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With the following data, I believe the difference in performance between two athletes can be measured with a (one- or two-sided) paired $t$-test:

              | Tournament 1 | Tournament 2 | Tournament 3 | ... | Tournament 30 | 
    Athlete 1 |            8 |            5 |            9 | ... |             4 |
    Athlete 2 |            6 |            3 |            2 | ... |             5 |

Which statistical test do I use if every tournament gives multiple data for each athlete, like so:

              | Tournament 1 | Tournament 2 | Tournament 3 | ... | Tournament 30 | 
    Athlete 1 | 9, 7, 6, ... | 2, 1, 4, ... | 8, 1, 3, ... | ... | 6, 5, 4, ...  |
    Athlete 2 | 8, 8, 9, ... | 3, 3, 2, ... | 7, 2, 3, ... | ... | 7, 4, 3, ...  |

?

If the multiple data is paired, i.e., $(9, 8)$, $(7, 8)$, $(6, 9)$, I guess this boils down to an ordinary paired $t$-test, since we then have

    Athlete 1 | 9, 7, 6, ...   2, 1, 4, ...   8, 1, 3, ...   ...   6, 5, 4, ...  |
    Athlete 2 | 8, 8, 9, ...   3, 3, 2, ...   7, 2, 3, ...   ...   7, 4, 3, ...  |

But what if the multiple measurements are not paired, i.e., what if

              | Tournament 1 | Tournament 2 | Tournament 3 | ... | Tournament 30 | 
    Athlete 1 | {9, 7, ... } | {2, 1, ... } | {8, 1, ... } | ... | {6, 5, ... } |
    Athlete 2 | {8, 8, ... } | {3, 3, ... } | {7, 2, ... } | ... | {7, 4, ... } |

and order does not matter (as the set notation attempts to express)?

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