Shouldn't ROUGE-1 precision be equal to BLEU with w=(1, 0, 0, 0) when brevity penalty is 1? I am trying to evaluate a NLP model using BLEU and ROUGE. However, I am a bit confused about the difference between those scores. While I am aware that ROUGE is aimed at recall whilst BLEU measures precision, all ROUGE implementations I have come across also output precision and the F-score. The original ROUGE paper only briefly mentions precision and the F-score, therefore I am a bit unsure about what meaning they have to ROUGE. Is ROUGE mainly about recall and the precision and F-score are just added as a compliment, or is the ROUGE considered to be the combination of those three scores?
What confuses me even more is that to my understanding ROUGE-1 precision should be equal to BLEU when using the weights (1, 0, 0, 0), but that does not seem to be the case.
The only explanation I could have for this is the brevity penalty. However, I checked that the accumulated lengths of the references are shorter than the length of the hypothesis, which means that the brevity penalty is 1.
Nonetheless, BLEU with w = (1, 0, 0, 0) scores 0.55673 while ROUGE-1 precision scores 0.7249.
What am I getting wrong?
I am using nltk to evaluate BLEU and rouge-metric for ROUGE.
Disclaimer: I already posted this question on Data Science, however after not receiving any replies and doing some additional research on the differences between Data Science and Cross Validated, I figured that this question might be better suited for Cross Validated (correct me if I am wrong).
 A: BLEU computes a similarity score based on 1) n-gram precision(usually for 1, 2, 3, and 4-grams); 2) a penalty for too-short system translations.
$$\text{BLEU}=\text{BP}*\exp(\sum_{n=1}^N w_n \log p_n)$$
where $p_n$ is the modified precision for n-gram, the base of log is the natural base $e$, $w_n$ is weight between 0 and 1 for $\log p_n$ and $\sum_{n=1}^N w_n =1$, and BP is the brevity penalty to penalize short machine translations.
\begin{equation}
\text{BP} = 
    \begin{cases} 
    1 & \text{if $c>r$}\\
    \exp(1-\frac{r}{c}) & \text{if $c\le r$}
    \end{cases}       
\end{equation}
Plug in $w = (1, 0, 0, 0)$ and $\text{BP} = 1$, we obtain this: $\text{BLEU}=p_1$ which is the precision of the uni-gram overlap.
I thought in your case the BP might be not 1. The penalty is not one if $r$, the effective reference length which is the length of the reference that’s closest to the hypothesis, is greater than the length of the candidate sentence. I don't know how you calculated the accumulated lengths of the references to get the brevity penalty 1.

Is ROUGE mainly about recall and the precision and F-score are just added as a compliment, or is the ROUGE considered to be the combination of those three scores?

ROUGE is based on recall but sometimes $F_1$ version (combination of precision and recall) of it is reported anyway. Please refer to this answer.
References:

*

*Bilingual Evaluation Understudy (BLEU)

*BLEU: a Method for Automatic Evaluation of Machine Translation

*What is ROUGE and how it works for evaluation of summarization tasks?

*Lecture 15: Natural language generation
