Example 6 In the Mathematical Olympiad training team, there are 30 members, each of whom has the same number of friends in the team. It is known that in a test, everyone's scores are different. If a member scores higher than the majority of their friends, they are called a "pro". Question: What is the maximum number of pros in the training team?

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The above text is the English translation of the provided Chinese text, maintaining the original format and line breaks.
Let each team member have $k$ friends, and this exam has produced $m$ experts, the best-performing member of the team, is the best in their $k$ "friend pairs," and is naturally an expert. Each of the other experts is at least the best in $\left[\frac{k}{2}\right]+1 \geqslant \frac{k+1}{2}$ (where [x] denotes the greatest integer not exceeding the real number $x$) of their friend pairs. Therefore, the experts collectively dominate at least $k+(m-1) \frac{k+1}{2}$ friend pairs.

Since any friend pair can contribute to an expert only once, it will not be counted repeatedly. Thus, the above number does not exceed the total number of friend pairs in the training team, i.e.,
$$
k+(m-1) \frac{k+1}{2} \leqslant 15 k \Rightarrow m \leqslant \frac{28 k}{k+1}+1 \text {. }
$$

On the other hand, the number of team members who perform worse than the worst expert is no more than $30-m$. The worst expert also wins at least $\frac{k+1}{2}$ people, so
$$
\frac{k+1}{2} \leqslant 30-m \Rightarrow k \leqslant 59-2 m \text {. }
$$

Substituting equation (2) into equation (1) gives
$$
\begin{array}{l}
m \leqslant 28 \times \frac{59-2 m}{60-2 m}+1 \\
\Rightarrow m^{2}-59 m+856 \geqslant 0 \\
\Rightarrow m(59-m) \leqslant 856 .
\end{array}
$$

The maximum value of the positive integer $m$ that satisfies the above inequality and the condition $m \leqslant 30$ is 25, meaning the number of experts does not exceed 25.

On the other hand, it can be shown that the scenario with 25 experts is possible.
Using $1,2, \cdots, 30$ to represent the rankings of the team members (with better performance having a higher ranking).
When $m=25$, from equation (2) we get $k=9$, meaning each person has nine friends.
Now, construct a $6 \times 5$ table and define the following friendship relationships.
If two students are friends, it is only if one of the following conditions is met:
(1) They are in the same row of the first row;
(2) They are in the same column, but one of them is in the bottom row;
(3) They are in adjacent rows but different columns.
This way, each person has exactly nine friends, and the top 25 are all experts.