SQL Data type for "Reference" fields in table - SQL Server
Here is what I would do based on your requirements:

CREATE DATABASE [demo];
GO

USE [demo];



CREATE TABLE [dbo].[Player](
    [playerID] [int] IDENTITY(1,1) NOT NULL,
    [firstName] [varchar](50) NULL,
    [secondName] [varchar](50) NULL,
    [fk_team] [int] NULL,
 CONSTRAINT [PK_Player] PRIMARY KEY CLUSTERED ([playerID] ASC)
 );
GO


CREATE TABLE [dbo].[EventTypes](
    [EventTypeID] [int] IDENTITY(1,1) NOT NULL,
    [EventType] [varchar](50) NULL,
 CONSTRAINT [PK_EventTypes] PRIMARY KEY CLUSTERED ([EventTypeID] ASC)
 );

GO


CREATE TABLE [dbo].[Events](
    [eventsID] [int] IDENTITY(1,1) NOT NULL,
    [Minute] [varchar](50) NULL,
    [fk_EventType] [int] NULL,
    [fk_Player] [int] NULL,
 CONSTRAINT [PK_Events] PRIMARY KEY CLUSTERED ( [eventsID] ASC)
 );
GO
SET ANSI_PADDING OFF
GO

ALTER TABLE [dbo].[Events]  WITH CHECK ADD  
CONSTRAINT [FK_Events_EventTypes] FOREIGN KEY([fk_EventType])
REFERENCES [dbo].[EventTypes] ([EventTypeID])
GO

ALTER TABLE [dbo].[Events] CHECK CONSTRAINT [FK_Events_EventTypes]
GO

ALTER TABLE [dbo].[Events]  WITH CHECK ADD  
CONSTRAINT [FK_Events_Player] FOREIGN KEY([fk_Player])
REFERENCES [dbo].[Player] ([playerID])
GO

ALTER TABLE [dbo].[Events] CHECK CONSTRAINT [FK_Events_Player]
GO



INSERT INTO [dbo].[EventTypes] ([EventType]) 
      VALUES('Try'), ('Conversion'), ('Penalty');
GO
select * from EventTypes;


This should be what you need.   Have a great day!