  A well-known theorem of Chung and Graham states that if $h\geq 4$ then a
tournament $T$ is quasirandom if and only if $T$ contains each $h$-vertex
tournament the "correct number" of times as a subtournament. In this paper we
investigate the relationship between quasirandomness of $T$ and the count of a
single $h$-vertex tournament $H$ in $T$. We consider two types of counts, the
global one and the local one.
  We first observe that if $T$ has the correct global count of $H$ and $h \geq
7$ then quasirandomness of $T$ is only forced if $H$ is transitive. The next
natural question when studying quasirandom objects asks whether possessing the
correct local counts of $H$ is enough to force quasirandomness of $T$. A
tournament $H$ is said to be locally forcing if it has this property.
  Variants of the local forcing problem have been studied before in both the
graph and hypergraph settings. Perhaps the closest analogue of our problem was
considered by Simonovits and S\'os who looked at whether having "correct
counts" of a fixed graph $H$ as an induced subgraph of $G$ implies $G$ must be
quasirandom, in an appropriate sense. They proved that this is indeed the case
when $H$ is regular and conjectured that it holds for all $H$ (except the path
on 3 vertices). Contrary to the Simonovits-S\'os conjecture, in the tournament
setting we prove that a constant proportion of all tournaments are not locally
forcing. In fact, any locally forcing tournament must itself be strongly
quasirandom. On the other hand, unlike the global forcing case, we construct
infinite families of non-transitive locally forcing tournaments.
