# [Java (JDK)], 113 bytes

<!-- language-all: lang-java -->

 s->{int m=0,l=s.length(),t,L=0;for(;l>0;L=t>m?(m=t)-m+l:L)t=s.split("\\b[a-zA-Z]{"+l--+"}\\b").length;return-~L;}

[Try it online!][TIO-kdpnb7d3]

[Java (JDK)]: http://jdk.java.net/
[TIO-kdpnb7d3]: https://tio.run/##VZDNbhMxEMfveYrRQhQvWS@5cMl2l/YCVAqnIiHRVpWTOLsO/ljZsylpSK6ceqvUCwf6FnkclBfoIxhnEyQYaWzNzM9/z8ycLRidT796oWpjEeYhThsUMp01eoLC6PRV1plI5hx8ZELDqgNQN2MpJuCQYbgWRkxBhRq5QCt0eXkNzJYublGAT@Zc47uj2MkBKWAGuXe0WAmNoPJBInOXSq5LrEicYDLKB9nMWJLJYpCNcizUW6JyjKnqy@EoxkC7Wgok0dXV@JLRuzP65XoV9SWl/WgdclF8lMssx8Zquhlla5@1HQVhIAtmAbnD4X/NAlwsHXKVmgbTOrSKMxJ16ZuBA1pAd9rVUdI@S2CWsrqWyzMXxiP7VBwf5Nedva@9/8ClNHBrrJwCVsKFnzg4o3ir4I71YC2StEyapi12IM79iGPPwdh8A/J7@@N5@9SjveftrzgE/rMVGJZ5kNz9vCe7x4fd41M4Y6itKS1THitO/3Ht35u/VkoO@6Y0hEE8iU8K1n/tuEauJ/zli1NyeiuwGg4V00tK6Y1bqrGRbrX@vtl4pg3eVPywQ2ATbJiUyz8 "Java (JDK) – Try It Online"

## Explanation

This basically splits the String on ascii words of all possible lengths to count them, and returns the max value of the count.

```
s->{
 int m=0, // The maximum number of 
 l=s.length(), // The length of ASCII letters, going from high to low
 t, // Declare a temp variable.
 L=0; // Initialize the most present length to 0.
 for( // Loop
 ;
 l>0; // On each length, going down
 L=t>m?(m=t)-m+l:L // If a count is higher than the max count, the new count becomes the max count and the most present length becomes the current length
 )
 t= 
 s.split("\\b[a-zA-Z]{"+l--+"}\\b") // Count the number of parts between or around words of length l
 // Also, decrement l
 .length; // Store the count into t
 return-~L; // Return L + 1
}
```