Back in high school, when we had a really hard test all the smart kids would get together and produce a cheat sheet.
Over time, we learned there were a couple of hard and fast rules for doing this:
- It had to be simple and organized
- It had to be small (preferably fitting in the back of your sliding calculator or in the palm of your hand).
- It had to be readable (good bless laser printing)
- It only as good as the data ( take a preemptive bow Andres Alvarez, as the forthcoming post is All Powered by Nerd Numbers ).
It became a fun little game to make them better and better and cram more information into each one. Now this kind of thing might sound like cheating to the uninformed but we’re talking about AP math and physics. The formulas helped but really you needed to know how to do the problems (and it was graded on a curve ). It was really a handy dandy reference but you had to bring the brains.
Now I’ve done similar things before in this space for many of the reader questions (and for my own useI’m pretty sure I hit the Basics more than basically anyone for reference) .For this one, I’m taking on one of the big ones : how do changes in the Box score stats affect a Teams Win Produced? Now keep in mind I just showed that on a game to game basis Wins produced correlates at a 99.8% with point margin (Point Margin for a game = 0.0377 + 15.5 Wins Produced for that game) and for the season a 95% correlation has been shown repeatedly (the difference is down to blowout) . So a mapping of the box-score stats to WP will tell us the expected effect on both wins and point margin from a shift in a single box-score stat.
First let’s do Box score stats to Win Produced. For this mapping I’m looking at changing each stat by itself in increments of 1 (per game). That mapping looks like this:
Cool looking , isn’t it. This assumes an increment 0f 1 of any stat is done while keeping all other stats the same (and improtant point that we’ll come back to later). Now all these coefficients come from regression and regression does a really good job at assigning value. But sometimes it can obscure what’s happening. Fortunately, we have a handy dandy little equation available remember?
Point Margin for a game = 0.0377 + 15.5 Wins Produced
Note: I had a mistake when I put this up. To convert WP to expected Point Margin (and vice versa) for the team I have to account for the fact that for a single game half the win credit goes to the victor and half get charged to the loser so the equations for conversion become:
Expected Avg Point Margin for Team (season) = 31*(Wins Produced (team for the season) -41 )/82
Wins Produced (team for the season) = (Expected Avg Point Margin for Team (season)*82)/31 +41
Marginal Wins Produced (team for the season) = Expected Avg Point Margin for Team (season)*82/31 = PM*2.645
Point Margin = 31/82 * Marginal WP = .378 *WP
+1 Points = 2.645 wins over .500 (43.645 wins)
+10 Points = 26.45 wins over .500 (67.45 wins)
+1 WP = +.378 Points
+10 WP = +3.78 Points
And I’m resetting the tables from this point on to reflect this.
What if I used this to map and increase in boxscore stats to point margin increases? What if I did that and called it Point Margin Produced? Let’s find out. We take all the numbers in the above table and adjust them accordingly we get:
That really clear’s it up doesn’t it. Now before you start with the snarky comments, I see it too. And additional Three pointer assuming everything is held constant is only worth two points, and additional 2 point field goal is only worth a point if everything else is held constant. Let parse this before we go crazy. A field goal does not happen in a vaccumn . Multiple things have to happen for a field goal to be made . If we break it down:
We can get to a +1 on the number of 2PT FG for the same Number of Shots by getting :
+1 on a 2FG
-1 on FG Misses (there are some additional possibilities but this is the simplest one)
A similar story can be told for the Three pointer and if we add it up it looks like this:
And that looks right. The effect of increasing a FG adds up to 2 or 3 points (there’s some marginal effects i.e. assists,rebs etc. I’m not accounting for here, remember keep it simple and understandable) but regression splits up the value of those points among all the contributing stats.
So the numbers prove that making shots in basketball is really only part of the story.
One more table before we leave:
Oh hell. Let’s look at stats for this year (for everyone >100 MP) in WP48 converted to Points Margin produced per 48. This calculation is done as follows:
PM48= (WP48-.099)* 31.1
This should keep you amused for a few days