var/wininfo = "<b><font color=gray>WIN Info:</font> " // I made this to be reused easier since you use it a lot.
var/list/WINlist=list()
var/Guess_Time=1

// Removed the tmp var since nothing was assigned to it
mob/var/Number_Pick // Removed the brackets and quotations since you're randomizing ONLY a number -- Update after reading the rest of the code: Removed the entire value. You can set a random number through the WIN_Guess Verb
// The less you write, the faster your codes. Simplify it as much as possible. Even if it's simple stuff.

proc/Stat_WIN()
        var/Win_Number= rand(1,5)
        var/Stat_Amount= rand(100000,1000000)
        world << "[wininfo]Stat Points WIN is now taking number guesses to win statpoints."
        world << "[wininfo]The winners will be picked out in 4 minutes." // Grammatical error on winers
        sleep(2400) // 240 seconds in 4 minutes. This is correct. However, it doesn't need to be spawned. If you want to know why, ask me in pager.
                for(var/mob/player/M in WINlist) // Remember that this is "here"
                        if(M.client&&M.Number_Pick==Win_Number) // I haven't coded in a while. So, I don't know if M.client is the right thing to put. But, You surely need to check if they are still in the game. Otherwise, when you add the stats, you'll get a null error.
                                world<<"[wininfo][M] has won [Stat_Amount] statpoints."
                                Stat_Amount += M.statpoints
                                WINlist -= M // Not usr, but instead M. Because you're checking for "M" at "here"
                world<<"[wininfo]Stat Points WIN has ended. The next WIN will be in 3 hours."
                Guess_Time=0
        spawn(108000) // You need to spawn here so that the current Stat_WIN() proc ends. Sleeping would make this wait forever pretty much since it calls itself.
        Stat_WIN()



mob/verb/WIN_Guess()
        set category="Commands"
        if(Guess_Time==1)
                for(var/mob/player/M in PlayerList)
                        if(src.key in WINlist) // Don't use usr all the time. Page me and I'll explain.
                                alert(src,"You have already picked a number","Error")
                                return
                        WINlist + = src // Are you going to add the WINlist to src.key? Switch it around. Also, instead of adding the key, add the actual player.
            src.Number_Pick = rand(1,5) // Set the users guessed number to a random value of 1 - 5.
                        world << "[wininfo][M] has guessed the number [Number_Pick]."