the probabilities of the two methods simultaneously. The old probability (0.155) being a lower figure than the new probability (0.189) shows that the new system has a flaw.
Despite this, under both systems, the ultimate result of the fourth seeded team acquiring the third or fourth pick decreases as teams with fewer chances (better teams) receive the first and second picks as unconditional probabilities are calculated. Using the Golden State Warriors again in the same NBA Draft Lottery one can prove that the fourth worst team is at a significant disadvantage. Consider the event A as the fourth worst non-playoff team moving up in the draft to acquire the third overall selection, regardless of the teams that receive the first two picks. P(A) can be found by calculating all possible pairs of teams getting the first two picks which are a collection of mutually exclusive and exhaustive events (refer to equation set 2). Using these equations I will work out the probability of the Golden State Warriors having this pick:
π( ) = ββπ( β© , )
= ββπ( | , )
β π( ,
) 8
= π( | 1,2
) β π( 1,2
)+. . π( | 13,14
) π( 13,14
)
β΄ π( ) = 0.212
Finally using the same equation, one can work out the remaining probabilities (Golden State remains in fourth or drops to fifth, sixth or seventh). For simplicity, I will only produce the results rather than working through the equation multiple times. Ultimately, after adding all the probabilities one comes to this result using the new system β the probability of moving up being 0.284, the probability of remaining the same pick being 0.189 and the probability of dropping down being 0.527. This shows a significantly higher chance of dropping down the picks, making the system unbalanced. Looking back at other drafts, you can quickly realise that these probabilities effect previous lotteries in the same way (refer to table 5).
8 Florke, Chad and Ecker, Mark (December 1, 2003) βNBA Draft Lottery probabilitiesβ American Journal of Undergraduate Research VOL. 2, NO. 3 (2003) Page 24
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