MySQL 8.0

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create table activity (
  player_id int not null,
  event_date date not null
);
insert into activity values
(1, '2016-03-01'), (1, '2016-03-02'),
(2, '2017-06-25'),
(3, '2021-01-01'), (3, '2021-03-10'),
(4, '2000-01-01'), (4, '2000-10-01'), (4, '2000-10-02')
WITH temp AS(
    SELECT player_id,
    event_date - LAG(event_date, 1) OVER (PARTITION BY player_id ORDER BY event_date) AS difference, 
    RANK() OVER (PARTITION BY player_id ORDER BY event_date) as rn
    FROM activity
),

tp AS
(
    SELECT count(distinct(player_id)) as all_players
    FROM activity
)

SELECT ROUND(count(t.player_id)/tp.all_players,2) AS fraction

    FROM temp t
    JOIN tp

WHERE t.rn = 2
AND t.difference = 1
group by tp.all_players


fraction


0.25


WITH temp AS(
    SELECT DISTINCT(player_id), difference
    FROM (
        SELECT
            player_id,
            event_date - LAG(event_date, 1) OVER (
                PARTITION BY player_id ORDER BY event_date
            ) AS difference
        FROM activity
    ) x
    WHERE x.difference = 1
),
tp AS
(
    SELECT
        count(distinct(player_id)) as all_players
    FROM activity
)

SELECT
    ROUND(COUNT(*)/tp.all_players, 2) as fraction
FROM temp, tp
group by tp.all_players


fraction


0.50