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Probably they think that Stuart Broad is close to retirement and they wanted to give chance to some of the younger players (such as Jofra Archer, Mark Wood and Chris Woakes).
Stuart Broad is actually the highest wicket taker in the past tournaments and i was actually shocked to see him not selected in the first match and now he played the next two matches and yet he is again the highest wicket taker by a long margin in this series in both the teams and he just need 1 more wicket to reach 500 Test wickets which is incredible and 14 wickets in this series and with the way he started the day he will pick further wickets.
But IMO, Broad has got a raw deal from the selectors for the last few years. Despite being an all rounder, I have seen him batting at the no.11 slot. The younger bowlers on the other hand, are being given a flurry of opportunities, despite their bad form. Jofra Archer is not performing well for almost an year. But even now the English selectors treat him like he is some sort of divine invention.
The dip in batting form happened after Stuart broad was hit in the head by a Varun Aaron bouncer and broke his nose in 2014 and after that he himself said he lost his confidence in batting and in this series he wanted to perform again with the bat and he was training especially to change his batting and to start attacking rather than defense and it worked.