Judging Play Success, Panthro Style

Submitted by MCalibur on July 7th, 2010 at 9:32 PM

[Ed: MCalibur, apparenly an economist  found himself collateral damage on today's shotgun blast at "X is stupid" sports economists. Maybe I should have come up with a label like "freakonomists" so as to not implicate people who are just interested in the numbers without the look at me pub. Anyway, here's an excellent diary on what your goals should be on second and third down. Implications for a second and medium are interesting.]

panthro1 A while back The Mathlete sent out a Thundercat signal for some help shucking data for his database; at least that’s how I remember it. Any un-lame kid of the 80’s knows that when you see the Thundercat Crest you put on your spiked suspenders, pick up your laser shooting panther paw nun chucks, jump into the tank you built singlehandedly, and you roll; that’s all there is to it. I had no choice.

Anyway, we voltroned* our abilities together and came up with something pretty sweet. I have put together my own database, with Mathlete’s help, and can now do some of the same tricks he can. I’ve focused onto BCS-BCS matchups extending the thought of excluding mismatches; Michigan v. Eastern Michigan is still a significant mismatch.

*Oops, wrong cartoon but, then again, you simply cannot over-reference 80’s cartoons/shows. I pity the fool that disagrees. I feel bad for youngins that don’t know the glory of 80’s children’s programming. Also, am I the only one who thinks that Voltron and Zoltan might be related?

---

When I’m not eliciting unreasonable responses from otherwise reasonable people, I’m usually crunching numbers of some kind as if they were a motley band of mutants and aliens led by a grody and ancient mummy demon priest. Very often the numbers have something to do with football in general and, most often, Michigan football specifically. This time I wondered “how do we know if a play was successful or not?” This question has been asked and answered by some smart people before, but being the curious little twit that I am, I wanted to gauge it on my own.

Background

One way to go about it is Mathlete Style: Expected Points, a good but abstract method. One potential problem with focusing on EP is that doing so can drive you to scoring points where as the real goal is to win. It’s a subtle but important distinction. Depending on the situation, maximizing EP might not be the same as maximizing the probability that you will win. Maybe you would rather not score if doing so means giving Peyton Manning the ball back with 25 seconds left and less than a 1 score deficit. Besides, The Mathlete has this beat covered.

Another method is to use 1st Down Probability, the likelihood that a team will convert a new set of downs given the current down and distance. I think this is more appropriate to the microcosm of a play because the goal of a play is not necessarily to score it is to keep the ball and  move it forward, in that order. Scoring is the goal of an entire drive. To calculate 1DP, you do the same thing you would to derive EP, except you keep track of first downs instead of points.

Drawing Boundaries

Whenever you have a mountain of data, you need a way to focus your attention on what matters while still maintaining the value of having so much data in the first place. For this study, I’ve filtered on the following criterion:

  • Exclude plays involving a penalty of any kind.
  • The game must be close. My arbitrary definition is: all plays in the first and second quarter, third quarter plays where the lead is less than 17, and fourth quarter plays where the lead is less than 10. These values are arbitrary, but there are so many plays available that the sample sizes are still large enough that any additional precision is of negligible value. Also, any unimportant plays are swarmed by a large number of plays that are important, then math deals with the noise.
  • Results of the play are limited to –10 and +25 yards. The logic here is two fold. On the negative side, the average sack is good for about 6 to 8 yards, anything bigger than that is a fluke play (botched snap for example). On the positive side, most plays aren’t designed to go for huge gains. However, there are instances when an OC calls a play like that in order to exploit an advantage and not necessarily as part of a base strategy. Though relatively infrequent, both types of plays happen with enough regularity that they significantly shift the averages even though they are vastly outnumbered by more typical gains. This filter only excludes about 0.5% of all plays to the negative side and about 5.3% to the positive side.

Play Discrimination

Each play in the database has been assigned a 0 or 1 depending on whether or not it was part of a first down series, touchdowns are counted as first downs in this survey. Essentially, every play in a four down sequence is counted as a being part of a 1st down unless a punt or turnover occurs before a new set of downs is achieved.  Filtering the plays that made the cut (over 105k) by down results in the following scatter plot:

1stDnProb

Every point on the chart above has at least 15 samples, most have several hundred, some have several thousand, and 1st and 10 has almost 42,000 samples. The trends are self evident and really, really, strong.  A few comments on other decisions I’ve needed to make here:

  • The small black dots represent 4th down plays. They are essentially overlaid with the 3rd down plays which makes sense, the objectives in both cases is the same, convert to a 1st Down. If you’re in a 4th down decision, use the 3rd down line.
  • The curves for 1st and 2nd Down were both pegged to 100% probability of converting a new set of downs at zero yards to go; pretty obvious as to why, it’s the rules. On 3rd Down however, I opted not to peg it to y3 = 1 at x = 0 because even though the R-squared value doesn’t suffer by much (0.005 lower), the resulting curve significantly over estimates 3rd down success inside of 3rd and 5. Also, I think the gap could be real; how much error is there in spotting the ball (especially on QB sneak type plays)? To me this data implies that the ball is mis-spotted to deny a 1st Down conversion approximately 9% of the time. The incremental error of spotting the ball doesn't matter until you end up at 4th and inches.
  • For 1st down plays, I intervened on behalf of noise reduction by only including plays where the distance was in multiples of 5. The reason is that the rules say you start at 1st and 10 and the only way you end up with 1st and something other than a multiple of 5 is A) you’re inside the opponents 10, and B) multiple penalties or 1st down repeats after spot fouls. Plays that were rejected are largely noise; the legitimate plays (ex. 1st and X inside the opp. 10) act like 2nd down plays, so use that in those cases.

Generating Hard Targets

Now that we have a survey, we can use the information to answer the question I asked “what makes a successful play”? The question has been tackled before in the seminal tome The Hidden Game of Football. The DVOA system developed by Football Outsiders is based in concepts discussed in Hidden Game. Hidden Game presents the following goal schedule:

On first down, a play is considered a success if it gains 45 percent of needed yards; on second down, a play needs to gain 60 percent of needed yards; on third or fourth down, only gaining a new first down is considered success.

So, the goal schedule by down should be 4-ish yards on 1st Down10, 3 yards on 2nd and 6, and 3 yards on 3rd and 3. I haven’t read Hidden Game but this doesn’t look right, particularly in short yardage situations. For example, 2nd and 1 is a failure if you do not convert a new set of downs. Sure, the consequences of that failure are small because you are virtually guaranteed another chance to convert but gaining zero yards (we only have whole yard resolution) is failure by definition.

Brian Brown of Advanced NFL Stats fame has a better definition: a play is a success as long as your chances to convert a new set of downs are not hurt by the result of a play. The great thing about this definition is that it considers the opportunity cost of running a play. This simple idea probably explains why a lot of OC’s call conservative plays on 1st and 10, if you don’t advance the ball by about 4 yards, you’re worse off than you started.  Brown focuses his work on the NFL and has done this work for the League but he stopped at the first chart leaving the answer to the question abstract-don’t hurt your chances of getting a new set of downs. OK, but how do you avoid that?

Running an optimization routine on our curves gives us the concrete answer, a goal schedule by down and distance in chart form.

DnPlayYield

BULLETS

  • 3rd down is obvious, you need to gain all of the yards remaining or you’ve failed. Fourth down decisions should be avoided.
  • The 1st down requirement is virtually flat at a 37% yield, lower than what Hidden Game suggested.
  • The 2nd down requirement is asymptotic to 65% yield but reaches a requirement of 80% yield by 5 yards to go. Essentially,  you need at least 4 yards on 2nd and 5 to not have wasted the down.

 

Command Decisions

One last thing this data allows us to think about is a set of guidelines for when to be aggressive (B, E, aggressive) with the play call. Flee Flicker, anyone? Transcontinental (4:50)? Fumblerooski?

First down is all business, you must move the ball 37% of the way or you’re screwing yourself. Third down is also all business, you need to convert or risk deciding which poison tastes the best. Second down however, depending in the situation, that’s a down you can get jiggy with.

On a generic 1st and 10, there’s a 64% chance of converting a new set of downs. So, as long as you end up with about a 64% chance of converting on 3rd down, you can do whatever you want on second down as long as you don’t lose yards or give the ball away. That means, you need to end up at 3rd and 3 or better. On 2nd and 3 or better call in the B2s and Outkast, baby, ‘cause it’s time to drop bombs (over Baghdad).

Comments

Zone Left

July 4th, 2010 at 2:23 AM ^

When I was about 25, I noticed Thundercats was on the Cartoon Network.  I actually watched for a couple of weeks, and eventually saw an episode where the Thundercats actually won and Mumm-Ra was banished by the Ancient Spirits of Evil to somewhere  presumably bad for an undead mummy.

I felt like that completed my childhood in some small way.

Also, cool data.

victors2000

July 4th, 2010 at 8:08 AM ^

I never got into the Thundercats, but maybe I should, I'm still immature. I think our coaches experience with the system parrallels the knowledge here, else I would suggest that they take a gander at your data; then again, it certainly wouldn't hurt. Great diary, man!

colin

July 4th, 2010 at 8:32 AM ^

so glad you referenced HGoF.  Also love the resolution of the FO problem.  I always assumed I missed some seminal article where they decided on what constitutes success, but it felt off.  I still feel something's missing here, though I'm not in the correct state to determine what, if anything, is at issue.

zlionsfan

July 7th, 2010 at 11:21 PM ^

in this context, the problem is Palmer's: the description of success vs. failure is his, not FO's. (The link leads to a description of some of FO's current system, but not all. I don't believe they make the entire formula available, but I could be wrong.)

Nonetheless, I think all three are reasonable approaches. I like the idea of several similar systems, all kind of circling a particular idea and trying to outline it a little bit better. I think a bunch of people all saying "hey, here's a slightly different technique I used" is more likely to put us in a position to understand things better than that other approach, the people who say "I have done this because all these other people are flat-out wrong and stupid, plus I graduated from Princeton, ha ha."

Tacopants

July 8th, 2010 at 12:41 PM ^

The only thing I can think of is field position and timing.

Field position in that depending on your position, you may or may not get to use all 4 downs to generate yards, possibly throwing off the percentages given where you are.

Timing is a minor point, I'm not sure there would be enough data points to really skew the data negatively but includes: spikes, kneeldowns, and (unsuccessful) Hail Mary plays.  I'd think they're probably 1-2% of the data, not hugely significant, but still there.

03 Blue 07

July 4th, 2010 at 2:44 PM ^

Really good stuff, man. Thanks for this diary. I'm a bit of a dork, but not at all proficient in the type of statistical analysis you break out here. I think I might just print out your chart for reference and refer to it during some games. Yeah, that's dorky of me. But whatever. I like the opportunity cost aspect you've included. Well done.

EDIT: I think you and I and some others got into an e-slapfight over players suing USC recently. I remember seeing your handle and saying, "I feel like I know that handle- I think I usually agree with this guy/dig the stuff he puts up." Turns out that is correct. (Even though we were on opposite sides of the slapfight).

Swayze Howell Sheen

July 5th, 2010 at 12:01 AM ^

this is some awesome data and analysis. i could see a coach having a little copy of some of the graphs above on a crib sheet. 

do you have break downs of play calling (run vs. pass) on the fourth down plays? i'd be curious to see the results. in particular, is there a tendency to call runs too often on 4th and 4, vs. say 4th and 5? (i find myself trying to figure out why 4th and 4 looks so hard to convert -- perhaps a statistical anomaly, but the probability looked too low and i am guessing the number of samples was reasonable)

also, how big is the play database? why don't you all make it publicly available?

AAL

July 7th, 2010 at 10:22 PM ^

...honestly think unless you're Bill Belichick, you don't have that kind of analysis available. Maybe there are others in the pros. I've coached at the college level and I can tell this kind of stuff is the farthest thing from their (ignorant) minds. However, I think most sort of "know" it on an intuitive or subconcious level. First down, in particular, is always a point of emphasis.

Well done, MCalibur.

zlionsfan

July 7th, 2010 at 11:24 PM ^

I think that analysis is readily available to every single NFL team. Given the tools they have to examine specific plays in specific situations and the resources available to every team not owned by an absolute jackass who would rather spend money on a poo-flinging monkey than hire someone who understands what is necessary to win, I would guess the ability to look only at outcomes is widely prevalent. (Of course that says nothing about whether the analysis is ever used in game situations.)

It wouldn't surprise me if there were some college coaches who had something like this around and others who wouldn't touch it if you covered it with gravy.

Blue in Seattle

July 5th, 2010 at 1:05 AM ^

This is very interesting and from my memory of the Field position analysis by Mathlete, couldn't there be a cross referencing between these two?

Basically, if your field position indicates you should NOT punt, then doesn't 3rd down allow you to "get jiggy with it?"

I see this as another great tool to be used in the debate of the overall strategy on time of possession, or "if we've got the ball, they can't score".  Since the statistic "time of possession" seems to be viewed so skeptically.  But the reason I think that it is, comes from the belief that a drive that does not end in points, is a failed drive.

Just like in soccer, even if you do a great job of defense for 98% of the time, if you haven't scored then you can still lose when the opposing team finally gets a lucky shot from a goalie rebound.

or for football, that last second field goal.

That said, i like that you took this all the way to a decision making tool within the mini game of moving the sticks.  If you keep doing that successfully, eventually it ends in points.

good work.

 

zlionsfan

July 7th, 2010 at 11:34 PM ^

One problem with considering situations where a punt is not advisable is that it's difficult to use data like this to support that decision. We understand why 3rd down ought to be like 4th down, we can see the situations where punting really doesn't get you anything, but it's much more difficult to identify the "four-down territory" plays in an actual game. I think that becomes more important because current habits suggest that punting is almost always a good strategy and therefore 3rd-down defenses are typically geared toward preventing a 1st down rather than preventing non-1st-down success, presumably increasing the success rate of 3rd-down tries not intended to convert.

I think you're right that the idea behind ToP being less important is that it itself doesn't get you anything. Possessing the ball (usually) makes it more likely that you'll score and less likely that the opponent will, but posession itself isn't nearly as valuable as actually scoring until a certain point late in the game where points are less and less necessary to ensure a win.

Maybe it's just a counterpoint to the talking heads who constantly prattle about time of possession ... not that possession itself is bad, but that sometimes it's presented as if that were all that mattered. "Look at Team X's edge in ToP! Wow! You really win games that way!" And how often does it happen that it's actually the cart they're speaking of and not the horse? Well, yeah, Team X had a huge edge in possession because they were up 21 late in the third quarter and just started eating clock (and Team Y was in full-on panic mode). They had possession because they were winning, not the other way around. The same kind of thing you hear about "running the ball to win" ... "Team Z is 22-4 when Superplayer rushes for 100 yards or more."

Bosch

July 6th, 2010 at 7:43 AM ^

I did enjoy me some Thundercats but Cheetara was my favorite character....... largely because the show's run time coincided with me beginning puberty.

On a side note, I did not expect the type of photos that popped up when I google imaged "Cheetara."  It is apparent that I was not the only one who "favored" her.  Let's just say that it was difficult finding one that was actually of the cartoon character and not some fantastical representation.

Louie C

July 6th, 2010 at 9:17 AM ^

Great stuff, and I love the 80's cartoon refrences. Anybody else thinks Panthro was a brotha?

I hope you didn't jinx TC and Voltron. If I go to the movies one day and see a trailer/cuttout for either one of these, I will burn Hollywood to the ground myself.

oldcityblue

July 7th, 2010 at 10:16 PM ^

I will have to re-read and sit with this a bit but it's a great study. I certainly will be looking at 2nd down with a "time to get jiggy with it" approach!

steve sharik

July 7th, 2010 at 11:58 PM ^

  1. So, an offense with 2nd-and-10 has about a 55% chance of making a 1st down?  I find that hard to believe.
  2. Are the probabilities for defense simply 1-P(offense)?  If so this leads me to believe my hunch is correct: 1st down success is much more important for defense than offense.  It has been said that a defense needs to hold an offense to 3 yards or less on 1st down.  According to your model, an offense that gains 0-3 yards on 1st down still has at least a 55% chance at a 1st down.  However, a defense that gives up 4-9 yards on 1st down has about at least a 68% chance of giving up a 1st down.  Any defense that gives up 1st downs on 68% of its sequences is screwed.  (Heck, 55% is mediocre.)

MCalibur

July 8th, 2010 at 3:14 AM ^

1) That's what the data supports. If you plug x=10 into the y2 equation, you end up with P=0.522. Basically, 50/50 advantage offense. The average gain on a given play is a little over 5 yards. So, it does seem that it should only take 2 plays to get a new set of downs. To the overall 1DP, it's essentially 2 out of 3 -- y1(10)=0.664 -- two average plays gets the offense home.

2) I think that is the correct interpretation ("...probabilities for defense..."). However, I'd modify the rule of thumb down to 2 yard or less on 1st down. At 2nd 7 the math says the offense still has a 63% of converting as discussed previously. The offense literally has the ball in their court. Seven yards seems like a lot to go on 2nd down but it really isn't. I now see where a conservative offense can still be effective. That style is merely sitting on it's advantage instead of standing on it. I still think it's a inefficient style, but I understand it better now.

For me, this is yet more support that good defense is a special asset. If you have a defense that can tilt those odds in their favor, you're going to win a lot of games because all your offense has to do is not screw up because they already have an advantage.

I also think this data shows why bend-don't-break conservative defenses are fatally flawed. They bank on the fact that A) the clock will run out or B) eventually, the offense will screw up and ruin the advantage of being the offense. The problem is that the offense needs to fail on two out of three (or four) chances in order for the defense to eliminate/outlast the offense's inherent advantage. Apparently, that (2 failures out of 3 or 4 plays) only happens 11-ish % of the time for a typical BCS team facing par competition.

imafreak1

July 8th, 2010 at 9:21 AM ^

Regarding conservative defense, I think your data supports its use. If on 1st and 10 the offense has a 64% chance of getting a first down (I presume that means that the offense has a 64% chance of getting a first down before 4th down and not <b>on</b> first down) then one need only make them go 10 or so yards at a time and they will quickly fail. Because 64% is not 100%. Make them roll the dice 3 times and you're an odds on favorite.

Maybe I don't fully understand this analysis (clearly, I don't because I don't know what an 'optimization routine' is and as a biologist it sounds kind of like a bullshit, bullshit routine to me but that's a completely seperate issue and the world, apparently, needs economists so it's cool) but the following quote also confuses me;

"The problem is that the offense needs to fail on two out of three (or four) chances in order for the defense to eliminate/outlast the offense's inherent advantage."

I guess it's true regarding the 'inherent advantage' you mention but that advantage is only about 60% according to your data. The defense needs only for the offense to fail on 3rd down to win. Further, a 60% chance of success when an offense likely needs to 'succeed' several times to score does not strike me as such a great advantage.

I'm not arguing for a conservative defense but rather debating your interpretation of the data.

Anyway, I enjoyed it. Thanks.

steve sharik

July 8th, 2010 at 11:21 AM ^

Regarding conservative defense, I think your data supports its use. If on 1st and 10 the offense has a 64% chance of getting a first down (I presume that means that the offense has a 64% chance of getting a first down before 4th down and not on [ed.] first down) then one need only make them go 10 or so yards at a time and they will quickly fail. Because 64% is not 100%. Make them roll the dice 3 times and you're an odds on favorite.

Yes, but let's say the average starting field position is one's own 25.  They then have 75 yards to go for a TD, or 7.5 1st downs (assuming the offense goes exactly 10 yards).  That's 7.5 sequences of downs, so the expected value of 1st downs during a series is .65(7.5) = 4.875.  Let's round that up to 5 1st downs at exactly 50 yards.  Even if the offense fails, they are at the opponents' 25 with a 42-yard FG attempt. 

I think this actually supports conservative offense and stifling defense, b/c if you just churn out only 2 1st-downs, you're close to midfield.  You then punt to put the opponent inside its own 15 and so on and so forth, gaining 10 yards of field position each series until you are close enough to score. 

I personally despise these tactics, and we might as well watch baseball, golf, or soccer if this is the way the game is played, but that's how one bespectacled, sweater-clad, grecian-formula-using individual in C-bus does it (that and stacking his roster with NFL talent).

In reality, these statistics support a strong kicking game and good field position.  Make the offense go 80 and one will likely be very successful.

imafreak1

July 8th, 2010 at 12:32 PM ^

With respect, you've created a false choice. Given the choice between a defense that bends but does not break and a defense that never gives up any yards who would ever pick the former? But that is not the choice. One can only play stiffling defense if one indeed has a stiffling defense.

However, we agree on your final statement. I believe that the stats greatly support the following conclusion*;

"In reality, these statistics support a strong kicking game and good field position.  Make the offense go 80 and one will likely be very successful."

This not a conclusion that I think most of the mgoblog commentariot supports, so I am interested to see the response.

*I am not advocating this position but merely interpretting the data.

steve sharik

July 8th, 2010 at 3:18 PM ^

I did not make it a choice b/w bend-but-don't-break and zero yards.  I made it a choice b/c BBDB and stifilng (2 1st downs per series instead of 5).  So, start at your own 25, make it to midfield, put the opponent on his 15.  Give up 2 1st downs to his 35, he punts to you at your 30.  Make it to his 45, punt to his 5, etc.

MCalibur

July 9th, 2010 at 5:45 PM ^

The optimization routine was pretty straight forward actually, just finding the X value that makes y2 = y1. As an example, y1(x = 10) = 0.663, in order to maintain y2=0.663, you need 2nd & a little over 6. The optimization routine did that work quickly and automatically rather than me having to do it manually, hunt & peck style.

Your interpretation of the data is interesting and valid. I suppose we're just trying to gauge water levels in a cup at that point. I see having a 66% chance of succeeding without doing anything special as encouraging (and surprising I might add).

Tacopants

July 8th, 2010 at 12:31 PM ^

I think the key piece missing is the 4th down data.

Think about it like this, if you can pound out 3 yards on each of the first three downs... you still have a pretty good shot at obtaining that 1st down.  Theoretically you should go for it.

However, many times due to field position, coaches will elect not to go for it on 4th and short and elect not to go for it.  This makes the sequence of 3 plays for 9 yards a failure, while in this, it doesn't really consider that.

Putting it another way, I'm assuming that the probabilities for a 1st down on a 3rd down are a dependent series of 3rd and 4th down.  If you have a 3rd and 5 @ 50%, its the probability you get 5+ yards on a play + (failure rate) * (the probability you get 4 yards on 3rd and 1+ yards on 4th and so on).  If, due to field position, it is unacceptable to go for it on 4th and whatever, you eliminate the added benefit of the 4th down success probabilities.

So position on the field can define your ultimate success metrics, but the overall probability doesn't change.  Through your defenition of success and strategy, if your 3rd and 5 turned into 4th and 1 at your own 35, you would most likely punt.  However, if you were at your opponenet's 35, you would most likely go for it.  The probability of a 1st down has not changed, your willingness to go for it has.  Therefore, two identical yardage sequences can look very different given field position.

Six Zero

July 8th, 2010 at 8:40 AM ^

  • Maybe it was because he had the nunchuks, which are simply cool...
  • Maybe it was because he had a tank, which is simply cool...
  • Maybe it was because Lion-O or whatever the heck is name was had all that hair, and Panthro was the freakin' token bald cat dude... What the hell was up with that, anyway??
     

jg2112

July 8th, 2010 at 9:00 AM ^

Just so I've got this clear:

If Michigan gains 3 yards on a 1st and 10 this fall, I've got to feel disappointed because they've fallen short of the statistically averaged amount of yardage a team is supposed to get on first down?

Am I allowed to just watch the game without having these subliminal issues of success and failure attacking my brain on every play?

jamiemac

July 8th, 2010 at 9:36 AM ^

The information is neatly organized, but it hasnt proven anything I didnt know from just watching football all my life. I'm not sure what any of this proves. Maybe it helps you guys call plays on computer games or something.

I mean trying to get better down and distance from first down is like football101. My junior high football coach in 1984 told us just get 3-4 yards on first down. I dont think he was reading off any charts in the process.

IPKarma

July 8th, 2010 at 10:04 AM ^

We've seen the stats on when to go for it on 4th down, based on field position.

Combined with this, I say it's strong support for going for it EVERTIME you are past the 50 and have less than 4 yards to go.

 

Brady2Terrell

July 8th, 2010 at 12:15 PM ^

I'm not sure I 100% agree with the logic posited here (as I understand it).  It seems to me that you're saying there's a generic 64% chance of converting 1st and 10, and if your first down play improves your percentage to above 64% (say, 75%), then let it fly on 2nd down as long as the 3rd down percentage will remain above 64%, the starting probability.

To me, success would be measured by improving your odds of conversion; thus, if on 1st down you go from 64% to 75%, the judge of the 2nd down play should be whether you improved on 75% or not (that is, judge the play independent of the series).  If you throw an incompletion and lose 10% probability of converting (down to 65%), it seems to me that the 2nd down play was a failure.

What would be great to see would be a chart of down and distance, and how many yards are necessary on 1st and 2nd down to consider the play a success (I agree that on 3rd and 4th the only satisfactory outcome is conversion).  With the math you've got, that would just be the yardage required to maintain the odds of converting at the beginning of THAT PLAY, rather than the series.

I would think some modifiers would be necessary for certain scenarios as well; if it's 3rd and 22 and you gain 20 yards to get inside field goal position, for instance, that would be a successful play.  This would require layer-on analysis, but would probably be the next step for a coach to really use it.

Thanks for the number-crunching!

MCalibur

July 9th, 2010 at 5:50 PM ^

You're right. In the scenario I discussed at the end, if the aggressive play call does not gain a yard or two, then it is a failure. But that's kind of the point, since you have some room to work with because of the work you did on first down, you can afford to run a low probability play (deep pass for example) and go for a big reward while risking relatively little. So, even if the play  fails, it's a good gamble.

To your question, the last chart is exactly what you've requested, only in ratio form. Multiply the chart value by the distance to get back to yards needed.

Renn

July 10th, 2010 at 7:05 AM ^

You have really given us all a lot to think about here. Thank you so much for taking the time to provide us with these tips and instructions. Also, thank you for the graph. There really is a lot to ponder.

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