SouthEastern Hoops

Measuring a team's average height, part III

2006-12-19T14:21:00.000-06:00

I'm back.

So we've mentioned two ideas on quantifying "inside vs. outside" statistics for a team.

1. Inside shooting

2. Inside defense

Now we add a third:

3. Overall Inside Ratio (OIR) = 100*(FTA + OR + DR + BL)/(FTA + OR + DR + BL + 3FGA + S + A + TO)

The idea being, divide (post-like stats) by (post-like stats + guard-like stats).

To get an idea of what this stat looks like, here's the SEC's 10 most post-like statistical players, among those with at least 40% minutes played:

1. Morris, KY 94.0
2. Singleton, GA 92.1
3. Rolle, LSU 90.7
4. Barber, AU 89.7
5. Townes, AR 89.7
6. Crews, TN 88.4
7. Brown, VU 87.0
8. Parnell, UM 85.8
9. Archie, SC 84.5
10. Richard, FL 84.5

And taking overall outside ratio (OOR) to be 100-OIR, here are the top ten most guard-like statistical players in the SEC:

1. Humphrey,FL 78.4
2. Steele, AL 72.8
3. Reed, AU 70.3
4. Stukes, GA 68.3
5. Cage, VU 66.4
6. Minor, LSU 65.8
7. Sheldon, SC 65.1
8. Delk, MS 65.0
9. Temple, LSU 64.8
10. Hodge, FL 63.2

Finally, here are the team numbers for OIR:

1. AL 65.4
2. MS 63.5
3. KY 62.1
4. LSU 61.5
5. UM 61.5
6. SC 61.1
7. AR 61.1
8. FL 57.7
9. GA 57.5
10. TN 56.9
11. AU 55.8
12. VU 54.8

That's all very interesting, but it's still not what we wanted. Recall that what we wanted was a way to gauge a team's *height*, not their inside vs. outside stats.

So, here's the question: is there a way to "scale" an individual's height by his OIR? I.e., he is using his height more to advantage if he is actually mixing it up in the paint...does it make sense to take a team's average height, weighted by both minutes played and inside ratio?

It's worth thinking about.

Measuring a team's average height, part II

2006-11-28T14:16:00.000-06:00

In yesterday's post, I mentioned idea #1:

1. Inside shooting (due to Ken Pomeroy)

Today I want to mention a stat which, for lack of a better term, I'm currently calling

2. Inside Defense

The stat is

Inside Def = (blocks + 1)/(steals + blocks + 2)

Now, for an individual, this number is probably pretty useless. I could imagine an athletic SF or PF being tops on his team in both blocks and steals; moreover, a high ratio could mean either lots of blocks, or just not many steals.

For teams, though, I think this number might prove a little more interesting. At a quick glance around SEC stat pages, it appears that most teams get more steals than blocks, but the numbers are fairly comparable--the larger is never more than about twice the smaller.

Of course, there are numbers that speak more readily to where a team does its defensive damage. Opponents' offensive rebound rate, opponents' FG%, opponents' 3FG%, etc. I would love to have a way to combine all of the above in an interesting way, but of course rebounding and shooting stats dwarf steal and block stats, so there's no obvious way to do it.

For now, call my inside defense rating a novelty stat: interesting, but not really useful. It's a quick comparison of two largely under-noticed stats, which tend to come from two different areas of the floor.

I'll track it, and see if anything interesting can be said. I'll also try to come up with a more thorough inside/outside defensive number.

But as far as scaling a team's effective height, this one's useless. More tomorrow...

Measuring a team's average height, part I

2006-11-27T15:23:00.001-06:00

In Ken Pomeroy's 2006-2007 Big 12 Preview, he calculates a number he calls "effective height." He says the following about this stat:

Effective height is the average height of the team weighted by
minutes played. I thought it would be revealing, but there was only
a 1.2" difference between the tallest and shortest teams in the
conference.

Like Ken, I find the lack of interesting information provided by this number very dissatisfying. Some teams are just TALLER than others, and there should be a simple numerical method for quantifying this fact.

I ask (therefore) whether there is a way to tweak Ken's "effective height." For instance, a 6'5" PG may be a very nice thing to have, but--considering that he does most of his playing on the perimeter--does he REALLY affect your team's effective playing height by an entire six inches over (say) a 5'11" PG?

Said another way: isn't a 3-man team with a 5'11" PG and two 6'10" forwards somehow "taller" than one with a 6'5" PG and two 6'7" forwards, despite the fact that the average heights of the two trios are the same?

You might argue that if the PG is posting up and driving to the basket a great deal, or pulling lots of rebounds, then, yes, he DOES affect the team's height--though maybe still not as much as a PF would.

I might even agree with this argument. In fact, this line of thought leads me to several ideas. I'll look at the first one today.

1. An "inside shooting" stat. Ken Pomeroy calculates exactly this in the aforementioned Big 12 preview. He uses 100*(FTA-3PA)/FGA. Pomeroy says, "For regulars, values range from about -70 for pure perimeter players to +70 for pure post players."

If I'm going to eventually shoot for a weighted average of height based both on minutes played and on some sort of "inside rating," then I'm going to prefer a number between 0 and 1 rather than one between -70 and 70. To get there, we could (say) add a hundred to Ken's number and then divide by 200. Or we could do something like FTA/(FTA+3PA).

If we're just looking for a stat by which to scale "height" ratings for teams, I think we can do better than this one. Still, I find this stat fairly interesting (in either of the forms I mentioned above) as a measure of where a player does his shooting.

It may be even more interesting as a measure of where a team does its shooting. I'll keep track of it this season for SEC teams, so stay tuned.

In the meantime, idea #2 to follow tomorrow...

A couple of notes

2006-11-24T10:41:00.001-06:00

I'll try to begin previewing some of the big SEC games today. A couple of notes:

1. I will catch all the major SEC games that I can, but I'm a fan of UT and those will get first priority for now. If you are a particular fan of another SEC team and specifically want to see a preview, I'll accept requests.

2. I'll use a couple of experience-type stats in these previews. "Returning minutes" is nothing out of the ordinary. "Effective experience" is a stat I borrowed from Ken Pomeroy's excellent Big 12 preview. To calculate it, I give a newcomer 0 points, a sophomore 1 point, a junior 2 points, etc. Then I weight these numbers by last year's minutes ratio, and average the number over all returnees.

The basic numbers for individuals

2006-11-23T23:49:00.000-06:00

We've seen how to calculate team efficiency. Individual efficiency is a little dicier and less transparent. But by the same token, it's also a little more interesting, and there's more room to play. All stats in this post are individual stats unless otherwise noted.

Sometimes we need to normalize stats for minutes played, so we introduce percent-minutes (%min) and minutes-ratio:

%min = 100*(minutes played)/(minutes the team played)

min-ratio = (minutes played)/(minutes the team played)

Next we have to calculate individual players' possessions used. We use the same formula as for teams, except that we scale team offensive rebounds by (1) number of misses by the player in question, and (2) minutes played by the player in question. We get the following:

Poss = FGA + TO + .475*(FTA) - (Team OR)*(min-ratio)*(FGA-FGM)

We then ask who is using our team's possessions, and at what percentage? We introduce percent of possessions used (%poss):

%poss = poss/((team poss)*(min-ratio))

Next we proceed to scoring. We've already seen eFG and PPWS. Since we can estimate a player's possessions used, we may as well count points per possession (PPP):

PPP = Points/Possession

The other ways a player can end a possession are to turn the ball over:

TO-r = 100*(TO/Possession)

...or to go to the free-throw line (in which case we may as well go ahead and chart both how well he gets there, and how well he scores from there):

FTA-r = 100*(FTA/FGA)

FT-r = 100*(FT/FGA)

Rebounding is pretty straightforward, too. We want to know what percentage of rebounds a particular player grabbed out of those that were available when he was in the game. We chart offensive, defensive, and total rebounding rates.

OR-r = 100*(OR)/((Team OR + Opp DR)*(min-ratio))

DR-r = 100*(DR)/((Team DR + Opp OR)*(min-ratio))

TR-r = 100*(rebounds)/((Team rebounds + Opp rebounds)*(min-ratio))

Finally, we go to assists, steals, and blocks. Assist-rate (A-r) is number of assists a player recorded as a percentage of buckets that were made while he was in the game:

A-r = 100*Assists/((Team FG)*(min-ratio))

Steal-rate (S-r) is number of steals a player recorded as a percentage of opponent possessions that ended while he was in the game:

S-r = 100*(steals)/((Opp Poss)*(min-ratio))

Block rate (Bl-r) is number of blocks a player recorded as a percentage of opponent field goals that were attempted while he was in the game:

Bl-r = 100*blocks/((Opponent FGA)*(min-ratio))

The basic numbers for teams

2006-11-23T23:36:00.000-06:00

If we want to analyze statistics without things being skewed due to tempo--and we do--then what we need to look at is something called "tempo-free" or "possession-based" stats.

The main point is, we don't particularly care how many points per game a team averages, because PPG is dependent more on pace than on efficiency.

What we want to know is how effectively a team uses their possessions. Thus we are interested in stats like "points scored per possession" and "points allowed per possession."

But such stats are not published. In particular, "number of possessions" is not published. This is a problem, because we don't want to have to watch every single game to calculate them.

Luckily for us, basketball guru Dean Oliver developed a way of calculating number of possessions just from the box score. Ken Pomeroy has pulled Oliver's ideas into college hoops and built upon them. We borrow them.

The idea is to ask oneself in what way a team's possessions can end. And the answers one comes to are, (1) by a shot that isn't rebounded, and (2) by a turnover.

There is one difficulty: free throws. Sometimes one free throw ends a possession (if the front end of a one-and-one is missed); sometimes two free throws end a possession; and sometimes a free throw ends a possession that we already counted (if a player is fouled while making the FG). Ken Pomeroy actually watched a large sample of games, and determined that in college ball, about 47.5% of free throws end a possession. So that's the number we'll use. Our formula (therefore) is:

Possessions = FGA - OR + .475*(FTA) + TO

Now that we have possessions, we want to know what our individuals and teams are DOING with these possessions. The most obvious things they could be doing are scoring, missing shots, and turning the ball over. So we'll start with those.

We already have a couple of good stats for measuring missed shots (eFG and PPWS), so let's go on to scoring.

Team scoring is easy. We just ask how well a team converts possessions into points! We call the stat "offensive efficiency" (Oeff):

Oeff = Points/Possession

Likewise we can measure defensive efficiency--how well a team prevents the other team from converting possessions into points.

Deff = (Points allowed)/(opponents' possessions)

Since possessions are measured by means of shots, offensive rebounds, free-throws, and turnovers, we can break down a team's offensive (or defensive) efficiency by taking a closer look at these four categories. We call them the "Four Factors." The first is effective field goal percentage, which we've already looked at. The others are turnover rate (TO-r), offensive rebound rate (OR-r), and free-throw rate (FT-r).

TO-r just tells us what percentage of possessions end in turnovers:

TO-r = 100*(TO)/Possessions

OR-r tells us how well a team keeps its possessions alive by rebounding its own misses. But be careful--we don't want offensive rebounds per game, or even per possession. What we want to know is what percentage of our own missed shots we pull down. We set

OR-r = 100*(Team OR)/(Team OR + Opponent DR)

Finally, we want to know how often we get to the free-throw line, and make free-throws. We could take this as a fraction of possessions if we wanted, but the standard stat is to take free-throws as a percentage of field goal attempts:

FT-r = 100*(FT/FGA)

We just reverse all of the above team stats with opponent stats to analyze a team's defense, with one exception: we can't control how well our opponents shoot free-throws, so we use free-throw attempts instead for analyzing a team's defense:

FTA-r = 100*(FTA/FGA)

Refining field-goal percentage

2006-11-22T16:21:00.000-06:00

I'm going to begin with a few definitions and explanations of stats. The stats mentioned here and the ideas behind them are in no way original. They've been explained before, and better, by Ken Pomeroy and by John Gasaway and by Dean Oliver.

I include an explanation here mostly so that I can easily refer potentially confused readers to it when I invoke these stats later.

I'll start with shooting stats.

The problem is that "field goal percentage" is, in many ways, an inadequate stat. And by "inadequate," I mean "meaningless."

For instance, suppose Player A shoots 100 2-point shots, and makes 40 of them; and suppose Player B shoots 100 3-point shots, and makes 30 of them. Then Player A's field goal percentage is 40%, and Player B's is 30%. Yet Player B scored 10 more points from the field than Player A did, because 3-point shots count more than 2-point shots do.

There is an easy fix for this problem. Simply count threes half-again as much as twos when calculating field goal percentage. This stat is commonly called "effective field goal percentage" (eFG), and is calculated as

eFG = 100 * (2FG + (.5 * 3FG))/FGA.

Another problem comes in when a player shoots a lot of free-throws. To fix this we use another stat (borrowed from John Gasaway, who in turn borrowed it from John Hollinger), points per weighted shot (PPWS):

PPWS = (points)/(FGA + (.475 * FTA))

[The .475 is because Ken Pomeroy analyzed a large sample of college games and found that, between 2-shot fouls, one-shot fouls, and 1+1 bonus fouls, in the end approximately 47.5% of free-throws end a possession that wasn't already counted by a FGA.]

SouthEastern Hoops

2006-11-21T13:47:00.001-06:00

Welcome to my blog.

Allow me to introduce myself. My name is Hammie, and, for good or ill, I can no longer resist the world of the blogs.

The problem (you see) is that I enjoy analyzing numbers far too much. Any numbers will do, in fact; but I particularly like to stare at college basketball stats; I more particularly like to stare at SEC basketball stats; and I yet more particularly like to stare at UT basketball stats.

Worse, I like to talk about them.

I'll leave you to imagine how that goes over at parties.

This (therefore) is my very own basketball-numbers party. I'll throw around a few college basketball stats and numbers, with many a nod to Dean Oliver and Ken Pomeroy; I'll experiment wildly with numbers of my own; and, just for my friends at Hoopsville, I may even vacillate unpredictably between the first and third persons.

So, as I said, welcome! Drop by when you can, introduce yourself if you wish, and enjoy the 2007 season!