The Senior Prospects Metric: An Update

(Note: the following post might be stat-heavy and dwell obsessively on number crunching. If you have no interest in such things, you might just want to skip past this one.)

Q of Rethinking Basketball asked me in a comment about a post I had written which used the first version of the Senior Prospects Metric (SPM) to go back in time to the 2008 WNBA Draft and attempt to predict that draft. Here are the results:



So how did the SPM match up with how the players performed? And how well did the actual draft match up? The actual draft matched up very well, just creeping into the -0.5 area of large correlation. Whereas the SPM did not even reach -0.3, the generally hypothesized level of medium correlation.

Q suggested that instead of using Wins Score, I should use a metric that was more of a rate than a sum. Wins Score isn't high for players that don't get a lot of minutes, whereas a rate would measure "production per minute" and would not penalize players that had potential but didn't get a lot of minutes.

Therefore, instead of using Wins Score, I would use a metric I was already using for something else, called WS333 - "Wins Score for 33 1/3 minutes". WS333 asked the question, "how much Wins Score does the player produce per 33 1/3 minutes of play?". It would shrink the scores of players who had a lot of minutes, and expand the scores of players who didn't.

The results were...well....



AAAGGGHHH! When using a per/minute based metric, the SPM did worse - it got closer to randomness. Whereas the actual draft order got closer to a direct relationship.

I realized that I was going to have to add the height caveats that Hollinger wrote about in his inital ESPN article if I was to get any closer to an actual draft projection. I therefore added the height qualifications to the SPM and tried the entire result all over again.

Here are the final results. The "New Predicted Order" is the order you'd get if you use the updated version of the SPM to predict the draft outcome.



Kimberly Beck falls from 3rd to 10th. The new SPM punishes her for being a short point guard who didn't rebound well in college. Quianna Chaney also takes a hit for rebounding. Poor players get pushed down and the better players move up to take their places. Candace Wiggins moves to 8th from 10th, and Alexis Hornbuck moves all the way from 15th to 9th.

We'll look at the new correlations now.



The newest version of the SPM still does poorly against WS333 - but it does better than the older version. However, when using Wins Score, the correlation between SPM and actual player results actually moves from small correlation to medium correlation.

Even more interesting (to me anyway) is that the new SPM predicted order moves closer in correlation to the order from the 2008 WNBA Draft. It's still a small correlation, but it moves more in the direction of what the GMS of the WNBA actually do.

(* * *)

When thinking about this project, there were two matters on my mind.

The first matter is whether or not correlation is the correct statistical measure to use. As it turns out, correlation can be very misleading whenever non-normal variables are used.

A "normal variable" is a bell-curve type distribution. This implies a lot of numbers clumped up in the middle and trailing on both ends. If WNBA talent were normally distributed, it would indicate that most WNBA players have roughly the same amount of talent, with a few players being rather crappy and another few players being excellent.

This assumption is not true in baseball. In baseball, it's more of an exponential curve, with a whole lot of really crappy players and a small number of good players. (Go to this link for the image of an exponential curve.) I suspect that talent curves are the same way in the WNBA and this adds problems when using correlation.

The other matter on my mind is that we might not be explaining the relationship in the right terms - it might not be that draft position predicts player performance, but that player performance might be dependent on draft position! It might be the case that higher draft choices get more coaching attention to improving the fine points of their game than lower, non-playing draft choices. In short, there might not be some sort of "inherent ability" that never changes, but rather the ability is more likely to be coaxed out at the professional level by coaches and staff members the lower one is picked in the draft.

After all, if you're a first round draft pick, there's more pressure on GMs and coaches to get a better result. More attention is lavished on one's major investment than one's minor ones.

That's pretty much it for the conclusions. I hope to have an updated SPM at the end of the 2008-09 college season, so we'll see which players did better than the most recently concluded year, and which did worse. If your favorite college player does worse in the coming year, don't worry - Hollinger says that this happens in men's college basketall, and it will probably happen in the women's game as well.

"Predicting" the 2008 WNBA Draft with the Senior Prospects Metric

One of my recent posts used a convoluted metric to try to predict who would be the best senior prospects for the 2009 WNBA Draft. One of my commenters suggested that the metric be applied to the 2008 WNBA draft class. This way, we could determine if the metric could isolate who would be the most successful players out of that group of college seniors (and in the case of Candace Parker, juniors.)

I limited my analysis to the first three rounds of the draft. This involves 43 players (Sacramento was given a bonus third round pick - 14 x 3 + 1 = 43). Here is who the Senior Prospects Metric (SPM?) predicted for the draft.



At least we have the top four draft picks - Parker, Fowles, Wiggins and Hornbuckle - in the first round. The metric also brings a lot of third round draft picks into the first round, including two - Lauren Ervin of Arkansas ans Marscilla Packer of Ohio State - who ended up not playing a minute of WNBA ball. Ervin's season ended in December or January of 2008 with an ACL tear if I'm correct, which would explain why no one has heard of her - her position in the metric is based on the 16 or so games she played with the Razorbacks.

Let's look at how these player ended up in the actual draft. Furthermore, let's see how well each of these players have done in the 2009 season so far.

The last sentence where we "see how well" players have done is a loaded one. By what standard are you going to decide that players did "well" and players did not do "well"? There are several metrics you could use to evaluate players. I decided to use the same metric that SPM uses, the Wins Score metric. I like Wins Score because I think it evaluates shooting better than Efficiency.

Furthermore, using Wins Score solves the problem of players like Ervin who for whatever reason never made it into the league. Since Wins Score is an additive metric as opposed to some sort of rate, I can give those players who never made it into the WNBA( a Wins Score = zero. It works for me. These players have no positive stats, and no negative stats. It all balances out and furthermore strokes my ego by telling me that I'm a better player than Matee Ajavon).

The new picture:



It looks like Candace Parker and Nicky Anosike were the big wins of the draft. Both the SPM and the actual draft put them in the same locations.

Now, we need to know how much "correlation" the SPM and the Draft have to eventual Wins Score. Correlation implies a linear relationship between two lists of numbers.

A "zero" in correlation implies that there is no relationship.
A "one" in correlation implies that there is a strict relationship in the positive direction. As one list of numbers gets larger, the other list gets larger.
A "minus one" in correlation implies that there is a strict relationship in the negative direction. As one list of numbers gets larger, the other list gets smaller.

What we're hoping for is a negative relationship between draft position and overall performance. As position increases (#1, #2, #3....) the Wins Score associated with these numbers should start big, then start to drop.

Here are the correlation results:



These meanings of correlation depend on a lot. Let's look at the first one: the correlation between the SPM Predicted Order and the Actual Draft Order. 0.1220 is a very weak correlation, fairly close to random. The relationship between what the metric predicts and the actual draft pick order have little to do with each other.

Looking at the correction between the SPM Predicted Order and the Wins Scores of the Draftees, we get -0.2528. This is at the border of a small and medium correlation, more on the small side. At least the correlation is negative, which is what we want -- if it were positive, we would know that the SPM had no value.

Now, let's see how the actual GMs of the WNBA do against Wins Score. We get a correlation of -0.5925, a medium-large correlation on the large side of the border. The negative correlation is expected - as draft position goes up, performance should drop.

On the other hand, the -0.5925 number could be misleading. Remember that the Wins Score metric is linear additive - it gives you points whenever you do something well and takes points away whenever you do something poorly. It's not a "rate", but a sum. If a player is more likely to produce points than have points removed, then Wins Score and time played will have a strong positive correlation.

It is definitely likely that early draft picks will get more playing time than late draft picks - the draft pick has to be justified, or the player has to "get experience" and is more likely to be left in despite a low rate of Wins Score point production than a lesser pick. In short, early draft picks get better chances to build their Wins Score, so some of that good correlation might simply be a function of playing time.

(* * *)

Am I happy? so far I am. My next goal is to build in all of the height caveats. Hollinger stated that players of certain heights should be able to do certain things, and have points removed for failure. However, Hollinger is working with male height, and working in a different kind of game. This little side project of mine, it seems, is ever expanding - but at least, it's fun for a number cruncher!