One last thing with numbers

Ok, so I promised to get to my thoughts on going for the win at the end of a game as compared to kicking the tieing field goal as in KC - Oakland and TB - Washington. In both of these cases the ball was at the one-yard-line. Now, our stats from the last post do not apply, because your stats on converting a fourth and one at some yard-line which is not the one are higher than converting at the one, because the defense has to respect real passes when you are at the thirty (no, hokey passes to the eligible-receiver tackle or to the fullback running toward the sideline are not real passes). So we can say that we may have a sixty percent chance of making it on fourth and goal at the one (again, no definitive stats, but I would imagine this is in the neighborhood). Now if two teams are evenly matched, then they would pretty much have to each have a fifty percent shot at winning the overtime before it has started, right? So looking at it I don't really see how going for it could be a bad move. I mean, the players and the crowd want you to go for it, so you have nothing to lose there, and the media sure as hell wants you to go for it so they can blabber on about it forever. I commend Mr. Vermeil and Mr. Gruden for their decisions (and remember that a Mr. Leinart (yes him and not Mr. Carroll) was the first to do that this year, and when there was much more on the line (one loss does not ruin your NFL season, it does in college)), and I believe that I would have made the exact same decision in their shoes.

A few more Football Scoring Thoughts

Last time we talked a little about how sometimes getting one point all the time can be more valuable than getting two points most of the time. This time I want to talk about something that really bothers me in the NFL and college. I feel like coaches kick a field goal way too often, especially when they have a good offense. If it is 4th and 1 or 4th and 2 on the 25 or 30, and the game is up and down, with both offenses looking pretty good, then why settle for a FG that you will only make around 70% of the time (note: so far this year NFL kickers have made 69.3% of field-goals from 40-50 yards - number computed by taking data from http://www.nfl.com/stats/playersort/NFL/K-FIELDGOALS/2005/regular?&_3:col_1=19 and importing to an excel spreadsheet to get the sums quickly and accurately). I would choose my short yardage play of choice, whether that be a quick slant to a receiver, or banging it up the middle. If you don't make it, then the other team has to go a pretty long way to get a score, but if you do make it, then you leave the ball in the offense's hands to go and try to do something else good. If it ends up being 4th and 10 four downs later, then just kick the fg, 1-5 yards closer, and no harm done. The stats say that if you go for it on 4th and 1, you have a 70-75% chance of making it (see http://www.footballoutsiders.com/ramblings.php?p=131&cat=1 - I split out the 4th and 1 statistics from the chart and computed everything myself, and got 73.2% - the sample seems fairly large (183 attempts) so I figure 70%-75% is a fair range. On 4th and 2 it is impossible to calculate the exact data from that website, but I imagine it would be around 55%-60%, which still isn't a bad deal depending on the situation). So really, you have a better shot of making the 1st down than kicking the field goal... and not only that, but if you miss the field goal you lose seven or eight yards of field position too! And yet how many NFL coaches would go for it in this situation in the first quarter?

Now remember, we learned last time we always have to take all the factors of the game into account, but, with all things being equal I am surprised that we don't have people going for it more often. And remember also, getting a 1st down does not somehow guarantee us seven points, so it is a little more complicated than it seems. Lets just say that worst case we get seven or eight yards average in the next three downs (and I would imagine that the average is even higher than that - but if you can find me hard statistics that would be wonderful), and then we decide we want to kick. Assuming this moves us into the 30-39 yard field goal range, that improves our chances of making the field goal to 86.1%. Multiply that by the .732 probability you got the first on the last possession, and you get .630, which is only around 6% lower than the odds of making the 40-49 yarder.

I understand that the above was a very loose simulation, and a lot of things can go wrong in the next four downs as well (sacks and penalties moving you back behind where you were before, interceptions, fumbles, injuries, etc.) but we are assuming there is some inherent goodness to having your offense on the field despite all the bad things that could happen. And I am also assuming that the odds of you stringing together a few more first downs and getting into the endzone without having any more 4th down adventures is pretty reasonable, especially compared to the odds of the bad things happening.

That is all I want to say on that, because I could keep going deeper with various statistics, and field position ideas, and even looking at what bad things can happen on the kickoff if you make a field goal compared to losing it on downs. The thing about football is that you have to draw the line somewhere, because if you try to break every scenerio down into statistics, it gets really confusing, and you quickly realize it is impossible. You have to have some general ideas, and follow your gut. I say the above stats are mostly moot if you are a team like the Ravens or Bears (bad offense, great defense - three points goes a long way here, and you probably won't get seven anyway if you convert), and especially interesting if you are a team like the Colts or Seahawks (other way around - seven is what you really need, and you have a good shot at getting it if you get the 1st).

I promise this is my last super nerdy statistics post for a while, because honestly, the stats don't mean much, and I know it's boring for everyone else. I just want people to think about going for it as a much better idea than it already is (you can even think about going for it vs. punting it when you have it on your own 30 if you please - it will not be talked about by me however (and you can already hear the sighs of relief (and I think that nesting parenthesis is looked down upon moreso in writing than in Mathematics or Comp Sci, but that is what I am, so this is what you get))).

Thanks for bearing with all that (or ignoring it at reading the other posts anyway).

Kyle

Football Scoring and the Idea of Marginal Utility

While watching "Who Wants to be a Millionaire" one night with some friends, a few friends seemed to agree that if you were reasonably certain that you knew the answer, and you only lost half your money if you got it wrong, you were an idiot if you didn't guess. I mean, if you have $64,000 and if you get this question right you get $125,000, while if you get it wrong you get $32,000. Basic math says that if you have a 50/50 shot of getting it correct, if you guess you will have an average of $78,500 ($125,000 * .5 + 32,000 * .5), while if you don't you get $64,000. And the more sure you are that you know the answer, the higher the average amount of money you would get if you guessed becomes.

So, obviously, it seemed obvious to these very intelligent kids that you should take a stab and guess. However, they were assuming that your desire for money is linear. In other words you want $100 twice as much as you want $50, and $100 million twice as much as $50 million. However, this may or may not be the case, depending on the person. Personally I really don't want $100 million dollars more than $50 million dollars at all, and I'm sure that the utility of having $100 million dollars as opposed to $50 million dollars is minimal to the majority of people. The point is that just because you are willing to spend $X of money/effort to get one of something, you are not willing to spend $2X of money/effort to get the second one, and you sure wouldn't risk the first one to get three, four, or ten of more of these 'things'.

Now, how the hell does this relate to football? I mean, having more points is always beneficial right? Well, yes; however, there is always a cost involved, and things are never what they initially seem. Assume that extra points are made with 100% frequency (which they are not, but they are close, and the math does not significantly change if I lower this to 99%, it only gets more complicated), and also assume that the probability of winning the sudden death overtime is 50/50. Now, if Team A has a 60% chance to make all two point conversions, and Team B makes 50% of all of their two point conversions, then why wouldn't you always go for two? Unless there is a good reason get the sure point (to win the game for example) this will make it so that you will win more games than your opponent if you are otherwise evenly matched right?

Well, not quite. This relates to an essay I wrote in college, and is very similar to the deeply flawed college overtime system. Going second in the college overtime system gives you a tremendous strategic advantage. You know how many points you need to win/tie, and you can play your game based on that. If you need a TD to tie, you use all four downs, if you need a FG to win, you can just sit around and do nothing and then you have a 40 yard FG at the end of it. Now this would relate to the above example in the following way:

So lets say that in a tied game team A scores a TD with 3:00 left on the clock. In this case it would be a tremendous mistake to go for two, for the following mathematical reason. If B does not march down the field and score a TD, then the point is totally moot. However, if they do and they do not leave enough time on the clock for A to come back and win then A's decision is a bad one.

If A makes the two point conversion, then if B scores a TD they will go for two. If A misses then B will kick the extra point and win.

So if A makes the two point conversion and B scores a TD to tie, then there is a 30% chance A wins outright in regulation, a 30% chance it goes to the even money overtime, and a 40% chance that B wins outright in regulation.

Now, I will freely admit that this is one mostly irrelevant example, but it shows that it is not *always* a good idea to just follow the numbers. You have to take everything into context. While I believe that if you simulated these numbers with A blindly going for two and B playing "intelligently" then A would probably win the majority of the games, but I feel that is simply due to the very large difference between A and B's proficiency in making the two point conversion. If it was closer to a 1% difference I feel then you may see B winning more games than A, despite the apparent advantage that A has by merely going for two every time.

This was an introduction to this topic, and I will expand more on this tomorrow by adding the idea of going for 7 vs. going for 3.

Introduction to this blog

Football. The most watched sport in America, and probably the most closely scrutinized sport in America. In no other sport do you only have only 16 games to prove your worth as a team (and even fewer at the high school and college levels). In no other sport do you have so many people who all have a roll in contributing to your team's success. In no other sport do the coaches have as much influence on determining the outcome of a game as in football.

I am beginning this blog because I feel that there are many aspects of the game which are not covered by the major news outlets, and many angles that are not looked at. As I said in the first paragraph, offensive playcalling, defensive scheming, and game planning are all humongously important in football, and I do not think there is a sport in which the things done off the field have as large of an impact on what is done on the field. Now, this is only true to a point, because if you have defensive tackles who cannot clog the lanes, corners who cannot cover, or an o-line that cannot block, then what is done off the field is largely useless. However, I am of the opinion that in the NFL, all teams have the same skill level, to a point. Obviously the Texans have more problems than the Colts in terms of personnel; but, I feel that the gap is not sooo large that it cannot be overcome, or at least played down enough to make a game out of a meeting between the two. And any team can always improve their roster in the offseason.

Now, I am not likely to help out a team by being on their active roster for a game, but I figure I can at least make interesting comments about the coaching, and more specifically the playcalling and scheming that goes on during a game. Now, I will freely admit I am more or less the worst writer in the universe, but just know that my writing is meant to sound like it is spoken. Hopefully you can limp through it without exploding, and I promise I will try to make it as managable as possible (and yes, I imagine that my semicolon use in the previous paragraph has high school english teachers everywhere cringing... get used to it).

In this blog, I will also try to make some broad comments on various issues that swirl around this game, which always seems to be full of controversy. Hopefully this is an enjoyable read for everyone, and hopefully some of my posts make some people think, and I expect some responces to do the same for me. See you tomorrow with a look at the "risky calls" the last two weeks at the end of the Chiefs and Redskins games.

Kyle