Short index length (good or bad)

If you find the work load on DB server is disk bound and you do not have enough memory to increase innodb buffer pool size. We can help improve the performance by reducing the length of indexes, this will result more indexes fit into memory and would increase write operations. It may impact SELECT queries but not necessarly for bad. Allow me to show some example. I will lower the index length of my test table from 40 char to just 8 char:
Note: You may consider trying different lengths for your index and check which best fit your workload (both writing and reading speed).

ALTER TABLE csc52021 DROP INDEX value_40, ADD INDEX value_8(value(8));

To look all the rows that have a value between 'aaa' and 'b':

mysql> EXPLAIN SELECT COUNT(*) FROM csc52021 WHERE value>'aaa%' AND
mysql> <'b';
+----+-------------+----------+-------+---------------+---------+---------+------+------+-------------+
| id | select_type | table    | type  | possible_keys | key     | key_len | ref  | rows | Extra       |
+----+-------------+----------+-------+---------------+---------+---------+------+------+-------------+
| 1  | SIMPLE      | csc52021 | range | value_8   | value_8     | 11      | NULL | 9996 | Using where |
+----+-------------+----------+-------+---------------+---------+---------+------+------+-------------+
1 row in set (0.00 sec)

mysql> SELECT COUNT(*) FROM csc52021 WHERE value>'aaa%' AND value<'b';
+----------+
| COUNT(*) |
+----------+
| 5533     |
+----------+
1 row in set (0.02 sec)

As you can see, the index is used.
What if look for a specific value?

mysql> EXPLAIN SELECT COUNT(*) FROM csc52021 WHERE
mysql> value='a816d6ce93c2aa992829f7d0d9357db896d5e7de';
+----+-------------+----------+------+---------------+---------+---------+-------+------+-------------+
| id | select_type | table    | type | possible_keys | key     | key_len | ref   | rows | Extra       |
+----+-------------+----------+------+---------------+---------+---------+-------+------+-------------+
| 1  | SIMPLE      | csc52021 | ref  | value_8       | value_8 | 11      | const | 1    | Using where |
+----+-------------+----------+------+---------------+---------+---------+-------+------+-------------+
1 row in set (0.00 sec)

mysql> SELECT COUNT(*) FROM csc52021 WHERE
mysql> value='a816d6ce93c2aa992829f7d0d9357db896d5e7de';
+----------+
| COUNT(*) |
+----------+
| 1        |
+----------+
1 row in set (0.00 sec)

SELECT statements does a lookup for a value that have very low cardinality (for example, if we had millions of rows that starts with the same first 16 char "a816d6ce93c2aa99"), then a short index is not very efficient.
On the other hand, a short index length allows to fit more indexes value in memory, increasing the lookup speed.

In my test table, I can decrease the index length to 4 and still have good performance. For example:

mysql> ALTER TABLE csc52021 DROP INDEX value_8, ADD INDEX
mysql> value_4(value(4));

mysql> EXPLAIN SELECT COUNT(*) FROM csc52021 WHERE
mysql> value='a816d6ce93c2aa992829f7d0d9357db896d5e7de';
+----+-------------+----------+------+---------------+---------+---------+-------+------+-------------+
| id | select_type | table    | type | possible_keys | key     | key_len | ref   | rows | Extra |
+----+-------------+----------+------+---------------+---------+---------+-------+------+-------------+
| 1  | SIMPLE      | csc52021 | ref  | value_4       | value_4 | 7       | const | 2    | Using where |
+----+-------------+----------+------+---------------+---------+---------+-------+------+-------------+
1 row in set (0.00 sec)

mysql> EXPLAIN SELECT COUNT(*) FROM csc52021 WHERE value LIKE 'a816%';
+----+-------------+----------+-------+---------------+---------+---------+------+------+-------------+
| id | select_type | table    | type  | possible_keys | key     | key_len | ref  | rows | Extra       |
+----+-------------+----------+-------+---------------+---------+---------+------+------+-------------+
| 1  | SIMPLE      | csc52021 | range | value_4       | value_4 | 7       | NULL | 2    | Using where |
+----+-------------+----------+-------+---------------+---------+---------+------+------+-------------+
1 row in set (0.00 sec)

mysql> SELECT COUNT(*) FROM csc52021 WHERE value LIKE 'a816%';
+----------+
| COUNT(*) |
+----------+
| 2        |
+----------+
1 row in set (0.00 sec)

To summarize:
if you have good cardinality, a shorter index length will increase both writes and reads operations, especially if you are IO bound.