This is the 8th in a series of articles I am writing to analyze some common NFL statistics, focusing on how much value they have relative to team wins. I want to acknowledge the work of Brian Burke, Chase Stuart, and even our own Matt Grecco, who inspired this analysis and whose methodologies I have leveraged, as well as Pro Football Reference, Armchair Analysis, NFL.com and the nflSCrapR project as the sources of my data.
Last year, my articles focused on stats I hate, which in retrospect was a little negative. In my defense, Colts fans had just endured a season of replacement QB play for the 2nd time in 7 seasons with a mediocre 8-8 record sandwiched in between. So, maybe I was a little bitter.
However, since then, the Colts won 10 games, notched a playoff win, Andrew Luck looked great and the rookie class was outstanding — also Josh McDaniels did not become our coach and Ryan Grigson was still gone. So, feeling a little more positive, I’m changing tack and writing about a stat I love and why you should too.
Drive Success Rate (DSR) is one of my favorite NFL stats. It is simple to understand, easy to calculate, doesn’t require detailed data, ranks offenses and defenses well and is more predictive of wins than almost any other game level stat. It is also a stat that most people have never heard of.
. . . of which most people have never heard?
. . . for which most people it is unheard?
. . . whatever. Strap in, this might get mathy.
WHAT IS IT?
Pop quiz. Assume an offense starts a drive at their own 25 yard line and on each successful series, they gain 15 yards. Furthermore, assume that there is a constant 70% chance they convert each series into a first down. What is the probability that this drive ends in a TD?
ANSWER: Since the drive is 75 yards from the end zone and each series will be 15 yards, then we know it will take exactly 5 sets of downs (yards from end zone / successful series length). Therefore, thanks to some long-dead French gamblers and extremely lax assumptions about variability and event dependence, we know the probability of these 5 consecutive events is the probability of each multiplied together:
- TD probability: 70% ^ 5 = 16.8%.
Well, that wasn’t too difficult and we can even make a general solution if the inputs are allowed to vary:
- TD probability = % chance of series conversion ^ (yards from end zone / successful series length)
If I wanted to apply that model to historical NFL data, yards from end zone and successful series length is easy to understand and calculate but what the hell is % chance of series conversion? That, my friend, is DSR.
About the only thing I dislike about DSR is the name. It is much better described as a series success rate. DSR measures the average likelihood of an offense converting a series of downs into a first down (or TD). Simply put, it is the probability of moving the chains.
It is easily calculated by dividing the number of successful series (first downs or TD) by the total number of series.
- DSR = (First Downs + TDs) / (Drives + First Downs)
However, since the official NFL box score data already includes TDs in first down counts, the formula must subtract TDs to avoid double counting them:
- DSR = First Downs / (Drives + First Downs - TDs)
Now, the example I used above to determine a general formula for TD rate is a highly simplified model that contains only 3 variables (DSR, yards from end zone, successful series length) and ignores variables like fluctuating play lengths, increased red zone difficulty, shifting starting field position and even game script decisions. Therefore, it can’t be directly applied to actual game-play . . . or can it? (he wrote knowingly)
Since 2009, the average drive has started on the 28.4 yard line and notched a DSR of 67.9% with an average successful series length of 17 yards. Placing those 3 values into the formula creates a predicted TD rate that is remarkably close to the actual TD rate:
|Starting Field Position (yards from opponent goal)||71.6|
|Avg Succesful Series Length||17|
|- n (# of series needed)||4.2|
|- TD% Probability (DSR^n)||19.5%|
|- Actual TD% Rate||19.9%|
To see if this result was a fluke, I plotted the data by year and to even further simplify the model, I kept the starting field position and series length constant, so the number of series needed for a TD was always 4.2. This reduced the model to just a single variable of DSR:
- Est. TD Rate = DSR ^ 4.2
Well, this is not a boating accident. That’s just crazy accurate considering it uses only DSR as the input.
Interesting side note: 2011 Kick-off rule changes backed teams up an average of 1.5 yards of starting field position relative to 2009-10. So, with the shorter fields, the actual TD rates should be a little bit higher in those years and whaddayaknow? . . . that effect can literally be seen on the chart.
A similar approach can be used to estimate field goal rate but the math is much more complex. For those who are interested, I have detailed the calculation in an appendix and for those who are lame, I’ll just display the general formula and the notably precise results here:
- Est. FG Rate = 0.42 * DSR ^ 2.9
Using very simple formulas that can be calculated from box score data, DSR predicts TD and FG rates very accurately, at least on average. To test if that accuracy holds up for productive vs. unproductive offenses, I calculated every team’s offensive points per drive for each season and split them into 3 groups:
- “HI” (top 10 ppd teams),
- “LO” (bottom 10 ppd teams)
- “MID” (remaining 12 teams).
I then used the TD rate formula to determine each group’s estimated TD rates and plotted them against the actual rates.
Even when separating teams into efficient and inefficient offenses, DSR predicts TD rate well. Similarly, DSR predicts FG rate with a high level of accuracy, regardless of team efficiency.
Because DSR is so tightly connected to scoring rates, it can be used to calculate an expected amount of points for an offense. Using the 2009-18 league average DSR of 67.9%, the avg expected points per drive are:
- Exp TD points = 7 * 67.9% ^ 4.2 = 1.37
- Exp FG points = 3 * 0.42 * 67.9% ^ 2.9 = 0.40
That is a total of 1.77 expected points per drive, which is very close to the actual value of 1.72. Using these formulas, I took each team’s DSR, determined their expected ppd and multiplied that by their season drive volume to get their total season expected points. The following chart compares those amounts against the actual season point totals:
Those are very good estimates.
Let’s just take a second to consider that the only inputs into this, is the number of team first downs and the number of offensive series. That’s it. If you know those two numbers for any team in any year, you can guess their total number of season points with a pretty high level of accuracy. If that doesn’t blow your mind then all I can say is, WHY ISN’T YOUR MIND BLOWN?!
Of course, the model isn’t perfect. The diagonal black line represents perfect predictions and the points don’t all line up on it. Additionally, the slope of a trend line through the data is less than 1, which means there is a bias that over-estimates points for high DSR teams and under-estimates points for low DSR teams.
No problem. I can account for that by adding in an adjustment relative to the average DSR(1). Here is what it looks like after that adjustment:
The accuracy is about the same (same R^2) but most of the bias has been removed (slope= 1.01). If I want to increase the accuracy I can add back in the variables of starting field position and successful series length making it a 3 variable model:
I think those results are remarkable.
So, why all the fuss? Why not just use actual points per drive and be done with it?
I’m glad you asked. PPD is an excellent stat that usually, but not always “agrees” with DSR. However, it’s a bit of a cheat, stat-wise. PPD is a result. It’s points. It is literally what the team scored.
DSR is a prediction. It is an estimation of the quality of play, describing what a team should have scored. If you have ever watched a game and thought it wasn’t nearly as close as the final score made it out to be, then DSR likely captured what you inherently felt, but the score didn’t show.
I’ll use the 2018 week 1 match-up of SEA against DEN as an example. Here is Seattle’s offensive drive chart from that game.
The Denver defense pushed Seattle around all day forcing seven drives without a first down, 3 turnovers and 6 sacks. The Seahawks only managed a 52% DSR, which equates to an expected point value of around 8 and yet they put up 24 points and had a chance to win the game in the last few minutes. What gives?
They did this by having 2 TD drives start in opponent territory (the first of which was on the DEN 15) and 2 more scoring drives that broke open with big explosive plays. So, they didn’t have to utilize a lot of first downs to get points. This is an example of what I call outscoring the DSR and it is more luck than skill.
Now, I can already sense under-garments getting twisted, so breathe . . . unclench . . . and let me explain what I mean by that.
Beating expected points has nothing to do with how good an offense is. It is a stochastic process, which means actual points should exceed expected points about 50% of the time. Sometimes that is done by good offenses and sometimes by bad.
To illustrate this, I took every team between 2009-18 and randomly chose 8 games from their seasons. I then compared actual point totals to estimated points and as expected 50% of the teams outscored their DSR (technically 50.6%, but who’s counting . . . other than me). I then compared the previous results to each team’s remaining 8 games to see if they continued their over/under performance or regressed back towards the mean.
If the process is random, then only half of the outscoring teams should continue that performance and the same for the underscoring teams. In other words, 25% of teams should continue to outscore DSR, 25% should continue to underscore and 50% of teams should regress to the mean.
It’s not strictly 25/50/25 but it’s close enough for government work.
Additionally, I calculated the correlation between DSR and points over expected to be almost zero (-0.02). Even if I use an alternate offensive measure like DVOA, the correlation to points over expectation is still about zero (0.06). So there is no question that outscoring DSR has nothing to do with the quality of an offense and is not a repeatable skill.
As such, measuring that over/under can give a sense of if a team is “due“ for a regression in points scored. For that reason, I will be calculating Points Over Expected in my weekly stat articles for the upcoming season.
Last year, the Colts actually outscored DSR at the rate of 0.88 points per game. So, if there were zero changes year over year and the strength of schedule was the same, then I would say we were likely to see a slight scoring decrease. But of course, all things are never equal.
I can’t think of a stat that gives you more bang for the buck than DSR . It only requires a few pieces of publicly available information and can be calculated on a cocktail napkin (when I watch football there are always plenty of those lying around). It gives you a good feel for how an offense (or defense) played and is more predictive than almost any non-proprietary, non-black-box stat.
However, like any stat, it is not perfect. While I have shown that is closely tied to scoring, scoring can sometimes be misleading. In garbage time, defenses often let teams succeed on drives artificially boosting DSR. Conversely, leading teams will trade 4th qtr successful drives for time off the clock resulting in a lower DSR.
While these impacts don’t alter the DSR-to-points relationship, it can certainly mask the true proficiency of an offense. An alternate stat that wanted to capture this might start with DSR and adjust for game script to account for these potential inaccuracies.
. . . and maybe add in weighting for TDs
. . . and maybe partial success for FGs
. . . and apply negative success for turnovers
. . . . hmmmmm.
Links to other stats I
- The bias is solved by contracting the DSR ranges around the league average DSR. This is done by first subtracting the league avg DSR of 67.9%, multiplying the residual by 0.9 and re-adding the avg DSR back in:
- Adj DSR = 0.9 * (DSR - 0.679) + 0.679
This adjustment also changes the constant used in the estimated field goal points from 0.42 to 0.38.
- TD Rate = 7 * Adj DSR ^ 4.2
- FG Rate = 3 * 0.38 * Adj DSR ^ 2.9
APPENDIX (FIELD GOAL ESTIMATION)
Warning: lots of math ahead
Between 2009-18, the % of drives that ended with a successful field goal was 13.9%. To estimate that rate using DSR, I begin by using math similar to that of TD rate. The average drive still starts 71.6 yards from the end zone, but FG attempts don’t make it that far. Rather, the kicks occur from series that start at the 21.7 yard line. So, only 49.9 yards is needed.
|Starting Field Position (yards from opponent goal)||71.6|
|Fld Pos Needed||21.7|
|Avg Succesful Series Length||17|
|- n (# of series needed)||2.9|
|- % Probability (DSR^n)||32.5%|
Therefore, 32.5% is the probability of successfully reaching the 21.7 yard line. However, in terms of DSR, a FG attempt is actually a failure: it is what teams do when they don’t convert a series. To get to the actual FG rate, I have to tack on a failed series. Again, similar math.
The previous calculation ended at the 21.7 yard line, so that is my new starting field position and the average FG attempt happens at the 19.5 yard line, which means my failed series needs to gain another 2.2 yards. The average length of a failed series is 4.1 yards, so I only need about a half a series to get there (n = 0.53).
However, instead of using the league average DSR, I need a relevant drive fail rate (DFR). My original thought was 32.1%, which is just 100% - the 67.9% DSR, but that is actually too high of a number. The reason why, is because it can’t be just any failure, it has to be a failure where the offense still retains the ball. So, after removing safeties, turnovers and failed 4th downs attempts, the relevant fail rate is actually only 25.7%
|Starting Field Position (yards from opponent goal)||21.7|
|- Fld Pos Needed||19.5|
|- Yds Needed||2.1|
|Avg Failed Series Length||4.1|
|- n (# of series needed)||0.53|
|- % Probability (DFR^n)||48.80%|
As a reminder 32.5% is the probability of successfully reaching the 21.7 yard line and now I know 48.8% is the probability of getting another 2.2 yards and reaching the avg FG attempt yard line while still possessing the ball AND without scoring a TD. Multiplying the two together is the probability of a field goal attempt, but the kicker still has to put it through the uprights, which happens 84% of the time. Therefore, the probability of a successful field goal is:
- 32.5% * 48.8% * 84% = 13.3%
It’s not quite the league average 13.9%, but it’s pretty close.
Now, I professed about the simplicity of using DSR and clearly, this FG rate calculation is not simple. Not only are there a lot of calculations and inputs involved, but DFR is cumbersome to determine and requires a lot of specific data not found in any box score to get to the 48.8% number. So, instead of messing around with all of that, I just used 50% as a proxy. Then when multiplying by the 84% FG conversion rate, I get a universal multiplier of 42%:
- Est. FG Rate = 42% * DSR ^ 2.9
It dramatically simplifies the formula, reducing it to a single variable and is just about as accurate. Here are the results by year, using this single variable formula (labeled “easy way”).