball better and get hot.