# BM25

$BM25(t, d)=IDF(t) \cdot \frac{tf(t, d) \cdot (k_{1}+1)}{tf(t, d) + k_{1} \cdot (1 - b + b \cdot \frac{|d|}{\operatorname{avgdl}})}$ $BM25(t_{1}, d_{1})=IDF(t) \cdot \frac{tf(t_{1}, d_{1}) \cdot (k_{1}+1)}{tf(t_{1}, d_{1}) + k_{1} \cdot (1 - b + b \cdot \frac{|d_{1}|}{\operatorname{avgdl}})}$ $BM25(t_{1}, d_{1})=IDF(t) \cdot \frac{tf(t_{1}, d_{1}) \cdot (1.5+1)}{tf(t_{1}, d_{1}) + 1.5 \cdot (1 - 0.75 + 0.75 \cdot \frac{|d_{1}|}{\operatorname{avgdl}})}$ $BM25(t_{1}, d_{1})=IDF(t) \cdot \frac{2 \cdot (1.5+1)}{2 + 1.5 \cdot (1 - 0.75 + 0.75 \cdot \frac{|d_{1}|}{\operatorname{avgdl}})}$ $BM25(t_{1}, d_{1})=0.248 \cdot \frac{2 \cdot (1.5+1)}{2 + 1.5 \cdot (1 - 0.75 + 0.75 \cdot \frac{|d_{1}|}{\operatorname{avgdl}})}$ $BM25(t_{1}, d_{1})=0.248 \cdot \frac{2 \cdot (1.5 + 1)}{2 + 1.5 \cdot (1 - 0.75 + 0.75 \cdot \frac{8}{8.6})}=0.362$