In this post, I'll introduce you a brand-new, 100%
textbook stat,
T-Con [1]. It's designed to measure players' contribution in a game. Currently, Performance Index Rating
-PIR- is used to evaluate players efforts in the game and even to choose MVP of the Week in Euroleague. Yet, I've never get used to concept of PIR since I encountered it. Its
algorithm fairly inadequate to evaluate different stats and combine them.So, we decided to solve that problem.
First of all I tried to bring all stats into one common base
-points-, as
TDR and
TOR. It was a little with tricky this time, because it's more complex to evaluate pluses and minuses of a player's move than a team's move. For example, in the simplest term team shots with one field goal percentage as an organism while every player has his own field goal percentage regardless of his team mates.So, every shoot differ from each other depends on who use it. I'll expand on that a little later. Before that, let's remember what we have in a boxscore sheet;
Points, Field Goal and Free Throw Attempts[2], Assists, Steals, Turnovers, Rebounds,Blocks[3], Fouls Received and Committed. In order to
evaluate numbers in these stats we need to form up a few more stats too. I'll mention them while I'm explaining how I value the numbers in the stats above to avoid confusions. Let's start with Points
.
Points may be the most crucial entry in the boxscore since the fate of a game decided by how many points a team made. Value of a point changes slightly game by game. Points made in a low score game are more valuable considering its sample. Also, every point ,scored in a game which ended with lower score difference, is more important. So, first I determined the points should be scored -
by any player- per minute to win the game. Then, I calculated
Expected Points for any player by considering corresponding minutes played and calculated difference between expected points and points made -
Marginal Points-. After that, if marginal points of a players is less than '0'
-which means points made are less than expected points- I used points made as
Point Component of T-Con. On the other hand if marginal points of a player is greater than '0', I made a final calculation. I calculated the
importance of a point[4] by considering score difference at the end of the game. Afterwards, I valued every points made which exceeded the expected points with this importance. This final calculation yielded a result which I've chose to call
Value-Added Points. I sum up points made with value-added points and took result of it as
Point Component of T-Con.
Next stat we need to evaluate is
Field Goals Missed. Before that, I need to mention concept of
Projected Score per Play,PSP[5]. Basically, PSP represents estimation of how many points would a team score in a play
[6]. Now, let assume Player X, missed the shot. If he didn't use and miss the shot, his team mates would attack with PSP(TwP
[7]) which is calculated by taking his team mates field goal percentages,turnover and getting fouled rates.
Since, Player X prevent his team to score
PSP(TwP) many points, he should penalized as many as that.
Missed shots time
PSP(TwP) -multiplied with '-1' of course- would be
Field Goal Missed Component of T-Con.
Next stat is
Free Throws Missed. It's not too hard, since every missed free throw attempts worth '
Minus 1' points, I took
missed free throw attempts time '
minus 1' as
Free Throw Missed Component of T-Con.
As for
Assists, I used one of the stats we've introduced before,
FGT. Briefly, FGT is potential score of shot
-not a play,just shot-. Since every assist means a field goal made , we don't need to use field goal percentage for an assist. I multiplied players
assist numbers with team's
FGT(TwP) to calculate
Assist Component of T-Con.
Now, lets analyze
Steals. Steal is characteristically a play reverser stat. What am I trying to say is, a steal prevents opponent's one play and makes it your play. So, we need to consider benefits of the both sides while evaluating steal. So, value of a steal would be summation of opponent's PSP
-which you stop- and team's PSP
-which you lead-. Multiplying this summation with number of steals would yield
Steal Component of T-Con.
One of the stats which shows great resemblance to steal is
Turnover. Turnover also tends to be a play reverser stat. It's not quite the same as steal though. Not all turnovers leads transitions. For example, if
Player X stepped out of bounds, it wouldn't cause an transition offense for opponent team. Yet, if
Player X lost ball because
Player Y of opponent team stole his ball, then it would yield an transition offense for opponent team. Therefore, we need to find the ratio of how many of the team's turnovers are caused by opponent's steals -
S/T Ratio-. After that, we can safely presume that as much as
S/T Ratio, play would be reversed and team would lose as much as its PSP and opponent would score as much as its PSP. Also,team would lose the ball but not hand it over to opponent for that play as much as rate of
'1-S/T Ratio' . To sum up, we need to multiply
S/T Ratio with summation of
Team's PSP(TwP) and
Opponent's PSP and and multiply
1-S/T Ratio' with
Team's PSP(TwP) and then sum these two outputs up and multiply with '-1'
-to penalized turnovers- . It'll give us
Turnover Component of T-Con.
Rebounds are divided as defensive rebounds and offensive rebounds. Let's start with
Defensive Rebounds. Let's assume that
Player X grabbed 5 defensive rebounds. How can we value that effort? First of all, if he didn't show that effort and grab the ball, those rebounds would be shared between
Player X's team mates and players of the opponent team. Since
Player X would be out of the picture, probability of his team's grabbing rebound would decrease. It means that, some of
Player X's '5' rebounds
-let's assume 2 of them- would be grabbed by opponent. So, opponent would attack with its PSP(2C
[8]) for '2' times.
PSP(2C) times
'2' would be value of the Player X's defensive rebound effort which is
Defensive Rebound Component of T-Con. As for
Offensive Rebounds, we can use similar logic. Let's assume
Player X grabbed 4 offensive rebounds this time. If he didn't show that effort, these 4 offensive rebounds would be shared between his team mates and opponent's players. In this scenario
-like previous one- Player X's team would grab less offensive rebound
- let's assume 1 of 4- since
Player X would be out of the picture. So, they would lost the chance of attacking with their
PSP(2C) for
'3' times
- '4-1=3' -. Therefore,
'3' times Team's
PSP(2C) would give us value of
Player X's offensive rebound effort which is
Offensive Rebound Component of T-Con.
One of the remaining stats is
Blocks. Since it's impossible for me to reach data of how much percentage of blocks made behind the arc, I assumed that all blocks happens in 2-Pointer area. I know, sometimes blocks happen behind the arc, yet that numbers seems very insignificant to me -by considering sample size-. Also, I didn't want to overrate blocks, since sometimes block attempts leads teams to poor defenses. So, here is what I did, I multiplied
number of blocks with
opponent's 2-Pointer percentage and
'2'. Then, I took it as
Block Component of T-Con.
And last of all,
Fouls. Let's start with
Fouls Received. Let's assume our mighty
Player X is get fouled. If he couldn't go to free throw line, there would be no extra benefits to his team since his team would attack with its regular PSP as usual. However, if he manages to go to free throw line he would add as many point as he scored in free throw line. To calculate that number we need the frequency of player's getting to free throw line per foul,
line%. After that, we can easily calculate
Fouls Received Component of T-Con. As for
Fouls Committed, I've used same logic. Since, most of the players has a greater free throw percentage than field goal percentage, committing too many fouls would hurt the team. But again, we need to use opponent's line % since not every foul resulted with free throws. Then, I used the same calculation in fouls received and found
Fouls Committed Component of T-Con.
After all these calculation, we can finally evaluate all stats and combine them. Because, they are all in the same base now and all of them are weighted by calculating how much they help or hurt. We would share application of T-Con for some games
-Euroleague's Games of the Week maybe- later on.
_____________________________________________________________________________
[1]Tangible Contribution; T-Con only measures efforts which is represented in the boxscore sheet. Remember, not all efforts is written in boxscore, we are well aware of that and we don't claim that T-Con represents all efforts, but it represents all efforts which are reflected by numbers. We're working on "numberless efforts" also, but they are not in the T-Con.
[2]Since Field Goals Made and Free Throws Made are being evaluated in Points Component, I've just used Missed Attempts for these components.
[3]Even though Blocks Made shows defensive effort, Blocked Attempts doesn't show any extra poor offensive effort than a simple missed field goal, I' believe. Since, we evaluated every Blocked Attempts in Field Goal Missed Component, I didn't form up a new component just for Blocked Attempts.
[4]Triangle of Win; Tie in the score represent a line which can be formulated as f(x)=x, in X-Y dimensions. Every score which breaks the draw, created a triangle between f(x)=x line and new position of score in X-Y plane. Median of this Triangle of Win, shows the importance of a point.
[5]PSP is found by summing up outputs of every possible scenario in a play. Every play can be ended with a field goal attempt, a turnover or a foul. Calculating percentages of these options and their possible outcomes -as points- would yield PSP.
[6]Play is a little bit differentiated version of a possession. Every offense which set a new shot clock equals a play. (It's not the same play as Dean Oliver's)
[7]Team Without Player; it shows the stat which is written before TwP is calculated by ignoring players' own stats and using only his team mate's stats.
[8]Second Chance; since statistically probability of scoring is higher in second attempt, second chance PSP would be much higher than regular one.
