Improving query performance with Join, Full Table Scan - mysql

Question

I am trying to improve the query performance on a stats reporting website for a Battlefield game, and am having a little bit of trouble with a very specific query. The issue I am having is that EXPLAIN is stating this query is doing a full table scan. This is troublesome because I expect this table to get very large (potentially 1 million rows or more). I am using MySQL 5.7 as my database of choice.
Here is my table and Query: http://pastebin.com/DsiGe2UB
--
-- Table structure for table `player_kit`
--
CREATE TABLE `player_kit` (
`id` TINYINT UNSIGNED NOT NULL,
`pid` INT UNSIGNED NOT NULL,
`time` INT UNSIGNED NOT NULL DEFAULT 0,
`kills` MEDIUMINT UNSIGNED NOT NULL DEFAULT 0,
`deaths` MEDIUMINT UNSIGNED NOT NULL DEFAULT 0,
PRIMARY KEY(`pid`,`id`),
FOREIGN KEY(`pid`) REFERENCES player(`id`) ON DELETE CASCADE ON UPDATE CASCADE,
FOREIGN KEY(`id`) REFERENCES kit(`id`) ON DELETE RESTRICT ON UPDATE CASCADE
) ENGINE=InnoDB DEFAULT CHARSET=utf8;
ALTER TABLE `bf2stats`.`player_kit` ADD INDEX `reverse_ids` (`id`, `pid`);
--
-- My Full Scanning Query
-- SELECTS players, ordering them by kills and time in kit
--
SELECT p.name, p.rank, p.country, k.pid, k.kills, k.deaths, k.time
FROM player_kit AS k
INNER JOIN player AS p ON k.pid = p.id
WHERE k.id = 0 AND k.kills > 0
ORDER BY kills DESC, time DESC
LIMIT 0, 40
--
-- EXPLAIN results by MySQL
--
id select_type table partitions type possible_keys key key_len ref rows filtered Extra
1 SIMPLE k NULL ref PRIMARY 1 const 75 32.11 Using index condition; Using where; Using filesort
1 SIMPLE p NULL eq_ref PRIMARY PRIMARY 4 bf2stats.k.pid 1 100.00 NULL
--
-- Additional Tables just in case, for reference
--
--
-- Table structure for table `kit`
--
CREATE TABLE `kit` (
`id` TINYINT UNSIGNED,
`name` VARCHAR(32) NOT NULL,
PRIMARY KEY(`id`)
) ENGINE=InnoDB DEFAULT CHARSET=utf8;
--
-- Table structure for table `player`
--
CREATE TABLE `player` (
`id` INT UNSIGNED NOT NULL AUTO_INCREMENT,
`name` VARCHAR(32) UNIQUE NOT NULL,
`rank` TINYINT NOT NULL DEFAULT 0,
`country` CHAR(2) NOT NULL DEFAULT 'xx',
PRIMARY KEY(`id`)
) ENGINE=InnoDB DEFAULT CHARSET=utf8;
Here is the explain from phpMyAdmin:
I am hoping that one of you can help me improve the performance of this query, since any kind of index I have put on it does not seem to help much.

Answer 1

For this query:
SELECT p.name, p.rank, p.country, k.pid, k.kills, k.deaths, k.time
FROM player_kit k INNER JOIN
player p
ON k.pid = p.id
WHERE k.id = 0 AND k.kills > 0
ORDER BY kills DESC, time DESC
LIMIT 0, 40;
The optimal indexes are:
player_kit(id, kills, pid)
player(id) -- if this is not already there
You can also add the other columns in the index to get a covering index for the query.