This will take a little explanation – bear with me.
For game by game player ratings, I’ve created Points Above Opposition (PAO). Simply, it’s how many points better (or worse) a given player was over the opponent in that given game. The higher the PAO, the more dominant a game the player had. I used my normal HnI rating for every player, and calculated the PAO based on the game score differential and each player’s playing time. Adding all individual player PAO’s for a team in a given game will exactly equal that team’s point differential for the game.
I then use PAO to calculate Player Wins (PW) or Player Losses (PL) – obviously depending on whether the game was won or lost. If a team wins, I sum all the POSITIVE player PAOs, and each player is given his Player Win share by a ratio of his PAO to the summed PAOs. Just the opposite for a loss, all the NEGATIVE player PAOs are used in the calculation of the Player Loss share. In a win, summing the PW of all players with positive PAOs will equal 1 for the team (1 team win), while all players with negative PAOs will have a PW of 0. Just the opposite in a loss, the summed PL of all negative PAO players will equal 1 for the team (1 team loss), while all players with positive PAOs will have a PL of 0. No player gets any PL in a team win, and no player gets any PW in a team loss. No player can ever have a PW or a PL larger than 1.00 in a given game.
While PAO might show how dominant a player was over his opponent in a given game, PW shows more how VALUABLE that player might have been in that game. A player with a high PAO in a blow out win very well might not have as high a PW as a player with a lower PAO in a close win. The first player dominated, but maybe wasn’t as valuable since he obviously had teammates who played great as well. The 2nd player’s quality play was vital in getting a win – and his PW shows it.
Let me use the Arizona/Gonzaga round of 32 game as an example of PAO, PW, & PL:
Note the sum of the PAOs is zero (Arizona won by 23 – Arizona players sum to +23, Zags players sum to -23). Also note the Player Win shares (only Arizona players) and the Player Loss shares (only Zag players) each sum to exactly one. Rondae Hollis-Jefferson’s great play (+9.4 PAO, the rest of the team totals +13.6) earns him a 0.31 PW (31% credit for the win). Bell’s poor play for Gonzaga earns him a 0.26 PL (26% blame for the loss).
Onto the Tourney Game Results
After the Round of 32 – all 1035 player games ranked by Player Win share (PW):
The same rankings – but sorted by team:
And the same set of players – ranked by Points Above Opposition (PAO):
Despite a modest 45th ranked PAO of 6.8, Julius Randle of Kentucky had the highest Player Win share game of 1.00 in the 2 point win over Wichita State. It actually isn’t a perfect PW (true PW of 0.998), it was rounded to 1.00.
While Adreian Payne of Michigan State had the most dominant game so far in their 15 point win over Delaware (41 & 8 with a 87% TS% and a 16.1 PAO), it accounted for just the 13th highest Player Wins (0.56). The next two highest PAOs (Aaric Murray of Texas Southern and Bryce Cotton of Providence) actually had zero Player Wins – since they lost their games.
Player PAO/PW/PL Tourney Totals
All 709 players who have played in the 2014 NCAA Tourney so far are ranked.
Players ranked by Player Win/Loss differential (PW minus PL):
The same rankings, but sorted by team:
And the rankings by Points Above Opposition (PAO):
Julius Randle of Kentucky is #1 so far in Player Wins, while Jarnell Stokes of Tennessee is #1 in Points Above Opposition. Xavier Thames of San Diego State is #2 in both PW & PAO.