Random probability thoughts: Discussion of probability for coin flips almost always starts by saying you have a fair coin and the discussion looks at each coin flip as equally likely, independent events. After the first call/no call or pro/con call, is the next call still independent, equally likely when humans are involved? In loud stadium, in bad weather, early/late in the game, early season/late season, playoff race/game, etc? This leads to the concept of conditional probability as well. It is "the probability of an event ( A ), given that another ( B ) has already occurred." Sometimes this presents itself as a make up call/no call. Is every event in a game that might lead to a call or no call the same? No. Is every event independent? No. Is everything always fair? No. The sample size of referee calls in Revs games is also way too small to draw any conclusions. However, given an infinite amount of games and calls, the difference between number of calls that went against the Revs as compared to the number of events that went for the Revs would likely be statistically insignificant in a fair, random equally likely system, which cannot be guaranteed.
assuming an unbiased and impartial referee making refereeing decisions independent of prior decisions... (assume a can opener) ...then prior bad calls against the Revs will have no impact on future calls. Any bad calls in the past will not be "balanced" out because every call is independent. Thus all future calls 'should' balance out according to the odds, however past calls will not be balanced at all. Thus if in the past we had 5 bad calls against us and 0 calls in our favor, we should assume that they will not be balanced out by future calls in our favor. Only that future bad calls will be balanced out by future calls in our favor.
As I said in the past, if you're prone to think that refs might be out to get you, or even if you just favor a certain team, then your confirmation bias is going to tell you that more bad calls go against you than for you. This is due to the fact that marginal calls in your favor won't seem marginal to you, they'll seem completely correct, while marginal calls that go against you also won't seem marginal, they'll seem completely wrong. And if you want to believe something is true, then you'll remember every instance that supports what you want to believe, and either forget or minimize every instance that goes against what you want to believe. You're twisting the laws of probability to fit your needs. Yes, if you get 10 heads in a row, the 11th flip is just as likely to be heads as tails, however a) getting 10 heads in a row is incredibly unlikely, so it's not a good basis for an argument, and b) laws of probability don't really apply in such a small sample size - probability in no way says a single flip of a coin is supposed to start to even out an improbable run of previous coin flips, a very extended run of coin flips would be needed before things begin to even out. Though with all that, regarding this game, as I said, I still don't understand why people think it's a truly a bad call to give a hand ball when someone moves his arms up from beside his body to the front of his body to block a ball. I understand saying it's a little harsh or unfortunate for the player, but not bad, it's just the rules. It reminds me of a call against Luis Suarez a few years ago, where he he stuck his foot out to try to trap a ball that was coming over his head from behind him, and he ended up kicking an opponent he had no idea was there, because Suarez was looking the other way, tracking the ball, and the opponent wasn't in that spot before Suarez would have looked away. It seemed harsh to me because the foul was completely without malice or intent, just an unfortunate accident, but a red was in fact completely the correct call, as I was told by a ref friend.
I think we're using the concept of "even out" differently. It sounds like you are saying that it is likely the "breaks" are generally likely to "even out" the rest of the way. If so, I'd agree with that.
Again, assuming randomness of calls and breaks, it takes a long time for the "even out" to happen. As a student of statistical mechanics (back in the ancient history of the last century), we learned that when you get to truly large numbers of occurrences (like the number of atomic state changes in a chunk of matter made up of a few billion atoms), you are virtually guaranteed a consistent result, but if you measure just a few, you are virtually guaranteed an inconsistent result. So, we may have to wait for a few billion calls for this to even out. Not only do we have confirmation bias, most fans have observer bias (as in that fouls committed against us is a red-appropriate, but if committed by us is yellow-appropriate, for instance). As a fan, I know I'm guilty as charged, on this one.