New Site Feature: The Fourthdownulator

This is something that belongs in the long-overdue category. In effect, I've automated myself, which is not something one does eagerly.

The 4th Down Calculator estimates the Expected Points (EP) and Win Probability (WP) values for all three options--go for it, punt, and field goal attempt. All you need to do is enter the game state at the time of the 4th down and click 'calculate'. A table of results will appear that lists:

  • the league-average success rates for conversion attempts and FGs
  • the EP and WP values for success and failure
  • the total EP and WP values based on an expected utility calculation
  • and lastly, a break-even conversion probability

The break-even conversion probability is the minimum chance that a successful conversion  would make going for it worthwhile. This value can be important when considering specific match-up and play call considerations.

Results based on EP values will provide greater "resolution" and precision, but are only accurate during normal football situations. This is when the effects of score difference and time remaining are small and the game is simply one of net score optimization. When score and time become a factor, it's best to rely on results based on WP values, which account for score and time.

For example, up by 7 with 8:14 remaining in the 2nd qtr, on 4th and 11 from the PHI 33, CHI attempted a 51-yd FG. According to the 4thdownulator, the EP value for going for it is 0.40 and the EP value for the FG attempt is 0.67. The WP value for going for it is 0.75 and the WP value for the FG attempt is 0.77. In this case, both models suggest kicking the FG was the better decision.

In this scenario, the break-even conversion probability is 34% based on EP calculations and is 43% based on WP calculations. I'd rely more on the EP model than the WP model in this case because it offers more precision while time and score are not yet a factor.

Note that the results from the 4th Down Calculator will not always match the analysis I do for some situations depending on certain factors. In end-game situations, I'll often do a more refined analysis using additional techniques and make adjustments for timeouts remaining.

The 4th Down Calculator is always accessible through the WP Graphs menu.

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10 Responses to “New Site Feature: The Fourthdownulator”

  1. Dan Whitney says:

    Brian, I actually saw this up as early as last week. On Monday I plugged in the number for the Bears late in the game (4th and goal from the 4 and up 3 with 3:58 to go.) The calculator says that the WP of a made field goal is .87 and missed is .82, and yet the total WP=.76 I also plugged in other numbers and occasionally it would produce inconsistencies like that. Just wanted to let you know that the calculator produces some inconsistent data. Dan

  2. Anonymous says:

    Dan is right. The FG WP part of the calculator is not working correctly.

  3. Tarr says:


    It seems to me that how many time outs each team has matters a fair bit in the endgame situations. Aside from that, I have no complaints.

  4. Anonymous says:

    Can someone do Coughlins 4th and 6 call in the 4th quarter of the SF-NYG game. I plugged in the values but I have no idea what its trying to tell me.

  5. Justin says:


    This is wonderful, and you have automated what is probably the most frequent thing you get asked :).

    That said I was wondering how OT is handled in the WP model. I ran the numbers from the Falcons-Saints game, and it makes sense to me that going for it is the better choice in terms of WP.

    Then I was curious about what if this were the final minute of overtime?

    The WP doesn't appear to change no matter what time I put in for OT. It seems in this same situation with one minute left, punting probably preserves a tie and a successful 4th down conversion is less likely to lead to a game winning score, than if there were a couple minutes left.

  6. Brian Burke says:

    Dan-Thanks. There must be a bug in there.

    Justin-That's correct. The chance of an OT game going to a tie is less than 1%, so I made the assumption that one team will score, essentially ignoring the possibility of a tie. There are only 2 ties in the data at all, so even if I factored it in, it would make a negligible difference.

  7. Jonathan says:

    I just had a similar issue, with a punt having a higher WP (0.21) than a converted 4th down (0.17). So breakeven was 200%. :)

    Parameters: Deficit 14, 4th & 14 from the opponent's 35. 1:10 in the first quarter.

  8. Jonathan says:

    I should add that I laughed out loud when I saw the title to this post. This site is awesome.

  9. Brian Burke says:

    Should be working now. Thanks for the info on the bug.

  10. Eric says:

    I've had the same error a few times now. I get a "Warning: Division by zero in C:\wamp\www\4thDownCalc.php on line 117."

    The WP values are .99 across the board. Is this a bug or am I doing something wrong?

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