"Gym height changes at 8000 total CP. Use high CP (>2675) Pokemon to keep it tall."

#PokemonGO: I have high gym turnover in my area. They tend to be safe if they are tall gyms and at risk once they drop to short gyms. I found a few discussions about tall gyms being 8000 total CP, but no details. So I started gathering some data.http://ift.tt/2BKhd7Y is a spreadsheet that contains a bunch of gym defenders and gym height. I have screenshots if anyone wants to see them. This agrees that gym with total CP greater than 8000 will result in a tall gym. Full motivation doesn't do it. Having 6 pokemon doesn't do it. And mostly empty motivation doesn't guarantee a short gym either. This means putting in high CP pokemon will keep the total CP high for as long as possible. How can we maximize the duration that the gym is tall, using Pokemon under 2400 CP?http://ift.tt/2jrPYIB = 4.975 * 1.001616 ^ (MaxCP) This post gives the formula for CP decay at the gym. Any Pokemon below 2400 uses this formula and it drops a constant CP every hour. If 8000 is our target total CP, then we want to maximize the duration until one pokemon hits 1333 CP. We can use this equation: MaxCP - CP_drop/hour * hour = 1333MaxCP - 4.975 * 1.001616 ^ (MaxCP) * hour = 1333 To maximize the length of time, we rearrange the equation hour = (1 - 1333) / (MaxCP - 4.975 * 1.001616 ^ (MaxCP)) Then maximize! (break out calculus book, AKA Wolfram Alpha http://ift.tt/2BLGAGf we maximize the length of time with a CP of 1952 for a duration of 5 hours and 20 minutes until it reaches 1333 CP. If you check out the wolfram alpha plot, the curve really flattens out. Any CP from 1750-2200 will give a duration of 5 hours or more. How can we maximize the duration that the gym is tall, over 2400 CP?Above 2400, the CP decay formula changes to 10% of max CP per hour. This gives the equation.  CP_drop/hour = 0.1 * (MaxCP) This equation has no maximum CP. The higher your CP, the longer the Pokemon will stay above 1333. One question to ask is at what CP does this last longer than 1952? We can use this equation: Max CP - 0.1 * Max CP * hour > 1333Max CP - 0.1 * Max CP * 5.3217 > 1333 Solving this says that any CP > 2850 will take longer than 5 hours and 20 minutes until it reaches 1333 CP. Solving a similar equation says that any CP over 2675 will last longer than 5 hours.SummaryCPDuration until reaching 1333 CP1750-2200at least 5 hours19525 hours 20 minutes2675+at least 5 hours28505 hours 20 minutes3325+at least 6 hours And here is a graph of all CP and durations: http://ift.tt/2jruEmF is a sweet spot around 2000 CP, but there is always some low CP pokemon in the gym. To make up for it, I'm suggesting to put in high CP pokemon in order keep the total CP above 8000. There is discussion about using lower CP pokemon because CP decay is slower and it holds up better. But for gym height, it is total CP that matters and high CP pokemon would work best. via /r/TheSilphRoad http://ift.tt/2iCefut