the bell curve at work

SOM-ers enjoying mock-complaining (and sometimes really complaining) about bad luck and HAL. For example, on a team I've got now, one player is an inj-1 with 600+ PA ... he got injured 5 times in the first 60 games, and three of them were for 3 games, and 2 of those were in the first inning (meaning, really, an almost-4 game injury).

I don't know how many of you are familiar with the bell curve. It's about statistics. Imagine a bell-shaped curve with a line down the middle. The line goes through the bell's peak, and represents EXACT probability, if the universe were clockwork and all coins were tossed twice simultaneously, and never just once (since if you toss the coin once, you'll get heads either 0% or 100% of the time -- outrageous! ... it should be 50%!). The curve is high near the middle, and very low on the extreme right and left sides. As you move away from the middle, you're looking at standard deviation. A first standard deviation is the margin of error within which you'll be that close to exactly average about 2/3 of the time -- meaning a third of the time, you'll be even further away from "average." The second s.d. margin of error (much wider) is the one you'll be in 95% of the time -- so it's significant if something happens in that 5% outlier zone, suggesting chance alone is not the explanation. But one in a hudred or thousand or million times you'll be way over to the left or right (i.e., something happening much less often or much more often than it does on average). The smaller the sample size, the wider the standard deviation (i.e., weirder results may happen more often, just because you hit that one in a million on the first 5 tries); but the ultimate bell curve is based on a mathematical "infinite" sample size.

I've done a formula for average injuries in a season based on injury rating. But it's only AVERAGE -- the problem is, standard deviation. In other words, there's an average number of injuries and innings missed, but due to s.d. sometimes the guy will have 5 15-game injuries, and sometimes 5 0-game injuries (a roll of "1" gets a 0 game injury, one not even noted because the guy stays in the game). The higher the injury rating, the worse the standard deviation is -- that is, you're gambling. If you're lucky, the inj-6 guy gets a lot of low-number game injuries, and passes the savings on to your roster.

(Random note: my experience suggests that HAL never allows your position roster to go below 9 players; I think there's a maximum number of injured position players you can have at one time, and then there are no more injury rolls until one of the injured guys is back. That's ONLY position guys -- I don't know what the story is with pitchers.)

Anyway, here's an example of the bell curve at work -- a high-injury team, where Sam Fuld (inj-6) nevertheless got a total of at least 528 PA. My formula says that on average, an inj-6 guy playing every healthy day will miss more than 460 innings (I don't remember the exact number, but it's a bit higher). 460 innings is maybe -- what?, 250 PA?

http://onlinegames.strat-o-matic.com/team/1023809

So obviously this was the bell curve at work, with a slight assist from the minimum roster injury "rule." Compare this to the guy mentioned above, who got 5 injuries in 60 games but had a 600+ PA card.

Just something to keep in mind when looking at this relatively small sample sized SOM 162-game universe -- the bell curve rules the world, not just "averages."

(Random note: my experience suggests that HAL never allows your position roster to go below 9 players; I think there's a maximum number of injured position players you can have at one time, and then there are no more injury rolls until one of the injured guys is back. That's ONLY position guys -- I don't know what the story is with pitchers.)

This is not the case. I have played some high injury teams where six position players were hurt simultaneously and starting pitchers have taken the field. It's very rare, but it can happen.

The box scores aren't available anymore, but this was one team I remember from 2003:

http://onlinegames.strat-o-matic.com/team/sim/872815

I recall that Wilson Alvarez played RF and homered, then pitched a shut-out in the next game of the same series.

Crazy.

I first started playing on-line in April 2013, and I figured the injury chances somewhat crudely and then really appreciated clowntimeisover response at the time. I bookmarked that thread.

viewtopic.php?f=5&t=632610

I have used a couple of high injury players quite often, mostly Ortiz and Chisenhall---through 24 plus teams I seem to get more use than I should out of them, with about 15 teams for Ortiz he only missed the 502 PA leaders qualifying 3 times and then by less than 20 AB each--I assume he had over 600 PA on this team (adding in Sac Flies.) I pulled him with a lead for Loney all the time to try to limit the injury chances a little bit more.

http://onlinegames.strat-o-matic.com/team/1110342

This next was one of my early experimental failures with a few High injury types--It didn't work to well trying to cover Longoria and Ortiz with Tracy---but I have seen teams loaded with a lot more high injury guys than this do very well--especially in the PC tournament.

http://onlinegames.strat-o-matic.com/team/1106036

I think Steve F and some others have the right idea that when you use a High injury player you should calculate his average missed games and then spend on his back-up about that amount---if Ortiz is missing 25% on average then spend around 7.37M x .25 on a backup---I like Yonder Alonso or Wallace depending on the park---but Dobbs is a good cheap one. Kotchman seems perfect but just can't provide enough offense if a long injury occurs.

I recall a few of my teams in 2003 where Darren Driefort played the outfield because of injuries...

I remember my 2002 team where Larry Walker played 162 games (injury 3) and S Green only played 140 (injury 1, max 3 game).

Sometimes the good breaks with the bad!

check out freddy galvis

http://onlinegames.strat-o-matic.com/team/1024235

Based on my experience this week with an injury free player (injury free through 140 games, anyway) that is suddenly injured twice, I submit that, although Freddie Galvas played 161 games, his probability of injury (e.g. probability of rolling a 3-5 on his card) rose significantly toward the end of the season as HAL did his darndest to try to get his games missed due to injury inline with actual.

In other words, I think HAL doesn't respect the bell curve and will do his best to get the player injured in the final week or two of the season if his luck up to that point is way above average.