What are the odds of this?

Stephen Drew who has an injury on a 1, has been injured THREE TIMES already in his first 27 plate appearances.

https://onlinegames.strat-o-matic.com/team/1500837

What are the odds of a 1 in 216 chance happening 3 times in just 27 opportunities?

Simple math says it should happen 3 times for every 648 plate appearances. But as we all know there is nothing hidden in the game engine and certainly no bugs or flaws.

I had something similar happen in the computer game, playing at home. Lost Don Buford in a 60s replay twice in 3 appearances at start of season. Didn’t happen again, but it was a big pan early on.

Are the odds 512:1?


My calculation: 1/27 / (1/216) * 1/27 / (1/216) * 1/27 /(1/216)
The odds are 1:1 if he is injured once in 216 plate appearances: 1/216 divided by (1/216), so, that's how I came up with my calculation, by dividing what happened by what is expected to happen.


The odds of some event, any event, happening three times in 12.5 % of the standard sampling size (27 compared to 216) instead of the expected .125 times would not be impossible, although it's unclear what the event might be.

The problem with this specific event is that sufficient volume of chances has not been reached. Any dice roll resulting in this player's injury may have a 1/216 chance, but, statistical analysis does not predict when that dice roll will occur.

If he has 621 more plate appearances without an injury, then HAL is vindicated (perhaps).

But, I've heard there is something in the game engine that increases the risk of injury for a player who comes back too soon because of his competitive nature of wanting to play before fully healed. I don't believe it, but, there you go.

The odds of this occurring is one in 3,333 rounds about

The odds of this occurring is one in 3,333 rounds about

Thanks Charlie. I knew you'd put a pencil to it.

Amazingly there's another team in the same league who had Joe DiMaggio hurt 3 times in I think he said 11 plate appearances. Something crazy going on in that league if you ask me.

The odds of this occurring is one in 3,333 rounds about

But that's NOT the odds of it happening to YOU. That's the odds of it happening to ANYBODY in all of the games that are being run! (assuming this math is correct)

Way back when, I was using Arky Vaughn's 10M card a lot. I was curious about how many games he was playing (and missing) for each season, so I decided to count them for each season. Arky has an injury on the 1 with under 600 PA. I found that over the 13 seasons that I examined, Arky played a total of 1947 games, or an average of 148.8 per season.

In those 13 seasons, he twice played in 162 games and he played 161 and 160 once each. OTOH, he also played in as few as 134, 138 & 139 games. This doesn't directly speak to the original question, and we talking about a substantial but not gigantic sample. Still, what comes home to me is that random chance might allow for a fairly wide variation in the games played by a given card from season to season. (Note: I didn't track the number of injuries, just the total games played, and I certainly was playing Arky in any game where he was available.)

My personal belief is that while 3 injuries to a single player in 27 plate appearances is a lot--and would have a low chance of happening for any given player in any give season. But if we consider the volume of games played in SOM by multiple teams and multiple players, such results are far from impossible. Similar things have certainly happened to my players over the 200+ SOM seasons I've played in. But I've also seen a lot of players with an injury on the 1 go injury free.

Looking at a single recently completed 100M season as a sample, I found that this season had produced a total of 68,502 AB + 7167 BB + 419 SAC bunts. That's a total of 76,088 plate appearances in a single league. Such numbers seem fairly typical. A lot of unlikely things can happen, and probably will happen to one player or another, over that many PAs even in a single season.

For those who are interested, here's the count I did for Arky's games.

134 gms 90 wins /champs

161 gms 97 wins /semis

147 gms 88 wins /semis

139 gms 104 wins /champs

138 gms 95 wins /semis

147 gms 89 wins /finals

162 gms 79 wins

148 gms 80 wins

160 gms 96 wins / champs

157 gms 99 wins /finals

150 gms 104 wins / semis

142 gms 85 wins

162 gms 83 wins / champs

As in most things of this nature, in the land of HAL, the chance is 100 percent, 1/1 odds.



My citation for this is "Murphy's Law."

Well, what is 100% is that, of the thousands of guys used every day with a 1 injury roll, the one that gets injured 3 times in a week or so of games is going to get a thread posted here. I make this something like 1 in 3800. But there are probably 200 leagues running right now, and 70% of the players have 1 injury chance, so that' probably 75 guys per league who play regularly. 75 x 200 is 15000. It should happen about 4 times a week to some manager or other.

Lighten up.

I think if this is treated as a poisson distribution problem: Probability of a 1 in 216 event happening 3 times in 27 tries is ~.03% (about one in 3500).

If I've done this correctly:

Prob of 0 in 27 rolls = 88.25%
of 1 = 11.03%
of 2 < 0.69%
of 3 < 0.03%
then probs get VERY small