chance of bowl: 13.6%
On the heels of WatersDemos's excellent diary and the Bobby Knight Board discussion, I got to thinking that it might be worth while having a collaborative debate about the issue of payment to college football players. I would be especially interested in hearing from some MGoEconomists on this issue, given that there are some particularities of the labor market for football services that invite economic thinking.
The problem (if it is a problem) with the NCAA rule against players' selling their swag is that it seems to violate principles of personal property rights. So, the logical alternative is to allow players to sell their swag to whomever they choose. This creates an incentive structure in which recruits can be told by coaches that University X has a super rich booster who will give them $100,000 for a couple of signed jerseys. Lesser recruits might only be able to command, say, $50,000 over four years at a lesser school. At this point, college football becomes no different than minor league baseball or hockey, with the prearranged "jersey sales" being tantamount to signing bonuses.
But, this is only a problem if it is defined as a problem; that is, if our sepia-toned memories of what college football used to be like make us unwilling to accept that college football could be a farm system. On the other hand, humans use things like nostalgia and emotion to drive decision-making from time to time—it’s called “culture.”
So, one solution would seem to be a flat wage for all football players, outside of tuition, books, and whatever they currently get for pocket money. So, all players would be paid, say, $2,000 per month for 12 months, essentially a fairly lucrative campus job. That wage could even rise as they progress through college, so that by the time the NFL draft rolls around, the vast majority of players who don’t get selected might have a little money in their pockets to go to grad school, start a business, etc.
Two obvious problems with this:
- Other NCAA athletes don’t have access to this. It would only be football players; and
- Although the flat wage would prevent an above-board bidding war for recruits (since there would be no benefit to choosing University X over Y, unlike the return on choosing the Yankees over the Royals), it only creates a new level playing field on which rich boosters would compete under the table. In that sense, it doesn’t really solve any problems. That is, even if (and perhaps because) Terrelle Pryor would earn as much as Drew Dileo, there would still be incentives for back room payments.
Another solution is to create a farm system for the NFL, and force high school players to choose between college and the farm team. It stands to reason that if two of the three other major sports have farm systems, and the NBA has a sort of hybrid (the NBDL would be a true farm system if the players were allowed to sign directly from high school), there would be pressure for the NFL to follow suit.
It seems to me like the crux of the problem is that college football players (like baseball, hockey, and basketball players, and unlike college gymnasts or water polo players) possess a set of skills that, at their highest level, are highly in demand in the professional labor market. This creates all sorts of incentives for players to want to cash in on those skills.
This is what I want some economists’ take on: is it coincidence or causal that the two college sports where recruiting is dirty like dirt in a dirt sandwich are football and basketball, the two major revenue-generating pro sports that don’t have a fully-developed farm system, a la hockey and baseball? My working hypothesis is that having a well-developed farm system—which allows star players to get paid for their services prior to making it to the big show—that reduces the dirt in college baseball or hockey recruiting.
So, if we are truly concerned about such dirt, the solution would be to make the NBDL a true farm system, and to create a NFL farm system. The case of Brandon Jennings is instructive in this respect—recall that because he couldn’t go into either the NBA or NDBL right after high school, he went to Europe to play. I wouldn’t be surprised if this happens more in the future. In this sense, the Euro leagues are like the NBA farm system (see also: Ricky Rubio), but just a really inefficient one as of now.
Anyway, if the NFL did adopt a farm system, it would have to be done like the other farm systems, that is, in conjunction with the NFL. So, no competitive USFL or XFL or even Arena league nonsense. I actually think this could work, by the way. There are plenty of places where (1) football is beloved, (2) there is no local NFL team, and (3) plenty of rooting interest in a nearby NFL team. Or, more nationally, I’m sure the Dallas Cowboys’ farm team—even if it was located in, say, Louisville, KY—would generate plenty of suppport.
So I guess the three questions are:
- Is selling swag under the current system a problem?
- Would paying players more help the problem?
- Would an NFL (and true NBA) farm system be (a) economically viable, and (b) solve the problem of dirty practices in college football and basketball?
I'll hang up and listen.
[Ed.: Bumped for awesome.]
For pathos purposes only.
Rodriguez: Trouble at Schembechler!
Assistant: Oh no - what kind of trouble?
Rodriguez: One on't zone reed gone owt askew on spreadshred.
Rodriguez: One on't zone reed gone owt askew on spreadshred.
Assistant: I don't understand what you're saying.
Rodriguez: [slightly irritatedly and with exaggeratedly clear accent] One of the zone reads has gone out askew in the spread n’ shred.
Assistant: Well what on earth does that mean?
Rodriguez: I don't know – Mr. Magee just told me to come in here and say that there was trouble at Schembechler, that's all - I didn't expect a kind of Coaching Inquisition.
[The door flies open and Cardinal David Brandon of Domino’s enters, flanked by two junior cardinals. Cardinal Rosenberg has goggles pushed over his forehead. Cardinal Fatcatalumnus is just Cardinal Fatcatalumnus]
Brandon: NOBODY expects the Coaching Inquisition! Our chief Replacement Candidate is Hoke...Hoke and Miles...Miles and Hoke.... Our two Replacement Candidates are Miles and Hoke...and Patterson.... Our three Replacement Candidates are Miles, Hoke, and Patterson...and an almost fanatical devotion to Harbaugh.... Our four...no... Amongst our Replacement Candidates.... Amongst our Replacement Candidatery...are such candidates as Miles, Hoke.... I'll come in again.
[The Cardinals exit]
Rodriguez: I didn't expect a kind of Coaching Inquisition.
[The cardinals burst in]
Brandon: NOBODY expects the Coaching Inquisition! Amongst our Replacement Candidatery are such diverse candidates as: Miles, Hoke, Patterson, an almost fanatical devotion to Harbaugh, and nice red uniforms - Oh damn!
[To Cardinal Rosenberg] I can't say it - you'll have to say it.
Brandon: You'll have to say the bit about 'Our chief Replacement Candidates are ...'
Rosenberg: [rather horrified]: I couldn't do that...
[Brandon bundles the cardinals outside again]
Rodriguez: I didn't expect a kind of Coaching Inquisition.
[The cardinals enter]
Rosenberg: Er.... Nobody...um....
Rosenberg: Expects... Nobody expects the...um...the Coaching...um...
Brandon: Coaching Inquisition...
Rosenberg: I know, I know! Nobody expects the Coaching Inquisition. In fact, those who do expect -
Brandon: Our chief Replacement Candidates are...
Rosenberg: Our chief Replacement Candidates are...um...er...
Rosenberg: Hoke and --
Brandon: Okay, stop. Stop. Stop there - stop there. Stop. Phew! Ah! ... our chief Replacement Candidates are Hoke...blah blah blah. Cardinal, read the charges.
Fatcatalumnus: You are hereby charged that you did on diverse dates commit heresy against the House of Bo. 'My old Michigan Man said follow the--'
Rosenberg: That's enough.
[To Rodriguez] Now, how do you plead?
Rodriguez: I’m innocent.
Brandon: Ha! Ha! Ha! Ha! Ha!
Rosenberg: We'll soon change your mind about that!
Brandon: Miles, Hoke, and a most fanatical -- [controls himself with a supreme effort] Ooooh! Now, Cardinal -- the MAJOR VIOLATIONS!
[Rosenberg produces a ONE-PAGE LIST OF NCAA MAJOR VIOLATIONS. Brandon looks at it and clenches his teeth in an effort not to lose control. He hums heavily to cover his anger]
Brandon: You....Right! Tie him down.
[Fatcatalumnus and Rosenberg make a pathetic attempt to tie Rodriguez to the sheet of NCAA Major Violations]
Brandon: Right! How do you plead?
Brandon: Ha! Right! Cardinal, make the public [oh dear] make the public believe the violations.
[Rosenberg stands there awkwardly and shrugs his shoulders]
Brandon: [gritting his teeth] I know, I know you can't. I didn't want to say anything. I just wanted to try and ignore your crass mistake.
Brandon: It makes it all seem so stupid.
Rosenberg: Shall I...?
Brandon: No, just pretend for God's sake. Ha! Ha! Ha!
[Rosenberg pretends to publish the violations in the Free Press using a plastic coated dish rack as a printing press]
[Cut to them torturing Rodriguez]
Brandon: Now, Rodriguez -- you are accused of heresy on three counts -- heresy by Game Captains, heresy by Hick Accent, heresy by Not Understanding the Rivalry, and heresy by the Number One Jersey -- four counts. Do you confess?
Rodriguez: I don't understand what I'm accused of.
Brandon: Ha! Then we'll make you understand! Rosenberg! Fetch...THE INFLATABLE MICHIGAN MAN SEX DOLL!
[Rosenberg holds out an INFLATABLE MICHIGAN MAN SEX DOLL]
Rosenberg: Here it is, Lord.
Brandon: Now, Rodriguez -- you have one last chance. Confess the heinous sin of Tiny Slot Ninjas, reject the works of Casteel -- two last chances. And you shall be free -- three last chances. You have three last chances, the nature of which I have divulged in my previous utterance.
Rodriguez: I don't know what you're talking about.
Brandon: Right! If that's the way you want it -- Cardinal! Poke him with the Inflatable Michigan Man Sex Doll!
[Rosenberg carries out this rather pathetic torture]
Brandon: Confess! Confess! Confess!
Rosenberg: It doesn't seem to be hurting him, Lord.
Brandon: Have you got all the air in the schlong?
Rosenberg: Yes, Lord.
Brandon [angrily hurling away the Inflatable Michigan Man Sex Doll]: Hmm! He is made of harder stuff! Cardinal Fatcatalumnus! Fetch...THE $2.5 MILLION BUYOUT!
[Zoom into Fatcatalumnus's horrified face]
Fatcatalumnus [terrified]: The...$2.5 million buyout?
[Rosenberg pushes in a GIANT PILE OF MONEY]
Brandon: So you think you are strong because you can survive the Inflatable Michigan Man Sex Doll. Well, we shall see. Rosenberg! Put him in the Giant Pile of Money!
[They roughly push him into the Giant Pile of Money]
Brandon [with a cruel leer]: Now -- you will stay in the Giant Pile of Money until another coaching job opens up, with only a year-long break on ESPN as an analyst. [Aside, to Rosenberg] Is that really all it is?
Rosenberg: Yes, Lord.
Brandon: I see. I suppose we make it worse by shouting a lot, do we? Confess, man. Confess! Confess! Confess! Confess!
Rosenberg: I confess!
Brandon: Not you!
Inspired by all of the great statisticatin’ done by such MGoUsers as Misopogon, the Mathlete, and, most recently (and in the past), MCalibur, I decided to look into something I’ve been wondering about for a while. Well, four somethings really, all related to the importance of yards on first down in determining eventual success at getting first downs and sustaining drives:
How much do varying numbers of yards on first down affect the probability of getting a first down (or a touchdown) in that series?
Here I was simply wondering about the “how much?” question. It goes without saying that losing 10 yards on first down (or starting first and 20) reduces the probability that you will get a first down, but by how much? Similarly, obviously the more yards you get on first down, the better your chances are of getting a first down on the series, but by how much? Are there thresholds beyond which your probability of getting a first down increases appreciably, or is it more or less a linear relationship, where every additional yard on first down increases your probability of getting a first down by the same amount?
How much variation is there between teams in their ability to recover from bad first down plays?
My assumption here was that with principally running teams like the RR-era WVU, it is harder to overcome a bad first down play than with more balanced teams like the Lloyd-era UM or the Vest’s OSU teams. Conversely, I assumed that when the RR-era WVU or UM teams got at least four yards on first down, a first down on the series was virtually a lead pipe cinch. But, as these were only assumptions, I was interested in doing some analysis to check this out.
How much variation is there across games in the ease with which first downs are gotten, and in the effects of various numbers of yards on the probability of getting a first down?
For example, you would think that statistically it would be easier to get a first down on any given series in a home game, other things equal, right? Or, it would be harder to get a first down on any given series in a game against an opponent with a better defense, right?
Based on my data, the answer to both of these questions is NSFMF. I’ll explain later.
How much do things other than the focus of the analysis, like field position and penalties, affect first down probabilities?
When I started, I knew I wanted to compare Lloyd-UM with RR-UM and RR-WVU, since I wanted to see how the spread n’ shred in its mature form would compare with the more anemic version (UM 2008-2009) and with the DeBordian “rock, rock, rock, rock, rock, ICBM, rock, rock, rock (also rock)” approach. In compiling the sample, I made several choices:
- I did not look at UM in 2008 because I thought it would unfairly penalize Michigan and/or RR, and also I’m pretty sure we invaded Grenada that year and they called off the season.
- I added another comparison team, the 2006-2009 OSU juggernaut. Damn, those guys won a lot of games in those years. Fuckers…
- I omitted all Baby Seal U games (e.g., OSU vs. Youngstown State, UM vs. Delaware State, and WVU vs. Eastern Washington) except
- which I included. I debated about this latter non-omission because I didn’t want to unfairly stack the deck against Lloyd, but I figured (1) omitting Baby Seal U from the other coaches actually (slightly) stacked the deck in favor of Lloyd, and (2) there are Baby Seal Us and then there are Appy State Us.
This is a picture of an actual baby seal.
As for the unit of analysis (or “record” or “case,” depending on your disciplinary background), you may or may not know that ESPN.com publishes the play by play for each game, with pretty detailed information on each play.
At the game level, the sample consists of 122 games played from 2005 to 2009 by three schools (OSU, WVU, UM) and three coaches (Tressel, Rodriguez, Carr). For each game, I recorded:
- the game number in the season (i.e., first, second, …, thirteenth);
- the opponent’s total defense ranking (from NCAA.org); and
- whether it was a home game or not (away- and neutral-field games were coded the same. In retrospect I probably should have distinguished between these, but it didn’t end up mattering anyway).
At the play/series level, the sample consists of 3,529 first down plays and the series these plays began. For the teams of interest (i.e., not the opponents), I recorded the following data for each first down play:
The dependent variable was whether the series ended in a first down.
The primary independent variable was the number of yards gained on first down.
The control variables were:
- the field position on first down;
- the yards to go on first down;
- whether there was an offensive or defensive penalty (or both) on the series (penalties on first down, where first down was repeated, figured into the “yards to go” variable);
- whether there was a turnover on the series;
- whether there was low time (less than a minute) in the second or fourth quarters;
- whether there was a pass or run on first down;
- the quarter the series took place in; and
- the number of previous first downs for the drive in which the first down took place (so, if it is the first first down play in a drive, this variable would be scored 0; if a team makes a first down, this variable would be scored 1 for the second first down play in the same drive).
Table 1 below shows the sample by season and team.
Hierarchical Linear Models
My initial plan was to run two-level hierarchical linear models (HLM), in which first-down plays/series are nested within games. Briefly, HLM allows you to calculate how much of the variation in the dependent variable is due to level-1 (play/series-level) factors like yards on first down, field position, etc., and how much is due to level-2 (game-level) factors like opponent defensive strength, home/away game, etc.
Essentially, HLM would calculate the average probability of getting a first down, as well as the effect of the level-one independent variables on that probability, for each of the 122 games, and then those parameters would be the dependent variables to be predicted as a function of level-2 (game-level) variables.
Fortunately for those of you who are about to stop reading, one of the things I discovered is that there is not significant variation from game to game either in the probability of getting a first down, nor in the effects of the level-1 independent variables, to support an HLM analysis.
This does not mean that, for example, UM had exactly the same average success in getting a first down against OSU as they did against Eastern Michigan. What it does mean is that there is not so much variation from game to game in this average probability that it makes sense to predict that scant amount of variation with game-level factors.
The Probit Binary Response Model
Hence, the following is just a play/series-level analysis, which is probably more intuitive for the reader anyway. Because the dependent variable is dichotomous (0 if no first down on the series, 1 if first down or touchdown), I used the probit binary response model (PBRM). For those of you not steeped in this method, the PBRM is one of several regression-like methods for binary dependent variables.
Probit coefficients are in the metric of the standard normal cumulative distribution function (CDF), also known as z-scores. When you evaluate the standard normal CDF at a given value, it tells you the probability of scoring a “1” on the dependent variable.
The sign and magnitude of probit coefficients are interpreted in the standard way: a negative effect means that the variable lowers the probability of scoring a “1” on the dependent variable, positive coefficients mean that the variable increases the probability, and larger coefficients (in absolute value terms) mean stronger effects.
Except for Table 3 below, I have transformed all coefficients into probabilities, so you don’t have to worry about the metric of the coefficients.
Several Words on Sampling Error
You may remember from some statistics course that it is generally good practice to report not just the point estimates from any statistical analysis, but also an estimate of sampling error. This is why when networks report polling data, they usually say something like “Candidate X is leading Candidate Y by 5 points [the point estimate], with a margin of error plus or minus 3 points [the sampling error estimate].”
Virtually all statistical software packages (I used Stata/SE 10) assume that the data were gathered via a simple random sample, in which all samples of a given size have an equal probability of selection. Clearly, my choice to non-randomly sample three teams and five seasons, and then take a census of all games (except for Baby Seal U games) and first down plays violates this assumption. Hence, this analysis isn’t necessarily representative of the nation-wide effects of first down yards (and other variables) on first-down probabilities. You should interpret all of these findings as merely relating to UM, OSU, and WVU for the years specified.
Figures 1 and 2 below show, respectively, the number of yards gained on first down and the starting field position for any particular series. Recall that there can be multiple series within a drive, so Figure 2 should not be interpreted as the starting field position for the drive.
Note from Figure 1 that the modal number of yards gained on first down is zero. Obviously, this can occur via an incomplete pass, a completed pass for no gain, or a rush for no gain. The distribution is right-skewed, although fairly normally distributed (excluding the zero yards bar) within a range of about a loss of 10 yards and a gain of about 20 yards.
Note from Figure 2 that the modal starting field position is 80 yards from the opponent’s goal line (or the offensive team’s 20). This is largely due to touchbacks on punts or kickoffs, of course.
Table 2 below shows the descriptive statistics by team for the variables used in the analysis. Note that the percentage of first down plays where the series ended in a first down or touchdown ranges from 66% for the 2009 UM team to about 76% for the 2006-2007 WVU teams. This should explain in part the 5-7 record of the former team and the shredding of opponents achieved by the mature WVU teams. Interestingly, OSU and Lloyd-era UM had about the same overall probability of getting a first down.
Time will tell if the RR UM teams can recapture that glory, or whether the spread n’ shred was simply more effective (1) in the Big East, (2) with Pat White/Steve Slaton, or (3) both (1) and (2).
One bit of hopeful evidence comes from the opponent total defense rank (near the bottom of Table 2). It doesn’t appear as though WVU played an appreciably easier average schedule than OSU, and if anything, WVU’s opponents finished their seasons with, on average, better-ranked defenses than either Lloyd-era or RR-era UM.
In terms of the primary independent variable of interest, Figure 3 shows the distribution of yards gained on first down, by team. Note that RR-UM was more likely than the other teams to lose from 1 to 4 yards on first down, less likely to gain from 3 to 5 yards, more likely to gain 6 or 7 yards (there may be a small sample size problem here), and less likely to hit a big play on first down (10 or more yards) than OSU or WVU.
Interestingly, RR’s WVU teams were less likely to gain 0 to 2 yards on first down, which is probably largely due to the lower percentage of passing plays on first down for WVU (17% vs. about 32-34% for the other three teams. This should demonstrate that RR/Magee understand that when you have Pat White, you run the ball on first down (and most downs thereafter). When you have Tate, you have to be more balanced. Say, maybe these guys do know about football…
Other points of interest from Table 2:
- Lloyd’s teams were more disciplined on offense with respect to penalties than the Vest’s teams--about 4.7% of OSU’s series had at least one post-first down offensive penalty (recall that the first down penalties were folded into the “yards to go” variable), compared to 2.8% for Lloyd-UM. RR’s teams fall in between.
- On the other hand, the Vest’s teams drew more post-first down defensive penalties than RR’s teams. Perhaps the passing attack invites more encroachment/pass interference calls than a more ground-based attack?
- Turnovers! About 7.6% of RR-UM’s series ended in turnovers, compared to 4.0 to 4.7% for the other teams. Yikes.
Figures 4-6 show some results from the regression analysis. First, Figure 4 shows the probability of getting a first down after selected numbers of yards on each first down play, assuming (1) it was first and 10, and (2) there was no penalty on the series.
Note that losing five or more yards on first down gives you about a 0.25-0.30 probability of getting a first down, whereas, obviously, gaining 10 or more yards is by definition a first down (on first and 10 at least).
In between these extremes, the first down returns to yards on first down is basically linear, though there are fairly noticeably inflection points between losing 5 or more and losing 1 to 4 yards (the first two points in the curves) and between gaining 3 to 5 and gaining 6 or 7 yards. By the way, I chose these categories based on exploratory analyses that showed that there was no statistically significant difference between gaining, say, 0, 1, or 2 yards.
Finally, notice the similarity between the OSU and Lloyd-UM curves. This shouldn’t be particularly surprising, since those teams pursued fairly similar offensive strategies--lots of off tackle to Hart/Wells interspersed with daggers to Manningham/Ginn.
I was interested to see that WVU dominated the story, at all categories of yards gained on first down. That is, it isn’t true that the WVU offense bogged down especially on small losses or gains on first down. A great offense will overcome.
Figure 5 shows the probability of getting a first down by field position on first down, in 10-yard increments. There are basically four points here:
- Being inside your own 20 reduces your probability of getting a first down, probably because of more conservative play calling;
- There is basically no difference between the 20 and the 50;
- Probabilities go up between the 50 and field goal range (a field goal attempt was coded 0 on the dependent variable, since there was no first down or touchdown);
- The probability goes way down in field goal range, probably because coaches elect to take the 3 points instead of going for it on 4th (see the Mathlete’s excellent diary on this).
Figure 6 shows basically the same trends, broken down by teams. There isn’t much to see here, except that WVU was awesome, RR-UM sucked, and OSU/Lloyd-UM were basically indistinguishable. It looks like a good rule of thumb is that WVU had a 10-percentage point better probability of getting a first down than RR-UM and a 5-percentage point advantage over the Vest and Lloyd.
Table 3 shows the full regression results. There isn’t much new here, but just to recap:
- Yards on first down matters a lot (duh I);
- WVU kicked ass;
- It’s harder to get a first down on first and 20 than first and 5 (duh II);
- Field position doesn’t matter as much as you might think;
- Offensive penalties make it harder to get a first down; defensive penalties make it easier (duh III); and
- Ceteris paribus, passing on first down increases the probability of getting a first down on that series (though in analysis not shown here, I found that, not surprisingly, it increases the chances of a turnover [see Hayes, W.]).
One other thing: in the note to Table 3, it says that the “Pseudo R2” is .3008. This is a statistic calculated in the PBRM that is analogous to the R2 (r-squared) statistic in linear regression, which is interpreted as the percentage of the variation in the dependent variable that is explained by the model. It’s hard to say whether 30% is a lot or a little; all I know from the coding is that there were lots of series in which a team would lose 10 on first down and still get a first down, and others where they would gain 9 on first down and fail to get a first down. So, there is still a large stochastic component to the process.
Stuff You’d Think Might Matter but Didn’t, Statistically
Statistically, variables that had no significant (but see “Several Words on Sampling Error” above) effect on the probability of getting a first down (net of the other variables included in the model shown in Table 3) included:
- Home vs. not home game;
- Which game of the season it was;
- The quarter of the game;
- The drive number (these last two suggest that there is not a robust effect of either “bursting out of the gate,” nor of “starting sluggishly.” Sometimes teams start strong and finish weak, other times the reverse happens);
- Number of previous first downs on a drive. This was interesting to me, because one often thinks, I think, that teams get “hot” on a drive. In other words, each first down makes it successively easier to get the next first down. My analysis suggests this is not true, at least in these data. There are a couple of explanations for this: one is that it does get slightly easier to get a first down the closer you get to your opponent’s goal line (though not in the field goal zone), so the two effects are collinear--the more first downs you get on a drive, the better your field position is, and it is that latter issue that affects first down probabilities. The second goes back to the stochastic component--there are just as many drives where a team will gain 3 first downs and then stall as ones where they will gain 3 first downs and then 2 more.
I have few beyond the things I’ve already mentioned. Basically, yards on first down are incredibly important, but not in any surprising way. The more yards you get, the better your chances are of getting a first down. However, there is a large random component to getting first downs, so yards aren’t everything.
In terms of UM football, it is clear that the mature spread n’ shred is lethal. But you already knew that. The question is whether UM can recapture that WVU magic. I guess I’m optimistic, for several reasons:
- The RR offense requires experienced, athletic players, really at all offensive positions. This we now have, and/or are quickly cultivating.
- A heavily run-based offense is slightly less likely to turn the ball over and much less likely to suffer no gain on first down (due to the lack of incomplete passes). This bodes well for sustained drives.
- WVU played, on average, slightly better defenses (at least if you think total defense rank at the end of the season is a good indicator of defensive strength) than UM on average, and defenses that were as good as those played by OSU, on average. So, at least by this figuring, there is no reason to think that UM’s current schedule is too good for us to be successful.
Obviously, the $1M unanswered question is whether the RR offense will be as successful at UM as it was at WVU. The analysis I have done can’t really speak to this question, but neither does it suggest obvious reasons why it won’t be successful. It does show how powerful the WVU version was, and I for one support giving RR enough time to have a reasonable chance to put that offense into place.
Comments, suggestions, critiques? Let's have ‘em.
First off, I largely agree with ikestoys's diary (http://mgoblog.com/diaries/down-14-and-going-2). I have often thought that football is a game that rewards aggressive play calling, like going for two and on fourth down more often, and fake punts from your own 20... Eh...
Anyway, I disagree with a couple of points ikestoys made, both explicitly and implicitly, and I thought I'd chuck 'em out here.
Trials are not independent
This point was made by a commenter in the original diary, but the basic idea of treating the different sorts of trials (going for 2, going for 1, overtime) as independent events (and therefore as amenable to the application of the mathematics of garden-variety probability theory) is flawed.
In football the outcome of one trial affects the probability of another trial even occurring, and not in predictable ways. Let's say UM had made the first two-point conversion. Would State have played their next drive differently than they did? Maybe, maybe not. Perhaps they would have come out throwing and scored a field goal to go up by nine. We have no way of knowing how things would have unfolded in that alternative universe.
Relative frequencies are not probabilities
Second, and another point made by a commenter, is that ikestoys treats relative frequencies (the proportion of successful two-point conversions) as the same thing as probabilities of success. They are not. That's like saying that because 1% of adults die of lung cancer, you have a 1 in 100 chance of dying of lung cancer. Do you smoke? If so, then your probability is surely higher. If not, it's lower. The point here is that the probability of success of a two point conversion depends on many factors, as various people have noted.
Because relative frequencies =/= probabilities, I thought it would be interesting to see how the probabilities of winning fared if you didn't assume the probability of a successful two-point conversion was 0.44. So, two graphs for your viewing pleasure. The y-axis is the probability of winning the game after all events have unfolded (post-touchdown try after TD 1, TD 2, and possibly overtime). The x-axis is the probability of success of the two-point conversion (I limited the range of this probability to between 20 and 80%).
Graph the first
In the first graph, I have plotted the cumulative probabilities of winning for two strategies: going for 2 after scoring a TD to be down by 8 (iketoys's strategy--the black line), and going for 1 (RichRod's strategy--the blue line). The only thing I have allowed to vary is the probability of success of a two-point conversion (on the x-axis).
- Note that I have reproduced the probability ikestoys does, where the dashed red line intersects with the black curve at about 57% when Pr(success) for a two-point conversion is 44%.
- Note also that despite ikestoys's implicit claim that going for two is always the better move, if the probability of success falls below 35.5%, it is better to go for 1, as RichRod did. I'm not suggesting that this is what the probability would have been, though people's comments about a dog-tired Tate, a driving rain, etc., make this idea not too farfetched).
There are two other variables in the process: the probability of a successful PAT (which I held constant at 0.95), and the probability of winning in OT. The latter probability doesn't change the black curve below much, so I left it at 50/50, as did ikestoys.
In the graph below, the three non-black curves represent three different probabilities of winning in overtime: 40% (orange), 50% (blue), and 60% (green).
The only thing to take away here is that if you believe your probability of winning in overtime is high (based on your style of play, being at home, etc.) and if you believe your probability of a successful 2-point conversion is less than 44%(ish), then you should adopt RichRod's strategy. If you believe that your chances of winning in OT is 50/50, and you believe your chances of scoring on a two-pointer are > 35%, then you should follow ikestoys's strategy.
In conclusion (I know, finally)
Of course, coaches don't think this way in the heat of a game. Again, I basically agree with ikestoys, but the story is a bit more complex.
The bottom line: UM swept, 25-19, 31-29, 25-20. You can read about it at http://mgoblue.com/volleyball/article.aspx?id=184662. UM beat Tennessee, host Xavier, and ND in the three-day tournament, and are now 5-0 on the year.
Couple of observations from the match:
1. Juliana Paz is a beast. You know how when you watch women’s team sports and there’s often one or two players who just play differently from everyone else (struggling not to use the phrase “play like men”)? That’s Juliana. She’s got a nice vertical, a whip of an arm swing, and is super intense.*
2. On that note, the whole team is very intense, especially Megan Bower. She has the look that was once written about in a theme song for a boxing movie. I liked how she encouraged her teammates but also didn’t suffer foolish plays gladly. She got after her teammates, and I’d wager that they don’t want to get on her bad side.
3. The other terminator on the team is Alex Hunt. She’s a lefty, but plays on the left side (I think she follows the setter Zimmerman). I found this strange, since lefties are usually more effective on the right side. Maybe her blocking isn’t up to snuff, I don’t know. Anyway, she hits what people call a “heavy ball.” Very little rotation on it, and in fact her arm swing isn’t particularly impressive, but she really drives it.
4. Lexi Zimmerman, the setter, is a lot of fun to watch. Very athletic, but also very clever with the ball. She had 4 or 5 kills on dumps to the middle of the floor, but also 2 or 3 more on shots to the deep right corner. I thought her left-side and middle setting were only average, but she's among the best I've seen at flicking it to the right side. She set a back slide in the first game off a really tight pass that made the crowd gasp. Also, her two left-side hitters really make her look good (Paz hit .385 on 39 attacks and Hunt hit a ludicrous .458 on 24 attacks).
5. It was an interesting match in that UM didn’t overpower ND at the net, especially in terms of blocking. I’d say blocking was the weakest part of UM’s game. Attacking, digging, and especially passing are where UM gets it done. I would say that the only phase of the game in which UM clearly outplayed ND was in passing, with Zimmerman’s athletic ability a close second. In other words, the ND setter was probably better at just delivering a hittable ball to the outside, but she wasn’t nearly as able to improvise off a poor pass. So, with UM’s overall better passing and Zimmerman’s ability to make something out of a poor pass, UM usually had better scoring opportunities on every play.
Finally, I would encourage people who live in A2 (and other B11 towns) to go to some matches this year. The team is a lot of fun to watch. Paz, Hunt, and Zimmerman are truly worth the (likely very low) price of admission.
I’ve seen a few matches at Cliff Keen over the years when the team wasn’t very good. I hear good things about how raucous it’s been lately, and the quality of the team this year (and last, of course) should only serve to feed the fans.
* I also may or may not be more than a little in love with her.
I'm not sure this is worth a diary; in fact, I tried to post it as a comment to the minor foofaraw in the comments in the Terry Talbott commitment post but I am an old man and couldn’t figure out how to do it in the reply.
Anyway, there is some minor ongoing debate about whether or not OSU pwns UM or vice versa, with those adopting the former position wishing to ignore the first decade or two's worth of games and those adopting the latter wishing to, well, not ignore them.
So, below is a handy graph I put together that allows you to calculate the UM winning percentage (100 minus which is not the OSU percentage, since that figure includes ties) from 1897 to 2008, using two different cumulative percentages.
The blue line calculates, for each year, the cumulative winning percentage up to that year. So, if you take 1957 as the reference point, you'll see that UM had won about 63% of the games up to that point. If you go all the way to 2008, you'll see that UM has won 54% of the games (i.e., in the whole series).
The red line calculates, for each year, the winning percentage from 2008 back to that year. So, again taking 1957, the graph indicates that UM has won 44% of the UM/OSU games from 1957 to 2008.
Note that the first point in the red line is equal to the last point in the blue line, or 54%. Also, the blue line is generally more favorable to UM, the red line more favorable to OSU. That's how come I chose the colors!
Note also the, erm, distressing trend from 1987 to 2008. So, from 1987 to 2008, UM won about half the games. The more recent the window of observation, the worse things look for UM; hence the shorter preferred time horizon for many of the Buckeye faithful. Conversely, the longer back one goes the better things look for UM; hence, the longer preferred horizon for UM fans.
Now you have all of the data you need to make whatever selective, cherry picked point you want to make. You're welcome.