# Statistics question: appropriate test of significance?

The following question came to mind while I was playing tennis. Even when I'm taking a break, I can't turn the math brain off. I'm sure this is a simple question for the statisticians here.

Say a tennis player wins 100 out of 200 points in a match. The player faces 30 break points in the match (not serving so well, apparently), and saves 20 of them. Is there evidence that the player plays "better" when facing break point?

My thought (from my limited knowledge of statistics) is to compare the ratio $\frac{20}{30}$ of break-points-against won to the ratio $\frac{80}{170}$ of all other points won, with the expectation for each ratio being 50% $(=\frac{100}{200})$. We could use Pearson's chi-squared test with one degree of freedom. Is this an appropriate approach or am I missing something?