The coach of the Eagles used a computer analysis to determine the best combinations of players for games.
Premises
The coach of the Eagles used a computer analysis to determine the best combinations of players for games.
The analysis revealed that the team has lost only when Jennifer was not playing.
Conclusion
This sort of information confirms that Jennifer's presence in the game will ensure that the Eagles will win.
Evaluate
We could/should definitely worry about an illegal reversal / negation when we see that conditional premise ("only when").
That rule is saying Team Lost --> Jen didn't play
So an illegal reversal would sound like,
An illegal negation would sound like,
But the conditional is about the past tense. So an illegal negation or reversal would still take place in the past tense.
Instead, the conclusion is a future-looking conditional Jen plays --> Team Will Win
A past-tense conditional would have been logically valid: Jen played --> Team didn't lose
The reason the conclusion isn't valid is because it's future looking. The argument establishes that if Jennifer was playing, the Eagles won. But does that mean that if Jennifer plays in the next game that her team will win? Not necessarily, there could be something different about the next game compared with previous games. Maybe the next team is better, maybe the next game will the first one Jennifer has ever played indoors.