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Subject: Re: Numbers, Numbers, Numbers. I Love Numbers. Author: Northbounder [ Next Thread | Previous Thread | Next Message | Previous Message ] Date Posted: 19:02:42 09/22/24 Sun In reply to: An Observer 's message, "Numbers, Numbers, Numbers. I Love Numbers." on 15:08:35 09/22/24 Sun As you've implied, the assumptions at the top of my earlier post are just those: assumptions. Got Varga? Two-point odds go above even. You're Vanderbilt and you're keeping it close with Missouri? Maybe your overtime odds are below even. I assume NFL teams have models to provide estimates of such probabilities and reference them frequently in-game. Whether coaches listen to them - a different story. The "logical extrapolation" you've mentioned is seen in what the Houston Rockets did with the three-pointer and what many teams in Major League Baseball have done with hitting approaches. The question of a kick vs. a two-point try provides much more mathematical gray area (we're not talking a half-point per-possession spread on threes vs. elbow jumpers compounded out over dozens of possessions). But if one generates a higher expected point total than the other, why not default to it? Maybe there is no good rebuttal to that. But I tend to agree with you. Ultimately, you don't want to miss the forest for the trees. The goal is not points per possession; the goal is to win the game. Hopefully the models are oriented towards that. (And even then, in the case of scoring to go down 8 late in the fourth quarter, the "correct" mathematical — barring exceptional deviations from default assumptions — is clear. But as the poster above you wrote, where's the accounting for momentum, for crowd energy, for player belief?) [ Next Thread | Previous Thread | Next Message | Previous Message ]

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[> [> [> [> Subject: Why Going For Two Points When Down 8 Works, Mathematically Author: An Observer [ Edit | View ] Date Posted: 14:32:11 09/23/24 Mon Northbounder, I called a couple of my friends who are mathematically inclined and discussed your post with them, guys who are in the numbers business. You have just ruined the last 24 hours for us because we have been wrestling with not just HOW your two-pointer strategy works, but *WHY*. A few minutes ago, I was standing at a urinal taking care of some non-numbers business when suddenly the light bulb finally turned on in my head. It seems that, mathematically, by going for two points down by eight in the fourth quarter, the scoring team manufactures out of thin air the extra 12.5% probability of winning you say results from that choice. How can that possibly be? How can 12.5% probability of winning simply materialize from choosing from nothing but 50% outcomes (making a two-pointer and winning in overtime? It's taken me a full day to figure it out. Let's call the two strategies KICK-KICK and TRY-TRY. The expected value of KICK-KICK is 2. Because the probability of converting a two-pointer is 50%, the expected value of TRY-TRY is also 2. So why is TRY-TRY the better strategy? Because part of the value of TRY-TRY comes from scoring 4 points with MAKE-MAKE. The expected value of 2 comes from 0.25% probability of each of these outcomes: FAIL-FAIL = 0 prob-adjusted value of this outcome = 0.0 FAIL-MAKE = 2 prob-adjusted value of this outcome = 0.5 MAKE-FAIL = 2 prob-adjusted value of this outcome = 0.5 MAKE-MAKE = 4 prob-adjusted value of this outcome = 1.0 Expected value of TRY-TRY = 8/4 = 2.0 But as discussed, if the team MAKES the first try, it will kick after the second touchdown. There will never be a MAKE-MAKE outcome. So the scoring team sacrifices the possibility of scoring 4 and improves the possibility that they will score 3. FAIL-FAIL = 0 prob-adjusted value of this outcome = 0.0 FAIL-MAKE = 2 prob-adjusted value of this outcome = 0.5 MAKE-KICK = 3 prob-adjusted value of this outcome = 1.5 Expected value of TRY-(TRY or KICK) = 2.0 But scoring 3 wins you the game outright, whereas scoring 2 only gives you a 50% probability of winning in overtime. The scoring team is shifting expected value from MAKE-MAKE and moving it to MAKE-KICK. That's where the extra probability of winning comes from. The scoring team is giving up the useless value of [the probability of winning by two] and increasinging [the probability of winning by one or in overtime]. It's taken me a full day to realize this and explain it to my math friends. Gotta use the urinal more often. Thank you, Northbounder, for a fascinating 24 hours in our lives. [ Post a Reply to This Message ]

[> [> [> [> [> Subject: Re: Why Going For Two Points When Down 8 Works, Mathematically Author: An Observer [ Edit | View ] Date Posted: 16:23:13 09/23/24 Mon Northbounder, now that I've reached my own conclusion as to not just HOW going for two works, but *WHY*, I'm consulting with my old friend Mr Google. According to one article which takes a very mathematical approach to this decision, during the 2015 and 2016 seasons, not a single NFL coach went for two points with his team down by eight in the fourth quarter. Not a single one. No idea how large the sample size was. Fascinatingly, if your team scores a touchdown to trail by ONE, this analysis says KICK and play for overtime if the opponent will have time for any meaningful drive (that is, not mere seconds). Turning your opponent loose down by one after your successful MAKE is apparently a bad outcome for you. When a desperate team is driving with nothing to lose and needing only a field goal to win, guess what? They succeed a lot. You're better off with the KICK and forcing your opponent fear making a mistake and missing out on overtime. [ Post a Reply to This Message ]