The problem with NBA stats is many, but one that's glaringly obvious is the field goal percentage. It's hardly taken seriously as FG% differs significantly over player positions (guards are about 30%, forwards-centers 40-50%), doesn't reflect field goal attempts, and doesn't account for free throws and 3pters worth points other than 2. There's been attempts to solve the last issue (eFG%, TS%), so I've taken my focus on field goal attempts aka, the player's effort.
So what's effort...at least offensively? Field goal attempts that is.
An offense in basketball means making shots. The best way to measure how a team is run is by looking where the ball is distributed. Some teams have positions of primary scorers, while others have a balanced scheme. (This is due to the fact that only one individual can make a shot, not a team action). Sum up all the field goal attempts of that team, take an individuals FGA and then get a percentage of that. That's how much the offense is run through that player. That's a way of understanding the offense of a team. (Likewise one can have the same approach of getting a ratio of one's total points scored / total % of pts team scored)
The other reason to focus on FGA, is that it has the distinction of a raw stat. There is no outlying influence beyond the player and his coach/team's influence. (A block only happens when a ball is in the air, a rebound only happens when there's a FGA, an FTA depends on the other team getting contact, a steal depends on who has the ball, and etc.) Basically, the game of basketball in the stats world mostly determines on the FGA and a few other factors (pace). A player has all the command to pass or shoot, to know where to get his shot, and when. If it's a poor selection it will go up, bounce out, and give the opponent the opportunity to rebound (giving them another possible possession). This is comparable to batting avg vs. fielding stats. FGA like BA is individualized, whereas fielding is dependent on several factors.
There's no measure for efficiency of FGA however. True, there's FG%, but citing the previous problems above, there's obvious difficulties. Most notably is measuring the effective FG%. A bench warmer can score an easy basket, going (1/1) with a FG% of a 100, while a star player can go on a streak of (5/5) with a FG% of the same 100. Clearly, the star player has had a greater impact on the game, whist the benchwarmer provided a limited benefit. The FG% does not accurately reflect on the true performance of the player because it does not acknowledge the difference between the Field Goals Attempted. The more you shoot, the greater impact you have on the game.
This can be quick solved by looking at the points scored by player, but fuck that. I'm still thinking raw stats, not including pts yet. That has to be weighted.
For a player who goes (3/8) or (6/16), who's better? FG% tells us it's a (0.375v.0.353), so the (3/8) is better percentage wise, but the one who went (6/16) provided twice as many field goals.
The answer is to find a way to reward those who make many shots, and give irrelevance to those who go (1/1). Starting with FG%. It's a ratio, so larger the number on bottom will make the overall number smaller (1/5=0.2), and the smaller number on bottom will make the overall number larger(1/2=0.5) We need a way to find a function for the denominator that reverses that trend. That is to make the denominator get smaller in value when the overall number is getting larger, and to make denominator get larger when the overall number is getting smaller.Assuming the overall number and denominator are the same function of f(x) (becoming that every shot is made), the mystery function is (1/x).
f(x) = (1/x) is fairly simple. As "x" becomes large is, the overall number becomes smaller. As "x" is small, the over all number is larger. Compound this with the field goal ratio and the two inversely proportional effects cancel out. That is f(x) = x/(1/x). In the ideal world where every shot is made, the function becomes f(x) = x^2/x or f(x)= x. Benign as it is, but stands out when factoring in the misses.
For the idea example. If someone went (1/1) his true number would be 1 (1^2/1). If someone went (5/5) his true number would be 5 (5^2/5). That true number would have a difference of 1 to 5. That someone actually scored 5 field goals to 1 field goal. In the flawed FG% world, they both would have 100%. There would be no difference, even though one player scored 4 more field goals. That true number represents the difficulty of making one more shot, which in this case would be 1. **** [note this is not finalized]
In a true case tonight look at the Pacers. Who had a better night of scoring v. the Bulls? Was it Dunleavy who went (4-9; 44%) but provided 13 pts? Or was it Granger who went (6-14; 43%) with 19 pts? Let's find out using the "True FG #" (my new stat), shall we? Dunleavy [4^2/9] = 1.78. Granger [6^2/14] = 2.57.
Likewise what's better going (5/9: 55%) or (6/12: 50%); true FG# (5^2/9=2.77) (6^2/12=3). So whoever went 6/12 had a higher "true FG #" despite the fact him shooting a lower FG%.
That true number can be adjusted per minutes played. And then rebalanced/ prettified from it's lowly decimal form to by multiplying by 48 (the total minutes in a basketball game, just like how ERA is prettified by multiplying 9 to the earned run/innings pitched.)
Why does this matter? For the time being, it's a quick and dirty way for finding out who's on a streak during the game. The final minutes of the 4th quarter mean the most. Give the ball to the player on the hottest streak in the 4th quarter. It's not based purely off points scored, it's not based purely off field goal %. You can evaluate players by "True FG #", and that would be the guy.
It's roughly similar to
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